Sample records for exact renormalization group

  1. The Exact Renormalization Group -- renormalization theory revisited --


    Sonoda, Hidenori


    We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED in the four dimensional euclidean space.

  2. Fundamentals of the exact renormalization group (United States)

    Rosten, Oliver J.


    Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the intuitive picture provided for both renormalization in quantum field theory and universality associated with second order phase transitions. A qualitative discussion of triviality, asymptotic freedom and asymptotic safety is presented. Focusing on scalar field theory, the construction of assorted flow equations is considered using a general approach, whereby different ERGs follow from field redefinitions. It is recalled that Polchinski’s equation can be cast as a heat equation, which provides intuition and computational techniques for what follows. The analysis of properties of exact solutions to flow equations includes a proof that the spectrum of the anomalous dimension at critical fixed-points is quantized. Two alternative methods for computing the β-function in λϕ4 theory are considered. For one of these it is found that all explicit dependence on the non-universal differences between a family of ERGs cancels out, exactly. The Wilson-Fisher fixed-point is rediscovered in a rather novel way. The discussion of nonperturbative approximation schemes focuses on the derivative expansion, and includes a refinement of the arguments that, at the lowest order in this approximation, a function can be constructed which decreases monotonically along the flow. A new perspective is provided on the relationship between the renormalizability of the Wilsonian effective action and of correlation functions, following which the construction of manifestly gauge invariant ERGs is sketched, and some new insights are given. Drawing these strands together suggests a new approach to quantum field theory.

  3. Exact renormalization group study of fermionic theories (United States)

    Comellas, Jordi; Kubyshin, Yuri; Moreno, Enrique


    The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit N → ∞, with N being the number of fermionic species. For finite N some fixed point solutions, with their anomalous dimensions and critical exponents, are computed numerically. The issue of separation of physical results from the numerous spurious ones is discussed. We argue that one of the solutions we find can be identified with that of Dashen and Frishman, whereas the others seem to be new ones.

  4. On truncations of the exact renormalization group

    CERN Document Server

    Morris, T R


    We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

  5. On truncations of the exact renormalization group (United States)

    Morris, Tim R.


    We investigate the Exact Renormalization Group (ERG) description of ( Z2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. The approximation is seen to be a good one, both qualitatively and quantitatively. We then consider the further approximation of truncating the lagrangian to polynomial in the field dependence. Concentrating on the non-perturbative three dimensional Wilson fixed point, we show that the sequence of truncations n = 2,3,…, obtained by expanding about the field ϕ = 0 and discarding all powers ϕ2 n+2 and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. Within the sequence of truncations, no completely reliable method exists to reject the many spurious solutions that are also generated. These properties are explained in terms of the analytic behaviour of the untruncated solutions - which we describe in some detail.

  6. Massive Axial Gauge in the Exact Renormalization Group Approach (United States)

    Panza, P.; Soldati, R.

    The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

  7. Exact multilocal renormalization group and applications to disordered problems (United States)

    Chauve, Pascal; Le Doussal, Pierre


    We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(ɛ=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Δχ)2¯~Lθ/T, where θ is the energy exponent. Finally, we obtain the universal scaling function to O(ɛ1/3) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.

  8. An Exact Renormalization Group analysis of 3-d Well Developed turbulence

    CERN Document Server

    Tomassini, P


    We take advantage of peculiar properties of three dimensional incompressible turbulence to introduce a nonstandard Exact Renormalization Group method. A Galilean invariance preserving regularizing procedure is utilized and a field truncation is adopted to test the method. Results are encouraging: the energy spectrum E(k) in the inertial range scales with exponent -1.666+/- 0.001 and the Kolmogorov constant C_K, computed for several (realistic) shapes of the stirring force correlator, agrees with experimental data.

  9. Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group


    Vian, F


    The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived f...

  10. Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group (United States)

    Vian, F.


    The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.

  11. Optimized renormalization group flows (United States)

    Litim, Daniel F.


    We study the optimization of exact renormalization group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and nonvanishing temperature. We find that optimized flows at finite temperature factorize. This corresponds to the disentangling of thermal and quantum fluctuations. A similar factorization is found at second order in the derivative expansion. The corresponding optimized flow for a ``proper-time renormalization group'' is also provided to leading order in the derivative expansion.

  12. Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

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    Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)


    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

  13. Renormalization Group Functional Equations

    CERN Document Server

    Curtright, Thomas L


    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

  14. Exact renormalization flow and domain walls from holography (United States)

    Ketov, Sergei V.


    The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in N=2 supergravity background are interpreted as the exact renormalization group flow equations in two dimensions. Our geometrical description of the renormalization flow is manifestly covariant under general reparametrization of the 2d coupling constants. An explicit exact solution to the 2d renormalization flow, based on its dual holographic description in terms of the Zamolodchikov metric, is considered in the particular case of the four-dimensional NLSM target space described by the SU(2)-invariant (Weyl) anti-self-dual Einstein metrics. The exact regular (Tod-Hitchin) solutions to these metrics are governed by the Painlevé VI equation, and describe domain walls.

  15. Introduction to the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik


    This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)

  16. Renormalization scheme dependence with renormalization group summation (United States)

    McKeon, D. G. C.


    We consider all perturbative radiative corrections to the total e+e- annihilation cross section Re+e- showing how the renormalization group (RG) equation associated with the radiatively induced mass scale μ can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log, next-to-leading-log, etc., contributions to Re+e- using in turn the one-loop, two-loop, etc., contributions to the RG function β . A second summation shows how all logarithmic corrections to Re+e- can be expressed entirely in terms of the log-independent contributions when one employs the full β -function. Next, using Stevenson's characterization of any choice of renormalization scheme by the use of the contributions to the β -function arising beyond two-loop order, we examine the RG scheme dependence in Re+e- when using the second way of summing logarithms. The renormalization scheme invariants that arise are then related to the renormalization scheme invariants found by Stevenson. We next consider two choices of the renormalization scheme, one which can be used to express Re+e- solely in terms of two powers of a running coupling, and the second which can be used to express Re+e- as an infinite series in the two-loop running coupling (i.e., a Lambert W -function). In both cases, Re+e- is expressed solely in terms of renormalization scheme invariant parameters that are to be computed by a perturbative evaluation of Re+e-. We then establish how in general the coupling constant arising in one renormalization scheme can be expressed as a power series of the coupling arising in any other scheme. We then establish how, by using a different renormalization mass scale at each order of perturbation theory, all renormalization scheme dependence can be absorbed into these mass scales when one uses the second way of summing logarithmic corrections to Re+e-. We then employ the approach to renormalization scheme dependency that we have applied to Re+e- to a RG summed

  17. The analytic renormalization group

    Directory of Open Access Journals (Sweden)

    Frank Ferrari


    Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

  18. Contractor renormalization group and the Haldane conjecture

    Energy Technology Data Exchange (ETDEWEB)

    Weinstein, Marvin


    The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.

  19. Unitary networks from the exact renormalization of wave functionals (United States)

    Fliss, Jackson R.; Leigh, Robert G.; Parrikar, Onkar


    The exact renormalization group (ERG) for O (N ) vector models (at large N ) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on AdSd +1. This was established in the sense that at large N the generating functional of correlation functions of single-trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the O (N ) vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared recently in holographic contexts. In particular, the ERG tensor network appears to share the general structure of cMERA but differs in important ways. We comment on possible holographic implications.

  20. Corner Transfer Matrix Renormalization Group Method


    Nishino, T.; Okunishi, K.


    We propose a new fast numerical renormalization group method,the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfer matrices gives the densitymatrix. We formulate the CTMRG method as a renormalization of 2D classical models.

  1. Solving renormalization group equations with the Lambert W function (United States)

    Sonoda, H.


    It has been known for some time that 2-loop renormalization group equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed point to construct renormalization group invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.

  2. Renormalization group approach to density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Kemler, Sandra; Braun, Jens [Institut fuer Kernphysik, TU Darmstadt (Germany)


    We study a two-point particle irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. This approach relates to Density Functional Theory and can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. We apply our formalism to a 0+1-dimensional model, namely the quantum anharmonic oscillator and use the well-known exact solution to benchmark our approximations of the full RG flow. Moreover, we present flow equations for specific types of 1+1-dimensional field theories which allow us study the ground-state properties of self-bound systems of spinless fermions which can also be viewed as toy models of nuclei.

  3. Canonical demon Monte Carlo renormalization group

    CERN Document Server

    Hasenbusch, M; Wieczerkowski, C


    We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the O(3) nonlinear \\sigma-model.

  4. Perturbative dynamics of open quantum systems by renormalization group method (United States)

    Kukita, Shingo


    We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.

  5. Computing the effective action with the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)


    The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

  6. Accurate renormalization group analyses in neutrino sector

    Energy Technology Data Exchange (ETDEWEB)

    Haba, Naoyuki [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Kaneta, Kunio [Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8568 (Japan); Takahashi, Ryo [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Yamaguchi, Yuya [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)


    We investigate accurate renormalization group analyses in neutrino sector between ν-oscillation and seesaw energy scales. We consider decoupling effects of top quark and Higgs boson on the renormalization group equations of light neutrino mass matrix. Since the decoupling effects are given in the standard model scale and independent of high energy physics, our method can basically apply to any models beyond the standard model. We find that the decoupling effects of Higgs boson are negligible, while those of top quark are not. Particularly, the decoupling effects of top quark affect neutrino mass eigenvalues, which are important for analyzing predictions such as mass squared differences and neutrinoless double beta decay in an underlying theory existing at high energy scale.

  7. Renormalization group flow of the Higgs potential (United States)

    Gies, Holger; Sondenheimer, René


    We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.

  8. Renormalization group flows and continual Lie algebras

    CERN Document Server

    Bakas, Ioannis


    We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches...

  9. Functional renormalization group approach to neutron matter

    Directory of Open Access Journals (Sweden)

    Matthias Drews


    Full Text Available The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter.

  10. Renormalization group flow of the Holst action

    Energy Technology Data Exchange (ETDEWEB)

    Daum, J.-E., E-mail: [University of Mainz, D-55099 Mainz (Germany); Reuter, M. [University of Mainz, D-55099 Mainz (Germany)


    The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under spacetime diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three-parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way.

  11. Generalized geometry, T-duality, and renormalization group flow (United States)

    Streets, Jeffrey


    We interpret the physical B-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural ;Ricci flow; for generalized geometry. Next we show that the B-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the B-field renormalization group flow.

  12. Renormalization group approach to relativistic cosmology (United States)

    Carfora, Mauro; Piotrkowska, Kamilla


    We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a ``3+1'' formalism and invokes the coarse-graining arguments, provided and supported by the real-space renormalization group (RG) methods, in parallel with lattice models of statistical mechanics. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The possible relevance of the Ricci-Hamilton flow in implementing the averaging in cosmology has been previously advocated, but the physical motivations behind this suggestion were not clear. The RG interpretation provides us with such physical motivations. The properties of the Ricci-Hamilton flow make it possible to study a critical behavior of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheetlike structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by nontrivial scale-dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale dependence of the matter distribution.

  13. Fermionic functional integrals and the renormalization group

    CERN Document Server

    Feldman, Joel; Trubowitz, Eugene


    This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...

  14. Nonlinear relativistic plasma resonance: Renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

    Metelskii, I. I., E-mail: [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)


    An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

  15. From plasticity to a renormalization group. (United States)

    Ball, R C; Blumenfeld, R


    The marginally rigid state is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. The coordination number is identified as a discriminating characteristic, and for rough-surfaced particles we show that the low values predicted are indeed approached in simple two-dimensional experiments. We show calculations of the stress transmission, suggesting that this is governed by local linear equations of constraint between the stress components. These constraints can in turn be related to the generalized forces conjugate to the motion of grains rolling over each other. The lack of a spatially coherent way of imposing a sign convention on these motions is a problem for scaling up the equations, which leads us to attempt a renormalization-group calculation. Finally, we discuss how perturbations propagate through such systems, suggesting a distinction between the behaviour of rough and smooth grains.

  16. Renormalization group theory impact on experimental magnetism

    CERN Document Server

    Köbler, Ulrich


    Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...

  17. Transfer group for renormalized multiple zeta values


    Ebrahimi-Fard, Kurusch; Manchon, Dominique; Singer, Johannes; Zhao, Jianqiang


    We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at non-positive values appearing in the recent literature.

  18. Similarity renormalization group evolution of N N interactions within a subtractive renormalization scheme

    Directory of Open Access Journals (Sweden)

    Durães F.O.


    Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral effective field theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a fixed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoff through the SRG transformation.

  19. High Precision Renormalization Group Study of the Roughening Transition

    CERN Document Server

    Hasenbusch, M; Pinn, K


    We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.

  20. Renormalization group approach to superfluid neutron matter

    Energy Technology Data Exchange (ETDEWEB)

    Hebeler, K.


    In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)

  1. Functional renormalization group methods in quantum chromodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Braun, J.


    We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

  2. Renormalization Group Approach in Newtonian Cosmology (United States)

    Sota, Y.; Kobayashi, T.; Maeda, K.; Nakamichi, A.; Kurokawa, T.; Morikawa, M.

    There are many evidences that the matter distribution of the Universe show fractal well beyond the scale of hundred Mpc. This fractal matter distribution clearly conflicts with the widely assumed cosmological model in which the matter distribution asymptotically becomes homogeneous in larger scale. If this fractal distribution of matter, however, turns out to be true and the local density fluctuations do not reduce in larger scale, we have to change the present cosmological model of the Universe which is globally described by FRW space-time. Here, we analyze the global behavior of such fluctuation-dominated Universe by applying the renormalization group (RG) method. We derive the flow of the RG equations and clarify the properties of fixed points by using the model of Newtonian cosmology with dust fluid. This model allows the scale-invariance and a well defined procedure of space averaging, both of which make our RG analysis easier. Based on this RG analysis, we would like to argue (a) how the large fluctuations in all scales affect the global structure of the Universe, (b) how the age problem of the Universe is solved and (c) the nature of dark matter in fractal Universe.

  3. General Covariance from the Quantum Renormalization Group

    CERN Document Server

    Shyam, Vasudev


    The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...

  4. Renormalization group improved Higgs inflation with a running kinetic term

    Directory of Open Access Journals (Sweden)

    Fuminobu Takahashi


    Full Text Available We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.

  5. Renormalization group and continuum limit of quantum cellular automata

    Energy Technology Data Exchange (ETDEWEB)

    Zimboras, Zoltan [Quantum Information Theory Group, ISI, Torino (Italy)


    We develop a renormalization group formalism for quantum cellular automata (reminiscent of the algebraic renormalization group of Buchholz and Verch). Using this formalism, we can define the continuum limit for certain automata. As a particular example, we show that the continuum limit of the so-called ''Glider Clifford cellular automaton'' is the 1+1 dimensional relativistic QFT of free Majorana fermions.

  6. Functional renormalization group study of fluctuation effects in fermionic superfluids

    Energy Technology Data Exchange (ETDEWEB)

    Eberlein, Andreas


    This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature

  7. Quantum renormalization group for ground-state fidelity (United States)

    Langari, A.; Rezakhani, A. T.


    Ground-state fidelity (GSF) and quantum renormalization group (QRG) theory have proven to be useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method for calculating GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances the characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field (ITF) and the anisotropic spin-1/2 Heisenberg (XXZ) model. Explicitly, we find the scaling behavior of the GSF for the ITF model in both small- and large-size limits, the corresponding critical exponents, the exact value of the GSF in the thermodynamic limit and a closed form for the GSF for arbitrary size and system parameters. In the case of the XXZ model, we also present an analytic expression for the GSF, which captures well the criticality of the model, hence excluding doubts that GSF might be an insufficient tool for signaling criticality in this model.

  8. Renormalization group and the deep structure of the proton

    CERN Document Server

    Petermann, Andreas


    The spirit of the renormalization group approach lies entirely in the observation that in a specific theory the renormalized constants such as the couplings, the masses, are arbitrary mathematical parameters which can be varied by changing arbitrarily the renormalization prescription. Given a scale of mass mu , prescriptions can be chosen by doing subtractions of the relevant amplitudes at the continuously varying points mu e/sup t/, t being an arbitrary real parameter. A representation of such a renormalization group transformation mu to mu + mu e/sup t/ is the transformation g to g(t) of the renormalized coupling into a continuously varying coupling constant, the so-called 'running coupling constant'. If, for the theory under investigation there exists a domain of the t space where g(t) is small, then because it is not known how to handle field theory beyond the perturbative approach attention must be focused on the experimental range in which the g(t) 'runs' with small values. The introduction of couplings...

  9. Computing the effective action with the functional renormalization group

    DEFF Research Database (Denmark)

    Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław


    The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples of such...... of QED and of Yang–Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity....

  10. Renormalization group approach to matrix models via noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Kuroki, T. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Furo-cho, Chikusa-ku, Nagoya Aichi 464-8602 (Japan); Kawamoto, S. [National Center for Theoretical Sciences, Hsinchu 30013 (China); Tomino, D. [Department of Physics, Tunghai University, Taichung 40704 (China)


    We develop a new method for analyzing the large-N limit of matrix models. We assign the concept of energy to each matrix element and integrate the most highest energy to get a new matrix model which has reduced rank. By regarding this procedure as a renormalization group, we deduce the critical exponents in the large-N limit by elaborating fixed points of renormalization group transformation. For consistency of our method, we compare our result to that obtained by another method and find nice agreement. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  11. Random Vector and Matrix Theories: A Renormalization Group Approach (United States)

    Zinn-Justin, Jean


    Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly. Initiated by Br\\'ezin and Zinn-Justin, the approach has led to encouraging results, first for matrix integrals and then quantum mechanics with matrices, but has not yet become a universal tool as initially hoped. In particular, general quantum field theories with matrix fields require more detailed investigations. To better understand some of the encountered difficulties, we first apply analogous ideas to the simpler O(N) symmetric vector models, models that can be solved quite generally in the large N limit. Unlike other attempts, our method is a close extension of Br\\'ezin and Zinn-Justin. Discussing vector and matrix models with similar approximation scheme, we notice that in all cases (vector and matrix integrals, vector and matrix path integrals in the local approximation), at leading order, non-trivial fixed points satisfy the same universal algebraic equation, and this is the main result of this work. However, its precise meaning and role have still to be better understood.

  12. Tensor renormalization group methods for spin and gauge models (United States)

    Zou, Haiyuan

    The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

  13. Renormalization group improvement and constituent quark model

    Energy Technology Data Exchange (ETDEWEB)

    Mirjalili, A. [Physics Department, Yazd University, Yazd (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:; Khorramian, Ali N. [Physics Department, Semnan University, Semnan (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:; Atashbar Tehrani, S. [Physics Department, Semnan University, Semnan (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:


    The scale dependence in perturbative QCD remains on obstacle to making precise tests of the theory. To over come the scale ambiguity while people are usually using the standard MS-bar approach with a physical choice of renormalization scale, we try to employ the approach of complete RG-improvement. In this approach all ultraviolet logarithms involving the dimensionful parameter, Q, on which the observable depends are resummed, thereby building the correct Q-dependence. Based on these two approaches, sea quark densities in the nucleon are analyzed. To achieve the asymmetry of these densities, chiral quark model is used. To avoid from the unaccepted Q{sup 2} behavior of sea densities inside the constituent quark, we assume that the free parameter which exists in the vertex function of boson-quark splitting function, is Q{sup 2}-dependence. Using un-symmetrized sea densities of the nucleon, the Gottfried sum rule is calculated in these two approaches. The result of the latter one is very close to the reported experimental value.

  14. Nuclear Spectroscopy with the In-Medium Similarity Renormalization Group (United States)

    Parzuchowski, Nathan Michael

    The in-medium similarity renormalization group (IMSRG) is an ab initio many-body method which features soft polynomial scaling with system size and a Hermitian framework to create Hamiltonians tailored for use with low-level approximations such as Hartree-Fock (HF) theory or the random phase approximation (RPA). The flexibility that comes with these characteristics has made the IMSRG a mainstay in contemporary nuclear structure theory. However, spectroscopy with IMSRG calculations has been limited to scalar observables in nuclei accessible with shell model machinery, where the IMSRG is used to construct effective valence-space interactions. In this thesis, we present two novel developments which have greatly extended the IMSRG's capability to perform spectroscopic calculations. First is the introduction of the equations-of-motion IMSRG (EOM-IMSRG), which uses an approximate, but systematically improvable diagonalization scheme in conjunction with the IMSRG to produce spectra and wave functions. The method does not suffer the model-space limitations of the shell model, but sacrifices some accuracy due to the approximate diagonalization. We benchmark this new method with the well established equations-of-motion coupled cluster and full configuration interaction methods, where we demonstrate that the method is indeed viable for closed-shell systems, encouraging expansion to open shells using a multireference formalism. We also introduce a perturbative framework to add systematic corrections to the EOM-IMSRG, showing results for closed shell nuclei and quantum dots. The second development is a generalized effective operator formalism for the IMSRG, capable of consistently evolving non-scalar operators relevant for electroweak transitions and moments. This general framework is applicable to both the EOM-IMSRG and the valence-space IMSRG approaches. We benchmark electromagnetic transition strengths and moments using both of these methods, also comparing with the quasi-exact

  15. On the renormalization group flow of f(R)-gravity

    NARCIS (Netherlands)

    Machado, P.F.; Saueressig, F.


    We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \\int d^dx \\sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently

  16. Renormalization Group Flows, Cycles, and c-Theorem Folklore (United States)

    Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.


    Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  17. Renormalization group flows, cycles, and c-theorem folklore. (United States)

    Curtright, Thomas L; Jin, Xiang; Zachos, Cosmas K


    Monotonic renormalization group flows of the "c" and "a" functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  18. On Newton-Cartan local renormalization group and anomalies

    Energy Technology Data Exchange (ETDEWEB)

    Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)


    Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

  19. Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

    Energy Technology Data Exchange (ETDEWEB)

    Groh, Kai


    The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

  20. Holographic torus entanglement and its renormalization group flow (United States)

    Bueno, Pablo; Witczak-Krempa, William


    We study the universal contributions to the entanglement entropy (EE) of 2 +1 -dimensional and 3 +1 -dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2 +1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 γ . This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of γ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in 2 +1 dimensions and 3 +1 dimensions.

  1. Cyclic renormalization and automorphism groups of rooted trees

    CERN Document Server

    Bass, Hyman; Rockmore, Daniel; Tresser, Charles


    The theme of the monograph is an interplay between dynamical systems and group theory. The authors formalize and study "cyclic renormalization", a phenomenon which appears naturally for some interval dynamical systems. A possibly infinite hierarchy of such renormalizations is naturally represented by a rooted tree, together with a "spherically transitive" automorphism; the infinite case corresponds to maps with an invariant Cantor set, a class of particular interest for its relevance to the description of the transition to chaos and of the Mandelbrot set. The normal subgroup structure of the automorphism group of such "spherically homogeneous" rooted trees is investigated in some detail. This work will be of interest to researchers in both dynamical systems and group theory.

  2. Topologically twisted renormalization group flow and its holographic dual (United States)

    Nakayama, Yu


    Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (also known as topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a nontrivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS /CFT . We argue that the nontrivial fixed points require fine-tuning of the bulk theory, in general, but remarkably we find that the O (3 ) Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean anti-de Sitter metric.

  3. Renormalization group flow of f(R) gravity (United States)

    Machado, Pedro F.; Saueressig, Frank


    We use the functional renormalization group equation for quantum gravity to construct a nonperturbative flow equation for modified gravity theories of the form S=∫ddxgf(R). Based on this equation we show that certain gravitational interaction monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The nonperturbative RG flow of nonlocal extensions of the Einstein-Hilbert truncation including ∫ddxgln⁡(R) and ∫ddxgR-n interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some R-n truncations all physical trajectories emanate from a non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the ln⁡(R) truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.

  4. More on the renormalization group limit cycle in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga


    We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.

  5. Ising Spin Glasses and Renormalization Group Theory: the Binder cumulant


    Lundow, P. H.; Campbell, I. A.


    Numerical data on scaling of the normalized Binder cumulant and the normalized correlation length are shown for the Thermodynamic limit regime, first for canonical Ising ferromagnet models and then for a range of Ising spin glass models. A fundamental Renormalization Group Theory rule linking the critical exponents for the two observables is well obeyed in the Ising models, but not for the Ising spin glasses in dimensions three and four. We conclude that there is a violation of a standard Jos...

  6. New applications of renormalization group methods in nuclear physics. (United States)

    Furnstahl, R J; Hebeler, K


    We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

  7. Renormalization group theory of the critical properties of the interacting bose fluid

    NARCIS (Netherlands)

    Creswick, Richard J.; Wiegel, F.W.


    Starting from a functional integral representation of the partition function we apply the renormalization group to the interacting Bose fluid. A closed form for the renormalization equation is derived and the critical exponents are calculated in 4-ε dimensions.

  8. Renormalization group procedure for potential -g/r2 (United States)

    Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.


    Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

  9. Holographic entanglement entropy of N =2* renormalization group flow (United States)

    Pang, Da-Wei


    The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.

  10. Real-space renormalization-group studies of low-dimensional quantum antiferromagnets

    Energy Technology Data Exchange (ETDEWEB)

    Lepetit, M. (Laboratoire de Physique Quantique, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX (France)); Manousakis, E. (Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Isntitute, Florida State University, Tallahassee, Florida 32306 (United States))


    We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.

  11. Renormalization group method for Farley-Buneman fluctuations: basic results

    Directory of Open Access Journals (Sweden)

    A. M. Hamza


    Full Text Available Sudan and Keskinen in [1979] derived a set of equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the E x B or gradient-drift instability. This problem is of fundamental importance in ionospheric physics. The nonlinear nature of the equations makes it very hard to write a closed form solution. In this paper we propose to use 'Dynamical Renormalization Group' methods to study the long-- wavelength, long-time behaviour of density correlations generated in this ionospheric plasma stirred by a Gaussian random force characterized by a correlation function (fk fk k. The effect of the small scales on the large scale dynamics in the limit k -> 0 and infinite 'Reynolds' number, can be expressed in the form of renormalized coefficients; in our case renormalized diffusion. If one assumes the power spectra to be given by the kolmogorov argument of cascading of energy, then one can not only derive a subgrid model based on the results of RNG, and this has been done by Hamza and Sudan [1995], but one can also extract the skewness of the spectra as we do in this paper.

  12. Numerical Calculation of Scaling Exponents of Percolation Process in the Framework of Renormalization Group Approach

    Directory of Open Access Journals (Sweden)

    Adzhemyan L. Ts.


    Full Text Available The renormalization group theory is used to the study of the directed bond percolation (Gribov process near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ε-expansion where ε is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.

  13. Quantum field theory and phase transitions: universality and renormalization group; Theorie quantique des champs et transitions de phase: universalite et groupe de renormalisation

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J


    In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

  14. The density matrix renormalization group and nuclear structure

    Energy Technology Data Exchange (ETDEWEB)

    Pittel, S.; Thakur, B. [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (United States); Sandulescu, N. [Institute of Physics and Nuclear Engineering, 76900 Bucharest (Romania)


    We briefly review the Density Matrix Renormalization Group (DMRG) method and its potential use in large-scale nuclear shell-model calculations. We propose the use of angular-momentum-conserving variant of the method (the JDMRG) and report the first test results of such an approach for the nucleus {sup 48}Cr The positive results of these calculations have motivated us to search for an even more efficient means of implementing the DMRG strategy and the status of these efforts is also described. (Author)

  15. Tensor renormalization group analysis of CP(N-1) model

    CERN Document Server

    Kawauchi, Hikaru


    We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.

  16. Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence (United States)

    Rubinstein, Robert


    Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

  17. A renormalization group study of the three-color Ashkin-Teller model on a Wheatstone hierarchical lattice (United States)

    Teodoro, R.; Bezerra, C. G.; Mariz, A. M.; da Costa, F. A.; de Araújo, J. M.


    A three-color Ashkin-Teller model (3AT) is investigated by means of a Migdal-Kadanoff renormalization group approach on a Wheatstone bridge hierarchical lattice. The exact recursion relations for the renormalized couplings are obtained through a decimation procedure. The phase diagram of the model is obtained from the analysis of the fixed points and the flow generated by the renormalization group transformation. Four distinct phases are obtained along with nine critical points and are graphically represented in a phase diagram in terms of the dual transmissivity vector. The correlation length (νT)and crossover (ϕ) critical exponents are numerically calculated. It is found that seven of the critical points are in the Potts model universality class (q = 2, 4 e 8). The remaining critical points are in a universality class which may belong to a sort of Baxter's line. The results can be considered as an approximation to more realistic Bravais lattices.

  18. Nonperturbative Renormalization Group and Bose-Einstein Condensation (United States)

    Blaizot, Jean-Paul

    These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature T_c of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the s-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in T_c: this comes from the fact that near T_c the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields. The ingredients needed to calculate the shift of T_c can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in T_c.

  19. Holographic renormalization group and cosmology in theories with quasilocalized gravity

    Energy Technology Data Exchange (ETDEWEB)

    Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John


    We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.

  20. Renormalization-group flows and fixed points in Yukawa theories

    DEFF Research Database (Denmark)

    Mølgaard, Esben; Shrock, R.


    We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar co....... In the regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared.......We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar...... coupling lambda by comparing the properties of flows obtained with the beta functions of these couplings calculated to different orders in the loop expansion. The results provide a determination of the region in y and lambda where calculations up to two loops can yield reasonably reliable results...

  1. Functional renormalization group study of the Anderson-Holstein model (United States)

    Laakso, M. A.; Kennes, D. M.; Jakobs, S. G.; Meden, V.


    We present a comprehensive study of the spectral and transport properties in the Anderson-Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron-phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson-Holstein quantum dot and find clear signatures of the presence of the phonon mode.

  2. Renormalization Group Running of Newton's G: The Static Isotropic Case

    CERN Document Server

    Hamber, H W; Hamber, Herbert W.; Williams, Ruth M.


    Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equati...

  3. Dimensional reduction of Markov state models from renormalization group theory. (United States)

    Orioli, S; Faccioli, P


    Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.

  4. Renormalization group flows of the N -component Abelian Higgs model (United States)

    Fejős, G.; Hatsuda, T.


    Flows of the couplings of a theory of an N -component (complex) scalar field coupled to electrodynamics are investigated using the functional renormalization group formalism in d dimensions in covariant gauges. We find charged fixed points for any number of components in d =3 , in accordance with the findings of [G. Fejos and T. Hatsuda, Phys. Rev. D 93, 121701 (2016), 10.1103/PhysRevD.93.121701] for N =1 . It is argued that the appropriate choice of the regulator matrix is indispensable to obtain such a result. Ward-Takahashi identities are analyzed in the presence of the regulator, and their compatibility with the flow equation is investigated in detail.

  5. Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)


    We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

  6. Complete renormalization group improvement - avoiding factorization and renormalization scale dependence in QCD predictions

    Energy Technology Data Exchange (ETDEWEB)

    Maxwell, C.J. E-mail:; Mirjalili, A. E-mail:


    For moments of leptoproduction structure functions we show that all dependence on the renormalization and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of effective charges. A direct and simple method for extracting {lambda}{sub MS-bar} from experimental data is advocated.

  7. A functional renormalization group approach to electronic structure calculations for systems without translational symmetry

    CERN Document Server

    Seiler, Christian


    A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on...

  8. Renormalization Group in the uniqueness region weak Gibbsianity and convergence.

    CERN Document Server

    Bertini, L; Olivieri, E


    We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. %We discuss the %Gibbs property of the renormalized measure and the convergence of %renormalized potential under iteration of the map. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale--adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached.

  9. Pokrovsky-Talapov model at finite temperature: a renormalization-group analysis

    NARCIS (Netherlands)

    Lazarides, A.; Tieleman, O.; de Morais Smith, C.


    We calculate the finite-temperature shift of the critical wave vector Qc of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential.

  10. A numerical renormalization group approach to non-equilibrium Green functions for quantum impurity models

    Energy Technology Data Exchange (ETDEWEB)

    Anders, Frithjof B [Institut fuer Theoretische Physik, Universitaet Bremen, PO Box 330 440, D-28334 Bremen (Germany)], E-mail:


    We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group (NRG). Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfils the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion U>0 is switched on at t = 0, and the asymptotic steady-state spectral functions are obtained for various values of U as well as magnetic field strength H and temperature T. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite U. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nanodevices.

  11. Strong-disorder renormalization group study of aperiodic quantum Ising chains (United States)

    Oliveira Filho, Fleury J.; Faria, Maicon S.; Vieira, André P.


    We employ an adaptation of a strong-disorder renormalization group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground-state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.

  12. Spectral functions and transport coefficients from the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Tripolt, Ralf-Arno


    In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.

  13. Anatomy of the magnetic catalysis by renormalization-group method

    Directory of Open Access Journals (Sweden)

    Koichi Hattori


    Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger–Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu–Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  14. Driven similarity renormalization group: Third-order multireference perturbation theory. (United States)

    Li, Chenyang; Evangelista, Francesco A


    A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N(6)) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST=ET-ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol(-1), a value that is within 0.1 kcal mol(-1) from multireference coupled cluster results.

  15. Anatomy of the magnetic catalysis by renormalization-group method (United States)

    Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho


    We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  16. Automatic calculation of supersymmetric renormalization group equations and loop corrections (United States)

    Staub, Florian


    SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, No. of lines in distributed program, including test data, etc.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose

  17. On higher order geometric and renormalization group flows (United States)

    Prabhu, Kartik; Das, Sanjit; Kar, Sayan


    Renormalization group (RG) flows of the bosonic nonlinear σ-model are governed, perturbatively, at different orders of α', by perturbatively evaluated β-functions. In regions where {α'}/{Rc2}≪1 ( {1}/{Rc2} represents the curvature scale), the flow equations at various orders in α' can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S2, H2, unwarped S2×H2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.

  18. Renormalization group and phase transitions in spin, gauge, and QCD like theories (United States)

    Liu, Yuzhi

    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare

  19. Renormalization group flows for the second Z{sub 5} parafermionic field theory

    Energy Technology Data Exchange (ETDEWEB)

    Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:


    Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub 5}. New fixed points are found and classified.

  20. Thermal Renormalization Group-Equations and the Phase-Transition of Scalar O(N)-Theories


    Bergerhoff, Bastian; Reingruber, Juergen


    We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the universal and the non-universal aspects of the critical behavior directly in terms of the zero-temperature physical couplings. They provide a nonperturbative method for a computation of quantities like real-time correlation functions in a thermal environment,...

  1. Renormalization-group theory for the eddy viscosity in subgrid modeling (United States)

    Zhou, YE; Vahala, George; Hossain, Murshed


    Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

  2. Many-body localization in one dimension as a dynamical renormalization group fixed poin (United States)

    Vosk, Ronen; Altman, Ehud


    We formulate a dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. Lack of true thermalization in the long time limit is attributed to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble. Within the RG framework we show that long range resonances are irrelevant at strong randomness, and formulate a criterion for when they do become relevant and may cause a delocalization transition.

  3. Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point (United States)

    Vosk, Ronen; Altman, Ehud


    We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as log⁡log⁡t found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.

  4. Renormalization-group approach to the vulcanization transition (United States)

    Peng; Goldbart


    The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-field percolation theory (i.e., random graph theory). This minimal model accounts for both the thermal motion of the constituents and the quenched random constraints imposed on their motion by the cross-links, as well as particle-particle repulsion which suppresses density fluctuations and plays a pivotal role in determining the symmetry structure (and hence properties) of the model. A correlation function involving fluctuations of the amorphous solid order parameter, the behavior of which signals the vulcanization transition, is examined, its physical meaning is elucidated, and the associated susceptibility is constructed and analyzed. A Ginzburg criterion for the width (in cross-link density) of the critical region is derived and is found to be consistent with a prediction due to de Gennes. Inter alia, this criterion indicates that the upper critical dimension for the vulcanization transition is 6. Certain universal critical exponents characterizing the vulcanization transition are computed, to lowest nontrivial order, within the framework of an expansion around the upper critical dimension. This expansion shows that the connection between vulcanization and percolation extends beyond mean-field theory, surviving the incorporation of fluctuations in the sense that pairs of physically analogous quantities (one percolation related and one vulcanization related) are found to be governed by identical critical exponents, at least to first order in the departure from the upper critical dimension (and presumably beyond). The relationship between the present approach to vulcanized

  5. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition (United States)

    José, Jorge V.


    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  6. Dirac relation and renormalization group equations for electric and magnetic fine structure constants

    CERN Document Server

    Laperashvili, L V


    The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\\alpha $ and magnetic $\\tilde \\alpha $ - were obtained. It was shown that the Dirac relation is valid for the renormalized $\\alpha $ and $\\tilde perturbatively only in the small region: $0.25 \\stackrel{<}{\\sim} \\alpha, relation: $\\alpha {\\tilde \\alpha} = \\frac 14 $.

  7. Ab initio excited states from the in-medium similarity renormalization group (United States)

    Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.


    We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

  8. Introduction to real-space renormalization-group methods in critical and chaotic phenomena (United States)

    Hu, Bambi


    The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Hénon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent

  9. Renormalization-group calculations of ground-state and transport properties of ultrasmall tunnel junctions

    DEFF Research Database (Denmark)

    Frota, H.O.; Flensberg, Karsten


    We have done a numerical renormalization-group calculation for a Hamiltonian modeling charging effect in ultrasmall tunnel junctions. We find that the conductance is enhanced by the quantum charge fluctuations allowing tunneling below the charging energy gap. However, in all cases the conductance...

  10. Renormalization group flows for the second Z{sub N} parafermionic field theory for N odd

    Energy Technology Data Exchange (ETDEWEB)

    Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:


    Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub N}, for N odd. New fixed points are found and classified.

  11. Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model. (United States)

    Ron, Dorit; Brandt, Achi; Swendsen, Robert H


    We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

  12. A density matrix renormalization group study of low-lying excitations ...

    Indian Academy of Sciences (India)


    Abstract. Symmetrized density-matrix-renormalization-group calculations have been carried out, within. Pariser–Parr–Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C2 symmetry and spin parity of the system to obtain excited states of ...

  13. Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group


    Jurgenson, E. D.; Navratil, P.; Furnstahl, R. J.


    The first practical method to evolve many-body nuclear forces to softened form using the Similarity Renormalization Group (SRG) in a harmonic oscillator basis is demonstrated. When applied to He4 calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force.

  14. Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Zi-Xiang, E-mail: [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States); Department of Physics, ChongQing University, ChongQing 400044 (China); Papić, Z.; Johri, S.; Bhatt, R.N. [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States); Schmitteckert, Peter [Institut für Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe (Germany)


    We report a systematic study of the fractional quantum Hall effect (FQHE) using the density-matrix renormalization group (DMRG) method on two different geometries: the sphere and the cylinder. We provide convergence benchmarks based on model Hamiltonians known to possess exact zero-energy ground states, as well as an analysis of the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy. The ground state energies of the Coulomb Hamiltonian at ν=1/3 and ν=5/2 filling are extracted and compared with the results obtained by previous DMRG implementations in the literature. A remarkably rapid convergence in the cylinder geometry is noted and suggests that this boundary condition is particularly suited for the application of the DMRG method to the FQHE. -- Highlights: ► FQHE is a two-dimensional physics. ► Density-matrix renormalization group method applied to FQH systems. ► Benchmark study both on sphere and cylinder geometry.

  15. PyR@TE. Renormalization group equations for general gauge theories (United States)

    Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.


    Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

  16. Gauge- and Renormalization-Group-Invariant Formulation of the Higgs-Boson Resonance

    CERN Document Server

    Papavassiliou, J; Papavassiliou, Joannis; Pilaftsis, Apostolos


    A gauge- and renormalization-group- invariant approach implemented by the pinch technique is formulated for resonant transitions involving the Higgs boson. The lineshape of the Higgs boson is shown to consist of two distinct and physically meaningful contributions: a process-independent resonant part and a process-dependent non-resonant background, which are separately gauge independent, invariant under the renormalization group, satisfy naive, tree-level Ward identities, and respect the optical and equivalence theorem individually. The former process-independent quantity serves as the natural extension of the concept of the effective charge to the case of the Higgs scalar, and constitutes a common ingredient of every Born-improved amplitude. The difference in the phenomenological predictions obtained within our approach and those found with other methods is briefly discussed.

  17. Renormalization group coefficients and the S-matrix

    Energy Technology Data Exchange (ETDEWEB)

    Caron-Huot, Simon [Niels Bohr International Academy and Discovery Center,Blegdamsvej 17, Copenhagen 2100 Ø (Denmark); Niels Bohr Institute,Blegdamsvej 17, Copenhagen 2100 Ø (Denmark); Wilhelm, Matthias [Niels Bohr Institute,Blegdamsvej 17, Copenhagen 2100 Ø (Denmark)


    We show how to use on-shell unitarity methods to calculate renormalisation group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by π. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.

  18. A novel functional renormalization group framework for gauge theories and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro


    In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for k{yields}{infinity} and the standard effective action for k{yields}0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NL{sigma}M) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or

  19. Dynamical density matrix renormalization group study of photoexcited states in one-dimensional Mott insulators


    Matsueda, H.; Tohyama, T.; Maekawa, S.


    One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, $U$ and $V$, respectively. We find that the lowest optically-allowed and forbidden excited states, which have odd and even parities, respectively, are degenerate for $V/t\\ltsim 2$ with $t$ being the hopping in...

  20. Tracing the evolution of nuclear forces under the similarity renormalization group


    Johnson, Calvin W.


    I examine the evolution of nuclear forces under the similarity renormalization group (SRG) using traces of the many-body configuration-space Hamiltonian. While SRG is often said to “soften” the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly...

  1. Density matrix renormalization group approach for many-body open quantum systems. (United States)

    Rotureau, J; Michel, N; Nazarewicz, W; Płoszajczak, M; Dukelsky, J


    The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum.

  2. A renormalization group study of persistent current in a quasiperiodic ring

    Energy Technology Data Exchange (ETDEWEB)

    Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)


    We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.

  3. Real-space renormalization group study of the Hubbard model on a non-bipartite lattice

    Directory of Open Access Journals (Sweden)

    R. D. Levine


    Full Text Available Abstract: We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.

  4. A functional renormalization group approach to non-equilibrium properties of mesoscopic interacting quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Pruschke, Th., E-mail: pruschke@theorie.physik.uni-goettingen.d [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany); Dirks, A.; Gezzi, R. [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany)


    We present an extension of the concepts of the functional renormalization group approach to quantum many-body problems in non-equilibrium situations. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations. We discuss the influence of finite bias voltage and temperature on the current and conductance.

  5. Application of renormalization group theory to the large-eddy simulation of transitional boundary layers (United States)

    Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.


    An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

  6. Irreversibility of the renormalization group flow in non-unitary quantum field theory (United States)

    Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Ravanini, Francesco


    We show irreversibility of the renormalization group flow in non-unitary but {{ P}T} -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s c-theorem to {{ P}T} -symmetric Hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is non-negative and monotonically decreasing along renormalization group flows. Its value at a critical point is the ‘effective central charge’ entering the specific free energy. At least in rational models, this equals ceff=c-24Δ , where c is the central charge and Δ is the lowest primary field dimension in the conformal field theory which describes the critical point. Dedicated to John Cardy on the occasion of his 70th birthday.

  7. Global aspects of the renormalization group and the hierarchy problem (United States)

    Patrascu, Andrei T.


    The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09 ± 0.24 GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. It is known that the hierarchy problem can be interpreted in terms of the near criticality between the two phases. The coefficient of the Higgs bilinear in the scalar potential, m2, is pushed by quantum corrections away from zero, towards the extremes of the interval [ - MPl2, MPl2 ] where MPl is the Planck mass. In this article, I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. In holographic terms, invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes.

  8. Nonperturbative renormalization group treatment of amplitude fluctuations for |φ| 4 topological phase transitions (United States)

    Defenu, Nicolò; Trombettoni, Andrea; Nándori, István; Enss, Tilman


    The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional |φ| 4 models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the contribution of density fluctuations to nonuniversal quantities. We introduce a functional renormalization group scheme in AP representation where amplitude fluctuations are integrated first to yield an effective sine-Gordon model with renormalized superfluid stiffness. By a mapping between the lattice X Y and continuum |φ| 4 models, our method applies to both on equal footing. Our approach correctly reproduces the existence of a line of fixed points and of universal thermodynamics and it allows to estimate universal and nonuniversal quantities of the two models, finding good agreement with available Monte Carlo results. The presented approach is flexible enough to treat parameter ranges of experimental relevance.

  9. Renormalization group summation of Laplace QCD sum rules for scalar gluon currents

    Directory of Open Access Journals (Sweden)

    Farrukh Chishtie


    Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.

  10. Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED (United States)

    Kondo, Kei-Ichi

    The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

  11. Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation

    CERN Document Server

    Guilleux, Maxime


    Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on the top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O(N) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induc...

  12. Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Kawamoto, Shoichi [Department of Physics, Chung-Yuan Christian University, Chung-Li 320, Taiwan, R.O.C. (China); Kuroki, Tsunehide [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe,Nagoya University, Nagoya 464-8602 (Japan)


    In the previous study Kawamoto, D. Tomino and T. Kuroki, Large-N renormalization group on fuzzy sphere, Int. J. Mod. Phys. Conf. Ser. 21 (2013) 151., we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.

  13. Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model

    Energy Technology Data Exchange (ETDEWEB)

    Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden)


    We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.

  14. Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables

    Directory of Open Access Journals (Sweden)

    Khellat M.R.


    Full Text Available We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions to QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA in which through a series of comparisons between lowerorder RG-induced estimates and the corresponding analytical calculations, one could modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of αs4 corrections for the Bjorken sum rule of polarized deep-inelastic scattering and for the non-singlet contribution to the Adler function.

  15. Implementation and assessment of the renormalization group (Rng) k - {epsilon} model in gothic

    Energy Technology Data Exchange (ETDEWEB)

    Analytis, G.Th. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)


    In GOTHIC, the standard k - {epsilon} model is used to model turbulence. In an attempt to enhance the turbulence modelling capabilities of the code for simulation of mixing driven by highly buoyant discharges, we implemented the Renormalization Group (RNG) k - {epsilon} model. This model which for the time being, is only implemented in the ''gas'' phase, was tested with different simple test-problems and its predictions were compared to the corresponding ones obtained when the standard k - {epsilon} model was used. (author)

  16. Tensor renormalization group analysis of ${\\rm CP}(N-1)$ model in two dimensions

    CERN Document Server

    Kawauchi, Hikaru


    We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$.

  17. Tracing the evolution of nuclear forces under the similarity renormalization group

    Directory of Open Access Journals (Sweden)

    Calvin W. Johnson


    Full Text Available I examine the evolution of nuclear forces under the similarity renormalization group (SRG using traces of the many-body configuration-space Hamiltonian. While SRG is often said to “soften” the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly smaller changes. By employing traces, I argue that this is a very natural outcome as one diagonalizes a matrix, and helps one to understand the success of SRG.

  18. Thermodynamics of isotropic and anisotropic layered magnets: renormalization group approach and 1/N expansion


    Irkhin, V. Yu.; Katanin, A. A.


    The O(N) model of layered antiferro- and ferromagnets with a weak interlayer coupling and/or easy-axis anisotropy is considered. A renormalization group (RG) analysis in this model is performed, the results for N=3 being expected to agree with those of the 1/M expansion in the CP^{M-1} model at M=2. The quantum and classical cases are considered. A crossover from an isotropic 2D-like to 3D Heisenberg (or 2D Ising) regime is investigated within the 1/N expansion. Analytical results for the tem...

  19. Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory

    CERN Multimedia

    CERN. Geneva


    The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.

  20. Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model (United States)

    Heller, Urs M.


    An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

  1. {gamma} (2) modular symmetry, renormalization group flow and the quantum hall effect

    Energy Technology Data Exchange (ETDEWEB)

    Georgelin, Yvon [Groupe de Physique Theorique, Institut de Physique Nucleaire, Orsay (France); Masson, Thierry; Wallet, Jean-Christophe [Laboratoire de Physique Theorique (UMR 8627), Universitdede Paris-Sud, Orsay (France)


    We construct a family of holomorphic {beta}-functions whose renormalization group (RG) flow preserves the {gamma} (2) modular symmetry and reproduces the observed stability of the Hall plateaus. The semicircle law relating the longitudinal and Hall conductivities that has been experimentally observed is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependence of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occurring in the crossover of the permitted transitions is discussed. (author)

  2. Singular perturbation analysis of a reduced model for collective motion: a renormalization group approach. (United States)

    Lee, Chiu Fan


    In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determine how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.

  3. Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

    Directory of Open Access Journals (Sweden)

    Uwe C. Täuber


    Full Text Available The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (subdiffusive model B with complex coefficients.

  4. Density Matrix Renormalization Group Approach to Two-Fluid Open Many-Fermion Systems

    Energy Technology Data Exchange (ETDEWEB)

    Rotureau, J. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Michel, N. [Kyoto University, Japan; Nazarewicz, Witold [ORNL; Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds (GANIL); Dukelsky, J. [Instituto de Estructura de la Materia, CSIC, Madrid, Spain


    We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow Shell Model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground state eigenvalue and discuss different truncation schemes within DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

  5. Density-matrix renormalization-group study of current and activity fluctuations near nonequilibrium phase transitions. (United States)

    Gorissen, Mieke; Hooyberghs, Jef; Vanderzande, Carlo


    Cumulants of a fluctuating current can be obtained from a free-energy-like generating function, which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the density-matrix renormalization group for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z . We also calculate the generating function of the dynamical activity (total number of configuration changes) near the absorbing-state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents.

  6. Renormalization-group flow of the effective action of cosmological large-scale structures

    CERN Document Server

    Floerchinger, Stefan


    Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input ...

  7. Renormalization group equation analysis of a pseudoscalar portal dark matter model (United States)

    Ghorbani, Karim


    We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle θ =6^\\circ , and find the scale of validity in terms of the dark coupling, {λ }d. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

  8. The renormalization-group flux of the conformally reduced quantum gravity; Der Renormierungsgruppen-Fluss der konform-reduzierten Quantengravitation

    Energy Technology Data Exchange (ETDEWEB)

    Weyer, Holger


    We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent nonperturbative renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG ow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity (QEG) in the ''conformally reduced'' theory which discards all degrees of freedom contained in the metric except the conformal one. The conformally reduced Einstein-Hilbert approximation has exactly the same qualitative properties as in the full Einstein-Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4}-theory. We employ the Local Potential Approximation for the conformal factor to generalize the RG flow on an infinite dimensional theory space. Again we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Since the RG flow depends on the topology of the

  9. Why one needs a functional renormalization group to survive in a ...

    Indian Academy of Sciences (India)

    In this paper, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions ...

  10. Numerical renormalization group studies of the partially brogen SU(3) Kondo model

    Energy Technology Data Exchange (ETDEWEB)

    Fuh Chuo, Evaristus


    The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy {Delta}{sub 0}. When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T{sub K}>{Delta}{sub 0})=k{sub B} ln 3, and the 2CK ground state value, S(0)=k{sub B} ln {radical}(2). This indicates a downward renormalization of the doublet below the non-interacting ground state, thus realizing the 2CK fixed point, in agreement with earlier conjectures. We mapped out the phase diagram of the model in the J-{Delta}{sub 0} plane. The Kondo temperature T{sub K} shows non-monotonic J-dependence, characteristic for 2CK systems. Beside the two-channel Kondo effect of the model, we also study the single-channel version, which is realized by applying a strong magnetic fi eld to the conduction band electrons so that their degeneracy is lifted and consequently having only one kind of electrons scattering off the impurity. This single-channel case is easier to analyze since the Hilbert space is not as large as that of the 2CK. We equally find a downward renormalization of the excited state energy by the Kondo correlations in the SU(2) doublet


    NARCIS (Netherlands)


    We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Our main results apply to local (in position space) RG maps acting on systems of bounded spins (compact

  12. Entanglement distance between quantum states and its implications for a density-matrix renormalization group study of degenerate ground states (United States)

    Vaezi, Mohammad-Sadegh; Vaezi, Abolhassan


    We study the concept of entanglement distance between two quantum states, which quantifies the amount of information shared between their reduced density matrices (RDMs). Using analytical arguments combined with density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we show that for gapless systems the entanglement distance has power law dependence on the energy separation and subsystem size, with αE and αℓ exponents, respectively. Using conformal field theory (CFT) we find αE=2 and αℓ=4 for Abelian theories with c =1 , as in the case of free fermions. For non-Abelian CFTs αE=0 , and αℓ is twice the conformal dimension of the thermal primary fields. For instance, for Z3 parafermion CFT αE=1 and αℓ=4 /5 . For gapped 1+1 dimensional (1+1D) fermion systems, we show that the entanglement distance divides the low energy excitations into two branches with different values of αE and αℓ. These two branches are related to momentum transfers near zero and π . We also demonstrate that the entanglement distance reaches its maximum for degenerate states related through nonlocal operators such as Wilson loops. For example, degenerate ground states (GSs) of 2+1D topological states have maximum entanglement distance. In contrast, degenerate GSs related through confined anyon excitations such as genons have minimum entanglement distance. Various implications of this concept for quantum simulations are discussed. Finally, based on the ideas developed we discuss the computational complexity of DMRG algorithms that are capable of finding all degenerate GSs.

  13. Renormalization in the gauge theories with spontaneously broken supersymmetry

    CERN Document Server

    Kazakov, D I; Velizhanin, V N; Kondrashuk, I N


    A review of recent results on renormalizations in gauge theories with spontaneously broken supersymmetry is given. It is shown that the renormalizations in a broken theory are completely defined by those in a rigid theory and may be obtained with the help of expansion over the Grassmannian variables. New exact as well as suitable approximate analytic solutions of the renormalization group equations are obtained in some particular models: the Minimal Supersymmetric Standard Model, supersymmetric Grand Unified Theories, softly broken finite theories, and N=2 supersymmetric Seiberg-Witten theory

  14. Scale Setting Using the Extended Renormalization Group and the Principle of Maximal Conformality: the QCD Coupling at Four Loops

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.; /SLAC; Wu, Xing-Gang; /SLAC /Chongqing U.


    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal {beta}{sub i} terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of R{sub e{sup +}e{sup -}}(Q) up to four loops is presented. By using the world average {alpha}{sub s}{sup {ovr MS}}(MZ) = 0.1184 {+-} 0.0007, we obtain the asymptotic scale for the 't Hooft associated with the {ovr MS} scheme, {Lambda}{sub {ovr MS}}{sup 'tH} = 245{sub -10}{sup +9} MeV, and the asymptotic scale for the conventional {ovr MS} scheme, {Lambda}{sub {ovr MS}} = 213{sub -8}{sup +19} MeV.

  15. Functional renormalization group approach for inhomogeneous one-dimensional Fermi systems with finite-ranged interactions (United States)

    Weidinger, Lukas; Bauer, Florian; von Delft, Jan


    We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance

  16. Renormalization group study of the minimal Majoronic dark radiation and dark matter model

    Energy Technology Data Exchange (ETDEWEB)

    Chang, We-Fu [Department of Physics, National Tsing Hua University,101, Sec. 2, KuangFu Rd., Hsinchu 300, Taiwan (China); Ng, John N. [Theory Group, TRIUMF,4004 Wesbrook Mall, Vancouver BC V6T 2A3 (Canada)


    We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos △N{sub eff}∼0.05, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, ρ, of mass 1.5–4 TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, S, of mass in the 10–100 GeV range and its mixing with the standard model Higgs as large as 0.1 is also predicted. The dominant decay modes are S into bb-bar and/or ωω. A sensitive search will come from rare Z decays via the chain Z→S+ff-bar, where f is a Standard Model fermion, followed by S into a pair of Majoron and/or b-quarks. The interesting consequences of dark matter bound state due to the sizable Sρρ-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at M{sub ρ} could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.

  17. Renormalization Group Flows from Holography-Supersymmetry and a c-Theorem

    CERN Document Server

    Freedman, D.Z.; Pilch, K.; Warner, N.P.


    We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function...

  18. Conductance Fano lineshapes for Kondo impurities on surfaces: A numerical renormalization group description. (United States)

    Sandler, Nancy; Dias da Silva, Luis; Ulloa, Sergio


    Scanning tunneling microscopy (STM) measurements of Kondo impurities on metallic surfaces has been an active field in recent years. For a flat density-of-states (DoS) near the Fermi energy in the host metal, the low-bias STM conductance acquires the characteristic Fano lineshape, with width proportional to the Kondo temperature TK. In this work, we study how this picture is modified when a structured DoS (non-flat) is considered. A variety of physical effects can introduce peak/dips in the DoS, including the presence of a second impurity, hybridization between surface and bulk conduction states, and a magnetic impurity embedded in a molecule. Using numerical renormalization group techniques, we calculate the low-temperature conductance for this system. The zero-bias dip in the Fano conductance is modified by the presence of resonances or anti-resonances in the DoS near EF. In particular, for DoS with pseudogaps and impurities in the mixed-valence regime, zero-bias Fano-like dips appear even when no Kondo state has developed, but governed by energy scales much larger than TK. We further show that measurements of the scattering phase could be used as an additional probe into the Kondo regime. Supported by NFS-NIRT.

  19. Density-matrix renormalization group studies on a magnetic impurity in graphene (United States)

    Shirakawa, Tomonori; Yunoki, Seiji


    Motivated by recent experiments on the emergence of magnetism in graphene induced by lattice defects or by magnetic adatoms, we have theoretically studied the ground state properties of single magnetic impurity in grapheme. First, we have developed a new numerical technique within the density-matrix renormalization group (DMRG) scheme for magnetic impurity model in general to study site-dependent quantities including local density of states even away from magnetic impurity site, Friedel density oscillations, and spin-spin correlation functions between the magnetic impurity and the surrounding conduction electrons. This new technique is applied to three different models: (i) a magnetic adatom on grapheme, (ii) a substitutional magnetic impurity in grapheme, and (iii) a model on defect in the graphene. Our systematic study of these models reveals that, in the presence of particle-hole symmetry, the ground state of model (i) exhibits the formation of local moments without Kondo-screening, whereas the others behave very similarly to the Kondo singlet states. We also discuss the real-space decay of spin-spin correlations between magnetic impurity and surrounding conduction electrons in these models.

  20. Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling (United States)

    Hristopulos, Dionissios T.


    The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [Water Resour. Res. 19 (1) (1983) 161]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1-2/ d⩽ α<1 (where d is the actual medium dimension) in the geostatistical power average.

  1. Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media (United States)

    Hanasoge, Shravan; Agarwal, Umang; Tandon, Kunj; Koelman, J. M. Vianney A.


    Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.

  2. Study of two dimensional anisotropic Ising models via a renormalization group approach (United States)

    Taherkhani, Farid; Akbarzadeh, Hamed; Abroshan, Hadi; Ranjbar, Shahram; Fortunelli, Alessandro; Parsafar, Gholamabbas


    A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K={J}/{kBT} and J, kB, and T are the spin coupling interaction, the Boltzmann constant, and the absolute temperature, respectively), are calculated for different block sizes. By increasing the block size, the critical line for three types of lattice, namely: triangular, square, and honeycomb, is obtained and found to compare well with corresponding results reported by Onsager in the thermodynamic limit. Our results also show that, for the investigated lattices, there exist asymptotic limits for the critical line. Finally the critical exponents are obtained, again in good agreement with Onsager’s results. We show that the magnitude of the spin coupling interaction with anisotropic ferromagnetic characteristics does not change the values of the critical exponents, which stay constant along the direction of the critical line.

  3. A low-cost approach to electronic excitation energies based on the driven similarity renormalization group (United States)

    Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.


    We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.

  4. An efficient density matrix renormalization group algorithm for chains with periodic boundary condition

    Directory of Open Access Journals (Sweden)

    Dayasindhu Dey


    Full Text Available The Density Matrix Renormalization Group (DMRG is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O(p x m^3, where p can vary from 4 to m^2. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O(m^3 and the conventional DMRG code can be easily modified for the new algorithm. Received: 2 August 2016, Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016

  5. Backward renormalization-group inference of cortical dipole sources and neural connectivity efficacy (United States)

    Amaral, Selene da Rocha; Baccalá, Luiz A.; Barbosa, Leonardo S.; Caticha, Nestor


    Proper neural connectivity inference has become essential for understanding cognitive processes associated with human brain function. Its efficacy is often hampered by the curse of dimensionality. In the electroencephalogram case, which is a noninvasive electrophysiological monitoring technique to record electrical activity of the brain, a possible way around this is to replace multichannel electrode information with dipole reconstructed data. We use a method based on maximum entropy and the renormalization group to infer the position of the sources, whose success hinges on transmitting information from low- to high-resolution representations of the cortex. The performance of this method compares favorably to other available source inference algorithms, which are ranked here in terms of their performance with respect to directed connectivity inference by using artificially generated dynamic data. We examine some representative scenarios comprising different numbers of dynamically connected dipoles over distinct cortical surface positions and under different sensor noise impairment levels. The overall conclusion is that inverse problem solutions do not affect the correct inference of the direction of the flow of information as long as the equivalent dipole sources are correctly found.

  6. In-medium similarity renormalization group for closed and open-shell nuclei (United States)

    Hergert, H.


    We present a pedagogical introduction to the in-medium similarity renormalization group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: the first is the multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of non-empirical valence-space interactions that can be used as input for nuclear shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+shell model approach provides immediate access to excitation spectra, transitions, etc, but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IMSRG and IMSRG+shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.

  7. Griffiths singularities in the random quantum Ising antiferromagnet: A tree tensor network renormalization group study (United States)

    Lin, Yu-Ping; Kao, Ying-Jer; Chen, Pochung; Lin, Yu-Cheng


    The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent z >1 , which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing z <1 , when the dynamics of the rare regions is hampered by the longitudinal field.

  8. Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity (United States)

    Toniato, Júnior D.; Rodrigues, Davi C.; de Almeida, Álefe O. F.; Bertini, Nicolas


    We apply the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism to a class of general relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant G is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the external potential effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales; for any of them the Solar System bounds need to be considered.

  9. Renormalization-group theory for cooling first-order phase transitions in Potts models. (United States)

    Liang, Ning; Zhong, Fan


    We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q-state Potts model for q>10/3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.

  10. Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

    Energy Technology Data Exchange (ETDEWEB)

    Katanin, A, E-mail: [Institute of Metal Physics, 620041, Ekaterinburg (Russian Federation); Ural Federal University, 620002, Ekaterinburg (Russian Federation)


    I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider the Polchinski or Wick-ordered scheme with amputation of full (instead of bare) Green functions, as well as more general schemes, and establish their relation to the 'dynamical adjustment propagator' scheme by Salmhofer (2007 Ann. Phys., Lpz. 16 171). While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is also not evident how the mean-field solution of these problems is recovered in this scheme. For the Wick-ordered scheme, fully or partly excluding tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize the usefulness of the schemes, which are local in the cutoff parameter, and compare them to the one-particle irreducible approach. (paper)

  11. Renormalization group theory for temperature-driven first-order phase transitions in scalar models (United States)

    Liang, Ning; Zhong, Fan


    We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of ϕ 3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found: a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from ϕ 3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two-loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as ϕ 3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.

  12. Renormalization group evolution of neutrino parameters in presence of seesaw threshold effects and Majorana phases

    Directory of Open Access Journals (Sweden)

    Shivani Gupta


    Full Text Available We examine the renormalization group evolution (RGE for different mixing scenarios in the presence of seesaw threshold effects from high energy scale (GUT to the low electroweak (EW scale in the Standard Model (SM and Minimal Supersymmetric Standard Model (MSSM. We consider four mixing scenarios namely Tri–Bimaximal Mixing, Bimaximal Mixing, Hexagonal Mixing and Golden Ratio Mixing which come from different flavor symmetries at the GUT scale. We find that the Majorana phases play an important role in the RGE running of these mixing patterns along with the seesaw threshold corrections. We present a comparative study of the RGE of all these mixing scenarios both with and without Majorana CP phases when seesaw threshold corrections are taken into consideration. We find that in the absence of these Majorana phases both the RGE running and seesaw effects may lead to θ13<5° at low energies both in the SM and MSSM. However, if the Majorana phases are incorporated into the mixing matrix the running can be enhanced both in the SM and MSSM. Even by incorporating non-zero Majorana CP phases in the SM, we do not get θ13 in its present 3σ range. The current values of the two mass squared differences and mixing angles including θ13 can be produced in the MSSM case with tan⁡β=10 and non-zero Majorana CP phases at low energy. We also calculate the order of effective Majorana mass and Jarlskog Invariant for each scenario under consideration.

  13. The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Hergert, H., E-mail: [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics, The Ohio State University, Columbus, OH 43210 (United States); Bogner, S.K., E-mail: [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Morris, T.D., E-mail: [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Schwenk, A., E-mail: [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Tsukiyama, K., E-mail: [Center for Nuclear Study, Graduate School of Science, University of Tokyo, Hongo, Tokyo, 113-0033 (Japan)


    We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

  14. Numerical Renormalization Group computation of temperature dependent specific heat for a two-channel Anderson model

    Energy Technology Data Exchange (ETDEWEB)

    Ferreira, J.V.B., E-mail: [Fundacao Universidade Federal de Mato Grosso do Sul (Brazil); Ferreira, A.I.I.; Leite, A.H. [Fundacao Universidade Federal de Mato Grosso do Sul (Brazil); Libero, V.L. [Instituto de Fisica de Sao Carlos, SP, Universidade Estadual de Sao Paulo (Brazil)


    The Numerical Renormalization Group (NRG) is applied to diagonalize a two-channel Anderson model describing a local magnetic impurity embedded in a fermionic bath. In spite of the difficulty in computing the specific heat using NRG, the interleaving discretization and multi-step iterative transformation virtually eliminate the numerical oscillations introduced by the logarithmic discretization of the conduction band. These allow to cover uniformly a large range of temperature, from the top of the band to a very small fraction of the bandwidth. This is relevant in describing, for instance, the presence of a low temperature Kondo resonance together with a high temperature Schottky peak, as well to cover Fermi and non-Fermi liquid regimes, like in the recent studied Ce{sub 1-x}La{sub x}Ni{sub 9}Ge{sub 4} family. We highlight the importance in describing the Schottky peak to define the number of degrees of freedom of the local levels, in order to correctly define the model to describe a given compound. - Highlights: Black-Right-Pointing-Pointer The two-channel Anderson model exhibits FL and nFL regimes. Black-Right-Pointing-Pointer NRG, with interleaving and the multi-step procedures, solve Hamiltonian. Black-Right-Pointing-Pointer Large temperature in the specific heat curves, from Kondo to Schottky peak. Black-Right-Pointing-Pointer Analysis of Ce{sub 1-x}La{sub x}Ni{sub 9}Ge{sub 4} compound. Black-Right-Pointing-Pointer Schottky-like peak in this compound suggests J=9/2 multiplet at the impurity level.

  15. Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula (United States)

    Bischoff, Jan-Moritz; Jeckelmann, Eric


    We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

  16. c-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow

    Directory of Open Access Journals (Sweden)

    V. Bacsó


    Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.

  17. Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

    CERN Document Server

    Rodrigues, Davi C; de Almeida, Álefe O F


    General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter $\\bar \

  18. Real-Space Renormalization-Group Approach to the Integer Quantum Hall Effect (United States)

    Cain, Philipp; Römer, Rudolf A.

    We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2 up to RL 20h/e2 when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance R H∝ R Lκ is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization

  19. Renormalization and plasma physics

    Energy Technology Data Exchange (ETDEWEB)

    Krommes, J.A.


    A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

  20. Exact Group Sequential Methods for Estimating a Binomial Proportion

    Directory of Open Access Journals (Sweden)

    Zhengjia Chen


    Full Text Available We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.

  1. Renormalization group flows from gravity in anti-de Sitter space versus black hole no-hair theorems (United States)

    Lowe, David A.


    Black hole no-hair theorems are proven using inequalities that govern the radial dependence of spherically symmetric configurations of matter fields. In this paper, we analyze the analogous inequalities for geometries dual to renormalization group flows via the AdS/CFT correspondence. These inequalities give much useful information about the qualitative properties of such flows. For Poincaré invariant flows, we show that generic flows of relevant or irrelevant operators lead to singular geometries. For the case of irrelevant operators, this leads to an apparent conflict with Polchinski's decoupling theorem, and we offer two possible resolutions to this problem.

  2. Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction. (United States)

    Liu, X M; Cheng, W W; Liu, J-M


    We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.

  3. Second-order functional renormalization group approach to one-dimensional systems in real and momentum space (United States)

    Sbierski, Björn; Karrasch, Christoph


    We devise a functional renormalization group treatment for a chain of interacting spinless fermions which is correct up to second order in interaction strength. We treat both inhomogeneous systems in real space as well as the translationally invariant case in a k -space formalism. The strengths and shortcomings of the different schemes as well as technical details of their implementation are discussed. We use the method to study two proof-of-principle problems in the realm of Luttinger liquid physics, namely, reflection at interfaces and power laws in the occupation number as a function of crystal momentum.

  4. Nonequilibrium dynamics of active matter with correlated noise: A dynamical renormalization group study (United States)

    Kachan, Devin; Levine, Alex; Bruinsma, Robijn


    Biology is rife with examples of active materials - soft matter systems driven into nonequilibrium steady states by energy input at the micro scale. For example, solutions of active micron scale swimmers produce active fluids showing phenomena reminiscent of turbulent convection at low Reynolds number; cytoskeletal networks driven by endogenous molecular motors produce active solids whose mechanics and low frequency strain fluctuations depend sensitively on motor activity. One hallmark of these systems is that they are driven at the micro scale by temporally correlated forces. In this talk, we study how correlated noise at the micro scale leads to novel long wavelength and long time scale dynamics at the macro scale in a simple model system. Specifically, we study the fluctuations of a ϕ4 scalar field obeying model A dynamics and driven by noise with a finite correlation time τ. We show that the effective dynamical system at long length and time scales is driven by white noise with a renormalized amplitude and renormalized transport coefficients. We discuss the implications of this result for a broad class of active matter systems driven at the micro scale by colored noise.

  5. Fermi liquid approach to the quantum RC circuit: Renormalization group analysis of the Anderson and Coulomb blockade models (United States)

    Filippone, Michele; Mora, Christophe


    We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum RC geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.

  6. Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators

    CERN Document Server

    Li, Chenyang


    The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. $\\mathbf{11}$, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker--Campbell--Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. $\\mathbf{124}$, 194106 (2006)]. The resulting MR-LDSRG(2) equations contain only 39 terms and scales as ${\\cal O}(N^2 N_{\\rm P}^2 N_{\\rm H}^2)$ where $N_{\\rm H}$, $N_{\\rm P}$, and $N$ correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrog...

  7. Lie group classifications and exact solutions for time-fractional Burgers equation


    Wu, Guo-cheng


    Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.

  8. Configured-groups hypothesis: fast comparison of exact large quantities without counting. (United States)

    Miravete, Sébastien; Tricot, André; Kalyuga, Slava; Amadieu, Franck


    Our innate number sense cannot distinguish between two large exact numbers of objects (e.g., 45 dots vs 46). Configured groups (e.g., 10 blocks, 20 frames) are traditionally used in schools to represent large numbers. Previous studies suggest that these external representations make it easier to use symbolic strategies such as counting ten by ten, enabling humans to differentiate exactly two large numbers. The main hypothesis of this work is that configured groups also allow for a differentiation of large exact numbers, even when symbolic strategies become ineffective. In experiment 1, the children from grade 3 were asked to compare two large collections of objects for 5 s. When the objects were organized in configured groups, the success rate was over .90. Without this configured grouping, the children were unable to make a successful comparison. Experiments 2 and 3 controlled for a strategy based on non-numerical parameters (areas delimited by dots or the sum areas of dots, etc.) or use symbolic strategies. These results suggest that configured grouping enables humans to distinguish between two large exact numbers of objects, even when innate number sense and symbolic strategies are ineffective. These results are consistent with what we call "the configured group hypothesis": configured groups play a fundamental role in the acquisition of exact numerical abilities.

  9. Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: Irrelevance of amplitude and out-of-plane fluctuations (United States)

    Krieg, Jan; Kopietz, Peter


    We develop a functional renormalization group (FRG) approach for the two-dimensional X Y model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010), 10.1103/PhysRevE.82.041128] with a duality transformation that explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

  10. Numerical renormalization group study of probability distributions for local fluctuations in the Anderson-Holstein and Holstein-Hubbard models

    Energy Technology Data Exchange (ETDEWEB)

    Hewson, Alex C [Department of Mathematics, Imperial College, London SW7 2AZ (United Kingdom); Bauer, Johannes [Max-Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart (Germany)


    We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density rho(x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to the infinite dimensional Holstein-Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.

  11. An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory. (United States)

    Hannon, Kevin P; Li, Chenyang; Evangelista, Francesco A


    We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.

  12. Strong-coupling phases of 3D Dirac and Weyl semimetals. A renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

    González, J. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas,Serrano 123, Madrid, 28006 (Spain)


    We investigate the strong-coupling phases that may arise in 3D Dirac and Weyl semimetals under the effect of the long-range Coulomb interaction, considering the many-body theory of these electron systems as a variant of the conventional fully relativistic Quantum Electrodynamics (QED). For this purpose, we apply two different nonperturbative approaches, consisting in the sum of ladder diagrams and taking the limit of a large number N of fermion flavors. We benefit from the renormalizability that the theory shows in both cases to compute the anomalous scaling dimensions of different operators exclusively in terms of the renormalized coupling constant, allowing us to determine the precise location of the singularities signaling the onset of the strong-coupling phases. We show then that the QED of 3D Dirac semimetals has two competing effects at strong coupling. One of them is the tendency to chiral symmetry breaking and dynamical mass generation, which are analogous to the same phenomena arising in the conventional QED at strong coupling. This trend is however outweighed by the strong suppression of electron quasiparticles that takes place at large N, leading to a different type of critical point at sufficiently large interaction strength, shared also by the 3D Weyl semimetals. Overall, the phase diagram of the 3D Dirac semimetals turns out to be richer than that of their 2D counterparts, displaying a transition to a phase with non-Fermi liquid behavior which may be observed in materials hosting a sufficiently large number of Dirac or Weyl points.

  13. Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

    KAUST Repository

    Kumar, Manoranjan


    An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.

  14. The theory of critical phenomena an introduction to the renormalization group

    CERN Document Server

    Binney, J J; Fisher, A J; Newman, M E J


    The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulation

  15. Spin filtering in a double quantum dot device: Numerical renormalization group study of the internal structure of the Kondo state

    Energy Technology Data Exchange (ETDEWEB)

    Vernek, E. [Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, MG 38400-902 (Brazil); Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos-SP 13560-970 (Brazil); Büsser, C. A. [Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München (Germany); Anda, E. V. [Departamento de Física, Pontifícia Universidade Católica, Rio de Janeiro-RJ (Brazil); Feiguin, A. E. [Department of Physics, Northeastern University, Boston, Massachusetts 02115 (United States); Martins, G. B., E-mail: [Department of Physics, Oakland University, Rochester, Michigan 48309 (United States); Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)


    A double quantum dot device, connected to two channels that only interact through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. Using a two-impurity Anderson model, and realistic parameter values [S. Amasha, A. J. Keller, I. G. Rau, A. Carmi, J. A. Katine, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Phys. Rev. Lett. 110, 046604 (2013)], it is shown that, by applying a moderate magnetic field and independently adjusting the gate potential of each quantum dot at half-filling, a spin-orbital SU(2) Kondo state can be achieved where the Kondo resonance originates from spatially separated parts of the device. Our results clearly link this spatial separation effect to currents with opposing spin polarizations in each channel, i.e., the device acts as a spin filter. In addition, an experimental probe of this polarization effect is suggested, pointing to the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.

  16. Density-Matrix Renormalization Group Study of Third Harmonic Generation in One-Dimensional Mott Insulator Coupled with Phonon (United States)

    Sota, Shigetoshi; Yunoki, Seiji; Tohyama, Takami


    We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr2CuO3. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.

  17. Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension (United States)

    Kaushal, Nitin; Herbrych, Jacek; Nocera, Alberto; Alvarez, Gonzalo; Moreo, Adriana; Reboredo, F. A.; Dagotto, Elbio


    Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g) 4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ , at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing λ at intermediate U . In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum 〈(Jeff)2〉≠0 near the excitonic phase, smoothly connected to the 〈(Jeff)2〉=0 regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.

  18. Renormalization group calculations for wetting transitions of infinite order and continuously varying order: local interface Hamiltonian approach. (United States)

    Indekeu, J O; Koga, K; Hooyberghs, H; Parry, A O


    We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

  19. Renormalization-group-improved radiatively corrected Higgs masses in the minimal supersymmetric standard model at LEP2

    CERN Document Server

    Ghosh, B


    Recently, using a very simple approximation scheme which includes the most important terms in the radiative corrections for the Higgs masses in the minimal supersymmetric standard model (MSSM), Haber et al. have estimated the Higgs masses over a very large fraction of MSSM parameter space. The purpose of this paper is to apply the method of solving the renormalization group equations for top quark and bottom quark Yukawa couplings in the two-Higgs doublet model given by Parida and Usmani to the above studies of Haber et al. Here the effects of the running vacuum expectation values (VEVs) in the two Higgs doublet model below mu =M/sub susy/ have also been taken into account in terms of solutions of RGEs for the VEVs nu /sub 1/( mu ) and nu /sub 2/( mu ). It may be mentioned that at mass scales below M/sub susy/, the solutions of the non-SUSY (supersymmetry) two Higgs doublet model are used. Interestingly, new results are obtained from systematic studies on the mass of lightest Higgs boson in MSSM which have im...

  20. Formation of selfbound states in a one-dimensional nuclear model—a renormalization group based density functional study (United States)

    Kemler, Sandra; Pospiech, Martin; Braun, Jens


    In nuclear physics, density functional theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and renormalization group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of N identical fermions interacting via a general two-body interaction. Moreover, we discuss the control of spuriously emerging fermion self-interactions in DFT studies within our framework. In general, our approach may help to guide the development of energy functionals for future quantitative DFT studies of heavy nuclei from microscopic interactions.

  1. Modelling of the flow at the last stage blade tenon in a geothermal turbine using renormalization group theory turbulence model

    Energy Technology Data Exchange (ETDEWEB)

    Sierra, F.Z. [Centro de Investigacion en Energia-UNAM, Temixo, Morelos (Mexico); Mazur, Z.; Kubiak, J.; Urquiza, G.; Zuniga, R.; Marino, C.; Hernandez, A. [Unidad de Equipos Mecanicos Rotatorios, Inst. de Investigaciones Electricas, Cuernavaca (Mexico)


    A bi-dimensional modelling investigation of the flow in the last stage of a 110 MW geothermal turbine has been conducted. The study was based upon a Renormalization Group Theory turbulence model. The results confirmed the existence of flow conditions which may play a main role in the erosion of the L-0 stage blade tenon, which had been detected in periodic overhauls. According to predicted results the relationship between erosion and flow patterns might exist due to: (1) a vapour jet hitting directly on tenon surface at velocities around 65 m/s; (2) a low-pressure region identified with recirculating flow, which may be causing cavitation on the damaged surface. Afterwards, the flow was simulated with changes on the geometry and grid. These changes are, indeed, practically feasible of being implemented. The simulations showed that it is possible to reduce the erosion process by enlarging a flat region close to the L-0 rotor stage. Namely, this change of geometry produces a flow pattern that diminishes the strength of recirculation flow making it possible to reduce both the flow rate through tenon region and its velocity on tenon surface. The pressure drop diminishes as well, clearly reducing a risk of cavitation. (Author)

  2. Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations (United States)

    Nakatani, Naoki; Guo, Sheng


    This paper describes an interface between the density matrix renormalization group (DMRG) method and the complete active-space self-consistent field (CASSCF) method and its analytical gradient, as well as an extension to the second-order perturbation theory (CASPT2) method. This interfacing allows large active-space multi-reference computations to be easily performed. The interface and its extension are both implemented in terms of reduced density matrices (RDMs) which can be efficiently computed via the DMRG sweep algorithm. We also present benchmark results showing that, in practice, the DMRG-CASSCF calculations scale with active-space size in a polynomial manner in the case of quasi-1D systems. Geometry optimization of a binuclear iron-sulfur cluster using the DMRG-CASSCF analytical gradient is demonstrated, indicating that the inclusion of the valence p-orbitals of sulfur and double-shell d-orbitals of iron lead to non-negligible changes in the geometry compared to the results of small active-space calculations. With the exception of the selection of M values, many computational settings in these practical DMRG calculations have been tuned and black-boxed in our interface, and so the resulting DMRG-CASSCF and DMRG-CASPT2 calculations are now available to novice users as a common tool to compute strongly correlated electronic wavefunctions.

  3. Functional renormalization-group approach to the Pokrovsky-Talapov model via the modified massive Thirring fermions (United States)

    Nosov, P. A.; Kishine, Jun-ichiro; Ovchinnikov, A. S.; Proskurin, I.


    We consider a possibility of the topological Kosterlitz-Thouless (KT) transition in the two-dimensional Pokrovsky-Talapov model with a finite misfit parameter and discuss its relevance to the theory of critical behavior in thin films of monoaxial chiral helimagnets. For this purpose, the initial model is reformulated in terms of the two-dimensional relativistic model of massive Thirring fermions and the Wetterich's functional renormalization-group (RG) approach is employed. In the new formalism, the misfit parameter corresponds to an effective gauge field that can be included in the RG scheme on an equal footing with the other parameters of the theory. Our main result is that the presence of the misfit parameter, which may be attributed to the Dzyaloshinskii-Moriya interaction in the magnetic system, rules out the KT transition. To support this finding, we provide an additional intuitive explanation of the KT scenario breakdown by using the mapping onto the Coulomb gas model. In the framework of the model, the misfit parameter has a meaning of an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.

  4. Renormalization: infinity in today microscopic physics; Renormalisation et groupe de renormalisation: les infinis en physique microscopique contemporaine

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J


    The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)

  5. Linear perturbation renormalization group method for Ising-like spin systems

    Directory of Open Access Journals (Sweden)

    J. Sznajd


    Full Text Available The linear perturbation group transformation (LPRG is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs1-xSex, UPd2Si2 or UNi2Si2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J121-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT2Si2 (T=Pd, Ni this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J2/J1 around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase.

  6. The Analytic Renormalization Group

    CERN Document Server

    Ferrari, Frank


    Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\\in\\mathbb Z$, associated with the Matsubara frequencies $\

  7. Multireference Ab Initio Density Matrix Renormalization Group (DMRG)-CASSCF and DMRG-CASPT2 Study on the Photochromic Ring Opening of Spiropyran. (United States)

    Liu, Fengyi; Kurashige, Yuki; Yanai, Takeshi; Morokuma, Keiji


    The photochromic ring-opening reaction of spiropyran has been revisited at the multireference CASSCF and CASPT2 level with a CAS(22e,20o) active space, in combination with density matrix renormalization group (DMRG) methods. The accuracy of the DMRG-CASSCF and DMRG-CASPT2 calculations, with respect to the number of renormalized states, the number of roots in state-averaged wave functions, and the number basis functions, was examined. For the current system, chemically accurate results can be obtained with a relatively small number of renormalized states. The nature and vertical excitation energies of the excited (S1 and S2) states are consistent with conventional CAS(or RAS)PT2 with medium active spaces. The capability of the DMRG-CASSCF method in the optimization of molecular geometry is demonstrated for the first time. The computation costs (several hours per optimization cycle) are comparable with that of the conventional CASSCF geometry optimization with small active space. Finally, the DMRG-PT2 computed S1-MEP for the C-O and C-N bond-cleavage processes show good agreement with our previous calculations with a CAS(12e,10o) active space [Liu, F.; Morokuma, K. J. Am. Chem. Soc. 2013, 135, 10693-10702]. Especially, the role of the HOOP valleys in the S1 → S0 nonadiabatic decay has been confirmed.

  8. A functional renormalization method for wave propagation in random media (United States)

    Lamagna, Federico; Calzetta, Esteban


    We develop the exact renormalization group approach as a way to evaluate the effective speed of the propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. A simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.

  9. Entanglement renormalization for disordered systems (United States)

    Goldsborough, Andrew M.; Evenbly, Glen


    We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007), 10.1103/PhysRevLett.99.220405]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered X X Z model demonstrates that this approach accurately captures ground-state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for one-dimensional systems, which may be understood as a generalization of the multiscale entanglement renormalization ansatz for disordered systems.

  10. Controlling sign problems in spin models using tensor renormalization (United States)

    Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan


    We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

  11. Non-equilibrium scaling properties of a double quantum dot system: Comparison between perturbative renormalization group and flow equation approach

    Energy Technology Data Exchange (ETDEWEB)

    Koerting, V., E-mail: koerting@nbi.d [Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel (Switzerland); Niels Bohr Institute, Universitetsparken, DK-2100 Copenhagen (Denmark); The Niels Bohr International Academy, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Fritsch, P. [Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333 Munich (Germany); Kehrein, S., E-mail: stefan.kehrein@physik.lmu.d [Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333 Munich (Germany)


    Since the experimental realization of Kondo physics in quantum dots, its far-from-equilibrium properties have generated considerable theoretical interest. This is due to the interesting interplay of non-equilibrium physics and correlation effects in this model, which has now been analyzed using several new theoretical methods that generalize renormalization techniques to non-equilibrium situations. While very good agreement between these methods has been found for the spin-1/2 Kondo model, it is desirable to have a better understanding of their applicability for more complicated impurity models. In this paper the differences and commons between two such approaches, namely the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.

  12. Anomalous non-equilibrium electron transport in one-dimensional quantum nano wire at half-filling: time dependent density renormalization group study

    Energy Technology Data Exchange (ETDEWEB)

    Okumura, M; Onishi, H; Yamada, S; Machida, M, E-mail: okumura@riken.j


    We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of 'doublon', which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.

  13. Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics. Phase diagram from position space renormalization group transformation (United States)

    Renklioglu, B.; Yalabik, M. C.


    Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T x and T y , and also different time-scale constants, α x and α y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.

  14. Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature. (United States)

    Oppermann, R; Sherrington, D


    Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0infinity, where x/T --> a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.

  15. Anomalies and entanglement renormalization (United States)

    Bridgeman, Jacob C.; Williamson, Dominic J.


    We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.

  16. Surface critical behaviour at m-axial Lifshitz points: continuum models, boundary conditions and two-loop renormalization group results

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, H W; Rutkevich, S; Gerwinski, A [Fachbereich Physik, Universitaet Duisburg-Essen, D-45117 Essen (Germany)


    The critical behaviour of semi-infinite d-dimensional systems with short-range interactions and an O(n) invariant Hamiltonian is investigated at an m-axial Lifshitz point with an isotropic wave-vector instability in an m-dimensional subspace of R{sup d} parallel to the surface. Continuum |{phi}|{sup 4} models representing the associated universality classes of surface critical behaviour are constructed. In the boundary parts of their Hamiltonians quadratic derivative terms (involving a dimensionless coupling constant {lambda}) must be included in addition to the familiar ones {proportional_to}{phi}{sup 2}. Beyond one-loop order the infrared-stable fixed points describing the ordinary, special and extraordinary transitions in d = 4 + m/2 - {epsilon} dimensions (with {epsilon} > 0) are located at {lambda} = {lambda}* = O({epsilon}). At second order in {epsilon}, the surface critical exponents of both the ordinary and the special transitions start to deviate from their m = 0 analogues. Results to order {epsilon}{sup 2} are presented for the surface critical exponent {beta}{sup ord}{sub 1} of the ordinary transition. The scaling dimension of the surface energy density is shown to be given exactly by d + m({theta} - 1), where {theta} = {nu}{sub l4}/{nu}{sub l2} is the bulk anisotropy exponent. (letter to the editor)

  17. Renormalization and effective field theory

    CERN Document Server

    Costello, Kevin


    This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in "mathematics" itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. --Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. --Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorio...

  18. Renormalization of fermion mixing

    Energy Technology Data Exchange (ETDEWEB)

    Schiopu, R.


    Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

  19. Combined study of Schwinger-boson mean-field theory and linearized tensor renormalization group on Heisenberg ferromagnetic mixed spin (S, σ chains

    Directory of Open Access Journals (Sweden)

    Xin Yan


    Full Text Available The Schwinger-boson mean-field theory (SBMFT and the linearized tensor renormalization group (LTRG methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ω k ∼ S σ 2 ( S + σ J k 2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization m tot z = N ( S + σ . At low temperature, the spin correlation length is inversely proportional to temperature (T, the susceptibility behaviors as χ = a 1 ∗ 1 T 2 + a 2 ∗ 1 T , and the specific heat has the form of C = c 1 ∗ T − c 2 ∗ T + c 3 ∗ T 3 2 , with ai (i = 1, 2 and ci (i = 1, 2, 3 the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO24(en2(en = ethylenediamine, is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials.

  20. Tachyonic instability of the scalar mode prior to the QCD critical point based on the functional renormalization-group method in the two-flavor case (United States)

    Yokota, Takeru; Kunihiro, Teiji; Morita, Kenji


    We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the Z2 critical point. The functional renormalization-group method is applied to the two-flavor quark-meson model with varying current quark mass mq even away from the physical value at which the pion mass is reproduced. We first determine the whole phase structure in the three-dimensional space (T ,μ ,mq) consisting of temperature T , quark chemical potential μ and mq, with the tricritical point, O(4) and Z2 critical lines being located; they altogether make a winglike shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions ρσ ,π(ω ,p ) in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the Z2 point from the lower density, even for mq smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous σ condensate. No such anomalous behavior is found in the pseudoscalar channel. We find that the σ -to-2 σ coupling due to finite mq plays an essential role for the drastic modification of the spectral function.

  1. Phase diagram of electronic systems with quadratic Fermi nodes in 2 renormalization group (United States)

    Janssen, Lukas; Herbut, Igor F.


    Several materials in the regime of strong spin-orbit interaction such as HgTe, the pyrochlore iridate Pr2Ir2O7 , and the half-Heusler compound LaPtBi, as well as various systems related to these three prototype materials, are believed to host a quadratic band touching point at the Fermi level. Recently, it has been proposed that such a three-dimensional gapless state is unstable to a Mott-insulating ground state at low temperatures when the number of band touching points N at the Fermi level is smaller than a certain critical number Nc. We further substantiate and quantify this scenario by various approaches. Using ɛ expansion near two spatial dimensions, we show that Nc=64 /(25 ɛ2) +O (1 /ɛ ) and demonstrate that the instability for N renormalization group equations in the dynamical bosonization scheme which we show to agree to one-loop order with the results from ɛ expansion both near two as well as near four dimensions, and which smoothly interpolates between these two perturbatively accessible limits for general 2

  2. Fully Internally Contracted Multireference Configuration Interaction Theory Using Density Matrix Renormalization Group: A Reduced-Scaling Implementation Derived by Computer-Aided Tensor Factorization. (United States)

    Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi


    We present an extended implementation of the multireference configuration interaction (MRCI) method combined with the quantum-chemical density matrix renormalization group (DMRG). In the previous study, we introduced the combined theory, referred to as DMRGMRCI, as a method to calculate high-level dynamic electron correlation on top of the DMRG wave function that accounts for active-space (or strong) correlation using a large number of active orbitals. The DMRG-MRCI method is built on the full internal-contraction scheme for the compact reference treatment and on the cumulant approximation for the treatment of the four-particle rank reduced density matrix (4-RDM). The previous implementation achieved the MRCI calculations with the active space (24e,24o), which are deemed the record largest, whereas the inherent Nact 8 × N complexity of computation was found a hindrance to using further large active space. In this study, an extended optimization of the tensor contractions is developed by explicitly incorporating the rank reduction of the decomposed form of the cumulant-approximated 4-RDM into the factorization. It reduces the computational scaling (to Nact7 × N) as well as the cache-miss penalty associated with direct evaluation of complex cumulant reconstruction. The present scheme, however, faces the increased complexity of factorization patterns for optimally implementing the tensor contraction terms involving the decomposed 4-RDM objects. We address this complexity using the enhanced symbolic manipulation computer program for deriving and coding programmable equations. The new DMRG-MRCI implementation is applied to the determination of the stability of the iron(IV)-oxo porphyrin relative to the iron(V) electronic isomer (electromer) using the active space (29e,29o) (including four second d-shell orbitals of iron) with triple-ζ-quality atomic orbital basis sets. The DMRG-cu(4)-MRCI+Q model is shown to favor the triradicaloid iron(IV)-oxo state as the lowest

  3. Renormalizations in softly broken SUSY gauge theories (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.


    The supergraph technique for calculations in supersymmetric gauge theories where supersymmetry is broken in a "soft" way (without introducing quadratic divergencies) is reviewed. By introducing an external spurion field the set of Feynman rules is formulated and explicit connections between the UV counterterms of a softly broken and rigid SUSY theories are found. It is shown that the renormalization constants of softly broken SUSY gauge theory also become external superfields depending on the spurion field. Their explicit form repeats that of the constants of a rigid theory with the redefinition of the couplings. The method allows us to reproduce all known results on the renormalization of soft couplings and masses in a softly broken theory. As an example the renormalization group functions for soft couplings and masses in the Minimal Supersymmetric Standard Model up to the three-loop level are calculated.

  4. Renormalizations in softly broken SUSY gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Avdeev, L.V.; Kazakov, D.I.; Kondrashuk, I.N. [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics


    The supergraph technique for calculations in supersymmetric gauge theories where supersymmetry is broken in a ``soft`` way (without introducing quadratic divergencies) is reviewed. By introducing an external spurion field the set of Feynman rules is formulated and explicit connections between the UV counterterms of a softly broken and rigid SUSY theories are found. It is shown that the renormalization constants of softly broken SUSY gauge theory also become external superfields depending on the spurion field. Their explicit form repeats that of the constants of a rigid theory with the redefinition of the couplings. The method allows us to reproduce all known results on the renormalization of soft couplings and masses in a softly broken theory. As an example the renormalization group functions for soft couplings and masses in the minimal supersymmetric standard model up to the three-loop level are calculated. (orig.). 16 refs.

  5. Variational solution of the Gross-Neveu model; 2, finite-N and renormalization

    CERN Document Server

    Arvanitis, C; Iacomi, M; Kneur, J L; Neveu, A


    We show how to perform systematically improvable variational calculations in the O(2N) Gross-Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the renormalization group. The final point is a general framework for the calculation of non-perturbative quantities like condensates, masses, etc..., in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a "two-loop" variational calculation are in very good agreement with exact quantities down to low values of N.

  6. Compressive Spectral Renormalization Method

    CERN Document Server

    Bayindir, Cihan


    In this paper a novel numerical scheme for finding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the governing equation is transformed into Fourier domain, but the iterations are performed for far fewer number of spectral components (M) than classical versions of the these methods with higher number of spectral components (N). After the converge criteria is achieved for M components, N component signal is reconstructed from M components by using the l1 minimization technique of the compressive sampling. This method can be named as compressive spectral renormalization (CSRM) method. The main advantage of the CSRM is that, it is capable of finding the sparse self-localized states of the evolution equation(s) with many spectral data missing.

  7. Critical properties of scalar field theory with Lorentz violation: Exact treatment of Lorentz-violating mechanism (United States)

    Carvalho, P. R. S.; Sena-Junior, M. I.


    In this work, we compute analytically the infrared divergences of massless O(N) self-interacting scalar field theories with Lorentz violation, which are exact in the Lorentz-violating Kμν coefficients, for evaluating the corresponding next-to-leading order critical exponents. For that, we apply three distinct and independent field-theoretic renormalization group methods. We find that the outcomes for the critical exponents are the same in the three methods and, furthermore, are identical to their Lorentz invariant counterparts. We generalize the results for all loop levels by employing a general theorem arising from the exact procedure and give the corresponding physical interpretation.

  8. Exact phase boundaries and topological phase transitions of the X Y Z spin chain (United States)

    Jafari, S. A.


    Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

  9. Renormalization for free harmonic oscillators


    Sonoda, H.


    We introduce a model of free harmonic oscillators that requires renormalization. The model is similar to but simpler than the soluble Lee model. We introduce two concrete examples: the first, resembling the three dimensional $\\phi^4$ theory, needs only mass renormalization, and the second, resembling the four dimensional $\\phi^4$ theory and the Lee model, needs additional renormalization of a coupling and a wave function.

  10. Renormalization and power counting of chiral nuclear forces

    Energy Technology Data Exchange (ETDEWEB)

    Long, Bingwei [JLAB


    I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.

  11. Wavelets and renormalization

    CERN Document Server

    Battle, G A


    WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the F 4 3 quantum field theory is presented. It is due to Battle and

  12. Renormalization and effective actions for general relativity

    Energy Technology Data Exchange (ETDEWEB)

    Neugebohrn, F.


    Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

  13. Infrared troubles of differential renormalization (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.

    The possibility of generalizing differential renormalization of D.Z. Freedman, K. Jonnson and J.I. Latorre in an invariant fashion to theories with infrared divergencies is investigated. It is concluded that the calculations on infrared differential renormalization lead to incorrect results.

  14. Hilbert space renormalization for the many-electron problem. (United States)

    Li, Zhendong; Chan, Garnet Kin-Lic


    Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.

  15. Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

    DEFF Research Database (Denmark)

    Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi


    . The renormalization group equations for the M S ¯ parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FeynArts model file, so that amplitudes and squared...

  16. Holographic renormalization in teleparallel gravity

    Energy Technology Data Exchange (ETDEWEB)

    Krssak, Martin [Universidade Estadual Paulista, Instituto de Fisica Teorica, Sao Paulo, SP (Brazil)


    We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analog of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed. (orig.)

  17. Differential renormalization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)


    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

  18. Construction and analysis of a functional renormalization-group equation for gravitation in the Einstein-Cartan approach; Konstruktion und Analyse einer funktionalen Renormierungsgruppengleichung fuer Gravitation im Einstein-Cartan-Zugang

    Energy Technology Data Exchange (ETDEWEB)

    Daum, Jan-Eric


    Whereas the Standard Model of elementary particle physics represents a consistent, renormalizable quantum field theory of three of the four known interactions, the quantization of gravity still remains an unsolved problem. However, in recent years evidence for the asymptotic safety of gravity was provided. That means that also for gravity a quantum field theory can be constructed that is renormalizable in a generalized way which does not explicitly refer to perturbation theory. In addition, this approach, that is based on the Wilsonian renormalization group, predicts the correct microscopic action of the theory. In the classical framework, metric gravity is equivalent to the Einstein-Cartan theory on the level of the vacuum field equations. The latter uses the tetrad e and the spin connection {omega} as fundamental variables. However, this theory possesses more degrees of freedom, a larger gauge group, and its associated action is of first order. All these features make a treatment analogue to metric gravity much more difficult. In this thesis a three-dimensional truncation of the form of a generalized Hilbert-Palatini action is analyzed. Besides the running of Newton's constant G{sub k} and the cosmological constant {lambda}{sub k}, it also captures the renormalization of the Immirzi parameter {gamma}{sub k}. In spite of the mentioned difficulties, the spectrum of the free Hilbert-Palatini propagator can be computed analytically. On its basis, a proper time-like flow equation is constructed. Furthermore, appropriate gauge conditions are chosen and analyzed in detail. This demands a covariantization of the gauge transformations. The resulting flow is analyzed for different regularization schemes and gauge parameters. The results provide convincing evidence for asymptotic safety within the (e,{omega}) approach as well and therefore for the possible existence of a mathematically consistent and predictive fundamental quantum theory of gravity. In particular, one

  19. Controlling sign problems in spin models using tensor renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.


    We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

  20. Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Friederich, Simon


    Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

  1. Dimensional renormalization: Ladders and rainbows

    Energy Technology Data Exchange (ETDEWEB)

    Delbourgo, R. [Physics Department, University of Tasmania, GPO Box 252C, Hobart, (Australia) 7001; Kalloniatis, A.C. [Institut fur Theoretische Physik, University of Erlangen-Nuremberg, Staudtstrasse 7, Erlangen, D-91058 (Germany); Thompson, G. [International Centre for Theoretical Physics, Grignano-Miramare, Trieste, 34100 (Italy)


    Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive the factors and renormalized Green{close_quote}s functions to {ital all} orders in perturbation theory for rainbow graphs and vertex (or scattering) diagrams at zero momentum transfer, in the context of dimensional regularization, and we prove that the correct anomalous dimensions for those processes emerge in the limit {ital D}{r_arrow}4. {copyright} {ital 1996 The American Physical Society.}

  2. Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS.. (United States)

    Siegel, J.; Siegel, Edward Carl-Ludwig


    Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

  3. Implicit vs explicit renormalization and effective interactions

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz Arriola, E., E-mail: [Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Fisica Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Szpigel, S., E-mail: [Faculdade de Computação e Informática, Universidade Presbiteriana Mackenzie (Brazil); Timóteo, V.S., E-mail: [Grupo de Óptica e Modelagem Numérica – GOMNI, Faculdade de Tecnologia, Universidade Estadual de Campinas – UNICAMP (Brazil)


    Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the outcoming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei Λ≲200 MeV. This amounts to a great simplification in the determination of the effective interaction parameters.

  4. Difficulties of AN Infrared Extension of Differential Renormalization (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.

    We investigate the possibility of generalizing the differential renormalization of D. Z. Freedman, K. Johnson and J. I. Latorre in an invariant fashion to theories with infrared divergencies via an infrared widetilde R operation. Two-dimensional σ models and the four-dimensional ɸ4-theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. A consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on the infrared extension of differential renormalization lead to incorrect results. We conclude that the procedure of extended differential renormalization does not perform the infrared widetilde R operation in a self-consistent way.

  5. Fixed point of the parabolic renormalization operator

    CERN Document Server

    Lanford III, Oscar E


    This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

  6. Renormalizing the kinetic energy operator in elementary quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail:


    In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

  7. Recursive renormalization group theory based subgrid modeling (United States)

    Zhou, YE


    Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.

  8. The renormalization scale-setting problem in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)


    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

  9. Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.


    We explicitly carry out the renormalization of non-abelian Chern-Simons field theories with matter in (2 + 1) dimensions. All the renormalization constants are calculated to the leading two-loop order both in terms of component fields and N = 1 superfields for the fundamental representation of the SU( n), Sp( n) and SO( n) groups. Renormalization-group fixed points are found, and their stability properties are examined. It is shown that the N = 2 supersymmetry is realized as an infrared fixed-point solution, where the ultraviolet divergencies cancel.

  10. Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter

    Energy Technology Data Exchange (ETDEWEB)

    Avdeev, L.V.; Kazakov, D.I.; Kondrashuk, I.N. (Lab. of Theoretical Physics, Joint Inst. for Nuclear Research, Dubna (Russia))


    We explicitly carry out the renormalization of non-abelian Chern-Simons field theories with matter in (2+1) dimensions. All the renormalization constants are calculated to the leading two-loop order both in terms of component fields and N=1 superfields for the fundamental representation of the SU(n), Sp(n) and SO(n) groups. Renormalization-group fixed points are found, and their stability properties are examined. It is shown that the N=2 supersymmetry is realized as an infrared fixed-point solution, where the ultraviolet divergencies cancel. (orig.).

  11. Holographic renormalization as a canonical transformation

    CERN Document Server

    Papadimitriou, Ioannis


    The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equati...

  12. E-cigarette marketing and older smokers: road to renormalization. (United States)

    Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas


    To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

  13. Physical renormalization schemes and asymptotic safety in quantum gravity (United States)

    Falls, Kevin


    The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

  14. BOOK REVIEW: Renormalization Methods---A Guide For Beginners (United States)

    Cardy, J.


    The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard phi4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

  15. Euclidean Epstein-Glaser renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Keller, Kai J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik


    In the framework of perturbative Algebraic Quantum Field Theory (pAQFT) I give a general construction of so-called 'Euclidean time-ordered products', i.e. algebraic versions of the Schwinger functions, for scalar quantum eld theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space (MQFT). An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction-) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of EQFT have a unique singularity structure, i.e. they are unique up to a smooth part. Second, one needs to (re-)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable. (orig.)

  16. Renormalization of minimally doubled fermions (United States)

    Capitani, Stefano; Creutz, Michael; Weber, Johannes; Wittig, Hartmut


    We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Boriçi-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Boriçi-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

  17. Power counting and Wilsonian renormalization in nuclear effective field theory (United States)

    Valderrama, Manuel Pavón


    Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

  18. ExactPack Documentation

    Energy Technology Data Exchange (ETDEWEB)

    Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory


    For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.

  19. Three Topics in Renormalization and Improvement

    CERN Document Server

    Vladikas, A


    This is an expanded version of lecture notes, delivered at the XCIII Les Houches Summer School (August 2009). Our aim is to present three very specific topics: (i) The consequences of the loss of chiral symmetry in the Wilson lattice regularization of the fermionic action and its recovery in the continuum limit. The treatment of these arguments involves lattice Ward identities. (ii) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. (iii) The modification of the Wilson fermion action, by the introduction of a chirally twisted mass term (known as twisted mass QCD - tmQCD), which results to improved (re)normalization and scaling properties for physical quantities of interest.

  20. Renormalized vacuum polarization of rotating black holes

    CERN Document Server

    Ferreira, Hugo R C


    Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2+1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization (and, more importantly, the renormalized stress-energy tensor), for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

  1. Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

    Energy Technology Data Exchange (ETDEWEB)

    Song, Xue-ke [School of Physics and Material Science, Anhui University, Hefei, 230039 (China); Wu, Tao [School of Physics and Electronics Science, Fuyang Normal College, Fuyang, 236037 (China); Xu, Shuai; He, Juan [School of Physics and Material Science, Anhui University, Hefei, 230039 (China); Ye, Liu, E-mail: [School of Physics and Material Science, Anhui University, Hefei, 230039 (China)


    In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.

  2. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)


    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  3. A note on convex renorming and fragmentability

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    A note on convex renorming and fragmentability. A K MIRMOSTAFAEE. Department of Mathematics, Damghan University of Sciences, P.O. 36715/364,. Damghan, Iran. E-mail: ... general, the domain of sn+1 consists of partial plays of the type. (A1,... ,Ai,Bi,Ai+1,... ,An+1), where, for every i ≤ n, (A1 ...

  4. Renormalized Perturbation Theory A Missing Chapter

    CERN Document Server

    Stora, Raymond


    Renormalized perturbation theory à la BPHZ can be founded on causality as analyzed by H. Epstein and V. Glaser in the seventies. Here, we list and discuss a number of additional constraints of algebraic character some of which have to be considered as parts of the core of the BPHZ framework.

  5. Time-dependent spectral renormalization method (United States)

    Cole, Justin T.; Musslimani, Ziad H.


    The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

  6. Renormalization of Magnetic Excitations in Praseodymium

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker


    The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...

  7. Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)


    In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

  8. On exact correlation functions in SU(N) $ \\mathcal{N}=2 $ superconformal QCD

    CERN Document Server

    Baggio, Marco; Papadodimas, Kyriakos


    We consider the exact coupling constant dependence of extremal correlation functions of ${\\cal N} = 2$ chiral primary operators in 4d ${\\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in ${\\cal N} = 2$ superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the ${\\cal N} = 2$ chiral ring of the SU(N) theory, and in all explicitly computed exampl...

  9. Exact Threshold Circuits

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.


    with the well-studied corresponding hierarchies defined using ordinary threshold gates. A major open problem in Boolean circuit complexity is to provide an explicit super-polynomial lower bound for depth two threshold circuits. We identify the class of depth two exact threshold circuits as a natural subclass...

  10. Stochastic light-cone CTMRG: a new DMRG approach to stochastic models 02.50.Ey Stochastic processes; 64.60.Ht Dynamic critical phenomena; 02.70.-c Computational techniques; 05.10.Cc Renormalization group methods;

    CERN Document Server

    Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J


    We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.

  11. Supersymmetric QCD: exact results and strong coupling (United States)

    Dine, Michael; Festuccia, Guido; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao


    We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius β, due to infrared effects, finite contributions indeed arise which are not visible in the formal β → ∞ limit.

  12. Renormalization of gauge theories without cohomology

    Energy Technology Data Exchange (ETDEWEB)

    Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa (Italy)


    We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

  13. Field renormalization in photonic crystal waveguides

    DEFF Research Database (Denmark)

    Colman, Pierre


    A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... Schro¨dinger equation is an occasion for physics-oriented considerations and unveils the potential of photonic crystal waveguides for the study of new nonlinear propagation phenomena....

  14. Effects of renormalization parameters on singularities and special soliton solutions of the modified complex Ginzburg-Landau equation

    Energy Technology Data Exchange (ETDEWEB)

    Kenfack-Jiotsa, A [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon); Fewo, S I [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon); Kofane, T C [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon)


    Considering a pulse-like ansatz, we derive different classes of exact soliton solutions of the modified complex Ginzburg-Landau equation. We then present the important variations which occur in the domain of stability of these solutions depending on the values of the renormalization coeffecients. This means that this term which can be considered for nonzero solutions and which does not generally occur in the literature could explain the lack of concordance between some theory and experiments.

  15. Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo; /SLAC


    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

  16. Spatial dependence of entanglement renormalization in XY model (United States)

    Usman, M.; Ilyas, Asif; Khan, Khalid


    In this article, a comparative study of the renormalization of entanglement in one-, two- and three-dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the quantum renormalization group (QRG) method using numerical techniques. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin {-}1/2 XY model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space, but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two-dimensional and three-dimensional spin {-}1/2 XY model, maximum value of the concurrence reduce by the factor of 1 / n (n=2,3) with reference to the maximum value of one-dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one-, two- and three-dimensional cases and illustrate how the system evolves near the critical point.

  17. Exact Relativistic `Antigravity' Propulsion (United States)

    Felber, Franklin S.


    The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

  18. Renormalization group approaches to low-dimensional systems. Scrutinization of the spin-functional RG for the 2D XXZ model and real-time RG study of a generic 2-level quantum dot in the Coulomb blockade regime in nonequilibrium

    Energy Technology Data Exchange (ETDEWEB)

    Goettel, Stefan


    In this thesis, we study two recently developed methods to tackle low-dimensional correlated quantum systems. In the first part, we benchmark the extension of the functional renormalization group to spin-systems. We apply it to the two-dimensional XXZ model and reproduce the prediction for the phase transition from planar to axial ordering at the isotropic point. The interpretation of the critical scale (where the flow of the susceptibility diverges) as the critical temperature of the system can be questioned, since it yields only good results in the Ising limit. Especially near the isotropic point, this interpretation becomes unsatisfactory as the Mermin-Wagner theorem is violated. We discuss several problems of the method and conclude that it should only be used to explore phase diagrams. In the second part, we extend previous works to two-level quantum dots in the Coulomb blockade regime with special hopping matrices in nonequilibrium, e.g., the Kondo model, to the generic form, including ferromagnetic leads, spin-orbit interactions etc. The dot and the transport observables are determined completely by the hybridization matrix, leading to one of our major results that all these models can be mapped to the Anderson impurity model with ferromagnetic leads. We investigate this model with a well-controlled real-time renormalization group approach and justify the results of a poor man's scaling analysis. By using a singular value decomposition of the tunneling matrix we can rotate the model to the anisotropic Kondo model in the high-energy regime to solve the flow equations analytically. With this, we calculate the stationary dot magnetization and the current. The minimum of the magnetization is found to be an ellipsoid as function of the magnetic field, where the stretching factor determines the distance to the scaling limit. Afterwards, we consider the special case of two external reservoirs and the system being in the scaling limit and discuss the golden

  19. BRST renormalization of the first order Yang-Mills theory (United States)

    Frenkel, J.; Taylor, John C.


    We examine the renormalization of the first order formulation of the Yang-Mills theory, by using the BRST identities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in perturbation theory. The renormalization involves non-linear mixings as well as re-scalings of the fields and sources, which lead to a renormalized action at all orders.

  20. Applications of noncovariant gauges in the algebraic renormalization procedure

    CERN Document Server

    Boresch, A; Schweda, Manfred


    This volume is a natural continuation of the book Algebraic Renormalization, Perturbative Renormalization, Symmetries and Anomalies, by O Piguet and S P Sorella, with the aim of applying the algebraic renormalization procedure to gauge field models quantized in nonstandard gauges. The main ingredient of the algebraic renormalization program is the quantum action principle, which allows one to control in a unique manner the breaking of a symmetry induced by a noninvariant subtraction scheme. In particular, the volume studies in-depth the following quantized gauge field models: QED, Yang-Mills t

  1. Efficient exact motif discovery. (United States)

    Marschall, Tobias; Rahmann, Sven


    The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. The method has been implemented in Java. It can be obtained from

  2. Finding optimal exact reducts

    KAUST Repository

    AbouEisha, Hassan M.


    The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.

  3. Sous le soleil exactement.

    Directory of Open Access Journals (Sweden)

    Jérôme Chenal


    Full Text Available © Benoît Vollmer, sans titre, Nouakchott, 2007. Le travail scientifique a toujours entretenu un rapport étroit avec l’image. Dans le domaine de la médecine, l’imagerie passe aujourd’hui pour être indispensable à la plupart des interventions sur les corps ; les scanners, irm et autres procédés montrent une utilisation possible de l’image dans le monde des sciences exactes. La police scientifique que popularisent Ncis ou Les Experts , qu’ils soient de Miami, de Manhattan ...

  4. Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata (United States)

    Young, Frederic; Siegel, Edward

    Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

  5. Perturbative and nonperturbative renormalization in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)


    We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)

  6. Complex-mass shell renormalization of the higher-derivative electrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Turcati, Rodrigo [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Laboratorio de Fisica Experimental (LAFEX), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil); Neves, Mario Junior [Universidade Federal Rural do Rio de Janeiro, Departamento de Fisica, Rio de Janeiro (Brazil)


    We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed. (orig.)

  7. Exact Solutions to Maccari's System (United States)

    Pan, Jun-Ting; Gong, Lun-Xun


    Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.

  8. Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function (United States)

    Ananthanarayan, B.; Das, Diganta


    We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the s -quark mass relevant in τ -decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass ms(2 GeV )=106.70 ±9.36 MeV and ms(2 GeV )=74.47 ±7.77 MeV from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

  9. Emergent space-time via a geometric renormalization method (United States)

    Rastgoo, Saeed; Requardt, Manfred


    We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of space-time can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group (RG). Furthermore, we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which, e.g., for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e., quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is noninteger. At the end of the paper we briefly mention the possibility that our network carries a translocal far order that leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.

  10. Exact consequences of the trace anomaly in four dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Cappelli, Andrea E-mail:; Guida, Riccardo E-mail:; Magnoli, Nicodemo E-mail:


    The general form of the stress-tensor three-point function in four dimensions is obtained by solving the Ward identities for the diffeomorphism and Weyl symmetries. Several properties of this correlator are discussed, such as the renormalization and scheme independence and the analogies with the anomalous chiral triangle. At the critical point, the coefficients a and c of the four-dimensional trace anomaly are related to two finite, scheme-independent amplitudes of the three-point function. Off-criticality, the imaginary parts of these amplitudes satisfy sum rules which express the total renormalization-group flow of a and c between pairs of critical points. Although these sum rules are similar to that satisfied by the two-dimensional central charge, the monotonicity of the flow, i.e., the four-dimensional analogue of the c-theorem, remains to be proven.

  11. Thermodynamics of the two-dimensional XY model from functional renormalization

    CERN Document Server

    Jakubczyk, Pawel


    We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.

  12. Semihard processes with BLM renormalization scale setting

    Energy Technology Data Exchange (ETDEWEB)

    Caporale, Francesco [Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15 and U. Autónoma de Madrid, E-28049 Madrid (Spain); Ivanov, Dmitry Yu. [Sobolev Institute of Mathematics and Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Murdaca, Beatrice; Papa, Alessandro [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy)


    We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.

  13. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    Directory of Open Access Journals (Sweden)

    Huan-Yu Bi


    Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  14. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale (United States)

    Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin


    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  15. The Neglected Exactness (United States)

    Endom, Joerg


    negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.

  16. Renormalization of the Lattice Heavy Quark Classical Velocity (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.


    In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

  17. Renormalization of tracer turbulence leading to fractional differential operators

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez, Raul [ORNL; Carreras, Benjamin A [ORNL; Newman, David E [University of Alaska; Lynch, Vickie E [ORNL; van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT


    For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides with a first step towards establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

  18. One-loop renormalization of the Polyakov string functional (United States)

    Cohen, E.; Kluberg-Stern, H.; Navelet, H.; Peschanski, R.


    This paper studies the divergences of the bosonic string coupled to background fields, the graviton, the dilaton and the tachyon fields. These divergences are computed to first order in the string tension parameter for the topologies of the sphere and the torus. In our modular invariant regularization, depending on a dimensionful parameter ɛ, quadratic divergences are present and they modify the renormalization scheme. As an alternative to the Fischler-Susskind mechanism, which leads to a contribution to the target-space cosmological constant from the torus, it is possible to absorb the main divergences in a renormalization of the string coupling constant which is related to the renormalization of the dilaton background field. The contribution from the torus leads to new effects which are not σ-model counterterms. If certain factorization properties apply for the partition function of higher-order topologies, this scheme could indicate the existence of a solution without target space metric renormalization at this order.

  19. Exact piecewise flat gravitational waves

    NARCIS (Netherlands)

    van de Meent, M.|info:eu-repo/dai/nl/314007067


    We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to

  20. Exponential and power-law renormalization in phonon-assisted tunneling (United States)

    Khedri, A.; Costi, T. A.; Meden, V.


    We investigate the spinless Anderson-Holstein model routinely employed to describe the basic physics of phonon-assisted tunneling in molecular devices. Our focus is on small to intermediate electron-phonon coupling; we complement a recent strong coupling study [Phys. Rev. B 87, 075319 (2013), 10.1103/PhysRevB.87.075319]. The entire crossover from the antiadiabatic regime to the adiabatic one is considered. Our analysis using the essentially analytical functional renormalization group approach backed up by numerical renormalization group calculations goes beyond lowest order perturbation theory in the electron-phonon coupling. In particular, we provide an analytic expression for the effective tunneling coupling at particle-hole symmetry valid for all ratios of the bare tunnel coupling and the phonon frequency. It contains the exponential polaronic as well as the power-law renormalization in the electron-phonon interaction; the latter can be traced back to x-ray edgelike physics. In the antiadiabatic and the adiabatic limit this expression agrees with the known ones obtained by mapping to an effective interacting resonant level model and lowest order perturbation theory, respectively. Away from particle-hole symmetry, we discuss and compare results from several approaches for the zero temperature electrical conductance of the model.

  1. Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions (United States)

    Lee, Yu-Wen; Lee, Yu-Li


    We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

  2. Aspects of renormalization in finite-density field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia


    We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

  3. Investigation of renormalization effects in high temperature cuprate superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Zabolotnyy, Volodymyr B.


    It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

  4. Technical fine-tuning problem in renormalized perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E.


    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  5. Bulk renormalization and particle spectrum in codimension-two brane worlds (United States)

    Salvio, Alberto


    We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

  6. Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz

    CERN Document Server

    Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei


    The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological order. MERA also shares many deep relationships with the AdS/CFT (gauge-gravity) correspondence by realizing a UV complete holographic duality within the tensor networks framework. Motivated by this, we have re-purposed the MERA tensor network as an analysis tool to study the real-time evolution of the 1D transverse Ising model in its low energy excited state sector. We performed this analysis by allowing the ancilla qubits of the MERA tensor network to acquire quantum fluctuations, which yields a unitary transform between the physical (boundary) and ancilla qubit (bulk) Hilbert spaces. This then defines a reversible quantum circuit which is used as a `holographic transform' to study excited states and their real-time dynamics from the point of the bulk ancillae. In the ga...

  7. Renormalization of aperiodic model lattices: spectral properties

    CERN Document Server

    Kroon, L


    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schroedinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubli...

  8. Renormalized Wick expansion for a modified PQCD

    Energy Technology Data Exchange (ETDEWEB)

    Cabo Montes de Oca, Alejandro [Instituto de Cibernetica, Matematica y Fisica, Group of Theoretical Physics, Vedado, La Habana (Cuba); Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)


    The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m{sub q} and m{sub g} associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m{sub q} and m{sub g} is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum. (orig.)

  9. Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices. (United States)

    Monthus, Cécile; Garel, Thomas


    We study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices. These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function. (These exact renormalizations on diamond lattices can also be considered as approximate Migdal-Kadanoff renormalizations for hypercubic lattices.) In terms of the rescaled partition function z=Z/Z(typ) , we find that the critical point corresponds to a fixed point distribution with a power-law tail P(c)(z) ~ Phi(ln z)/z(1+mu) as z-->+infinity [up to some subleading logarithmic correction Phi(ln z)], so that all moments z(n) with n>mu diverge. For the wetting transition, the first moment diverges z=+infinity (case 0infinity (case 1fixed point distribution coincides with the transfer matrix describing a directed polymer on the Cayley tree, but the random weights determined by the fixed point distribution P(c)(z) are broadly distributed. This induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions.

  10. Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

    Directory of Open Access Journals (Sweden)

    Segun Goh

    Full Text Available Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare bus stops are transformed into a (renormalized "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

  11. Exact cosmological solutions for MOG

    Energy Technology Data Exchange (ETDEWEB)

    Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)


    We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)

  12. Exact solution for generalized pairing


    Pan, Feng; Draayer, J. P.


    An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.

  13. n-Monotone exact functionals (United States)

    de Cooman, Gert; Troffaes, Matthias C. M.; Miranda, Enrique


    We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.

  14. Ultrasoft renormalization of the potentials in vNRQCD

    Energy Technology Data Exchange (ETDEWEB)

    Stahlhofen, Maximilian Horst


    The effective field theory vNRQCD allows to describe among others the production of top-antitop pairs in electron-positron collisions at threshold, i.e. with very small relative velocity {upsilon} << 1 of the quarks. Potentially large logarithms {proportional_to} ln {upsilon} are systematically summed up and lead to a scale dependence of the Wilson coefficients of the theory. The missing contributions to the cross section {sigma}(e{sup +}e{sup -} {yields} t anti t) in the resonance region at NNLL level are the so-called mixing contributions to the NNLL anomalous dimension of the S-wave production/annihilation current of the topquark pair. To calculate these one has to know the NLL renormalization group running of so-called potentials (4-quark operators). The dominant contributions to the anomalous dimension of these potentials come from vNRQCD diagrams with ultrasoft gluon loops. The aim of this thesis is to derive the complete ultrasoft NLL running of the relevant potentials. For that purpose the UV divergent parts of about 10{sup 4} two-loop diagrams are determined. Technical and conceptional issues are discussed. Some open questions related to the calculation of the non-Abelian two-loop diagrams arise. Preliminary results are analysed with regard to the consequences for the mentioned cross section and its theoretical uncertainty. (orig.)

  15. Gauge-independent renormalization of the N2HDM (United States)

    Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui


    The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

  16. Simplified parquet equations for the Anderson impurity model: comparison with numerically exact solutions

    Czech Academy of Sciences Publication Activity Database

    Pokorný, Vladislav; Žonda, M.; Kauch, Anna; Janiš, Václav


    Roč. 131, č. 4 (2017), s. 1042-1044 ISSN 0587-4246 R&D Projects: GA ČR GA15-14259S Institutional support: RVO:68378271 Keywords : Anderson model * parquet equations * numerical renormalization group Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.469, year: 2016

  17. Exact BPS bound for noncommutative baby Skyrmions

    Energy Technology Data Exchange (ETDEWEB)

    Domrin, Andrei, E-mail: [Department of Mathematics and Mechanics, Moscow State University, Leninskie gory, 119992, GSP-2, Moscow (Russian Federation); Lechtenfeld, Olaf, E-mail: [Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover (Germany); Linares, Román, E-mail: [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico); Maceda, Marco, E-mail: [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico)


    The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.

  18. Exact Algorithms for the Clustered Vehicle Routing Problem

    NARCIS (Netherlands)

    Battarra, M.; Erdogan, G.; Vigo, D.


    This study presents new exact algorithms for the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the capacitated vehicle routing problem (CVRP), in which the customers are grouped into clusters. As in the CVRP, all the customers must be visited exactly once, but a

  19. Exact discretization by Fourier transforms (United States)

    Tarasov, Vasily E.


    A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.

  20. Exact analysis of discrete data

    CERN Document Server

    Hirji, Karim F


    Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

  1. When 'exact recovery' is exact recovery in compressed sensing simulation

    DEFF Research Database (Denmark)

    Sturm, Bob L.


    In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...

  2. Peripheral NN scattering from subtractive renormalization of chiral interactions

    Energy Technology Data Exchange (ETDEWEB)

    Batista, E. F. [Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia, 45700-000 Itapetinga - BA (Brazil); Szpigel, S. [Centro de Rádio-Astronomia e Astrofísica Mackenzie, Escola de Engenharia, Universidade Presbiteriana Mackenzie, 01302-907 São Paulo - SP (Brazil); Timóteo, V. S. [Grupo de Óptica e Modelagem NumérIca - GOMNI, Faculdade de Tecnologia - FT, Universidade Estadual de Campinas - UNICAMP, 13484-332 Limeira - SP (Brazil)


    We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm{sup −1} and 1 fm{sup −1}. In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E{sub lab} = 150 MeV, with a cutoff at Λ = 30 fm{sup −1}.

  3. Parton distribution function with nonperturbative renormalization from lattice QCD (United States)

    Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang; Lin, Huey-Wen; Yang, Yi-Bo; Zhang, Jian-Hui; Zhao, Yong; Lattice Parton Physics Project LP3


    We present lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum-subtraction scheme (RI/MOM) renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-x dependence of a momentum-dependent quasidistribution is calculated on the lattice and matched to the ordinary light cone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

  4. Renormalization of modular invariant Coulomb gas and sine-Gordon theories, and the quantum Hall flow diagram

    Energy Technology Data Exchange (ETDEWEB)

    Carpentier, David [Laboratoire de Physique Theorique de l' Ecole Normale Superieure, Paris (France)


    Using the renormalization group (RG) we study two-dimensional electromagnetic Coulomb gas and extended sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following the proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram. (author)

  5. Running with rugby balls: bulk renormalization of codimension-2 branes (United States)

    Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.


    We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

  6. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.


    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  7. Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces

    Directory of Open Access Journals (Sweden)

    Hossein Soleimani


    Full Text Available In this paper we show that by renorming an ordered Banach space, every cone $P$ can be converted to a normal cone with constant $K=1$ and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

  8. Galilean invariance and vertex renormalization in turbulence theory. (United States)

    McComb, W D


    The Navier-Stokes equation is invariant under Galilean transformation of the instantaneous velocity field. However, the total velocity transformation is effected by transformation of the mean velocity alone. For a constant mean velocity, the equation of motion for the fluctuating velocity is automatically Galilean invariant in the comoving frame, and vertex renormalization is not constrained by this symmetry.

  9. Renormalization of one-pion exchange and power counting

    NARCIS (Netherlands)

    Nogga, A; Timmermans, RGE; van Kolck, U


    The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be

  10. Holographic renormalization of 3D minimal massive gravity

    Energy Technology Data Exchange (ETDEWEB)

    Alishahiha, Mohsen [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Qaemmaqami, Mohammad M.; Naseh, Ali [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Department of Physics, Isfahan University of Technology,P.O.Box 84156-83111, Isfahan (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)


    We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.

  11. Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

    Energy Technology Data Exchange (ETDEWEB)

    Higa, R; Valderrama, M Pavon; Arriola, E Ruiz


    The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.

  12. Simple perturbative renormalization scheme for supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)


    We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/ -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.

  13. Three resonating fermions in flatland: proof of the super Efimov effect and the exact discrete spectrum asymptotics (United States)

    Gridnev, Dmitry K.


    We consider the system of three nonrelativistic spinless fermions in two dimensions, which interact through spherically-symmetric pair interactions. Recently, a claim has been made by Nishida et al for the existence of the so-called super Efimov effect by Nishida et al (2013 Phys. Rev. Lett. 110 235301). Namely, if the interactions in the system are fine-tuned to a p-wave resonance, an infinite number of bound states appears, whose negative energies are scaled according to the double exponential law. We present the mathematical proof that such a system indeed has an infinite number of bound levels. We also prove that {{lim }E\\to 0}| ln | ln E |{{|}-1}N(E)=8/(3π ), where N(E) is the number of bound states with the energy less than -E\\lt 0. The value of this limit is exactly equal to the value derived in Nishida et al using the renormalization group approach. Our proof resolves a recent controversy about the validity of results in Nishida et al (2013 Phys. Rev. Lett. 110 235301).

  14. Non-perturbative renormalization of the lattice heavy quark classical velocity

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E. [Department of Energy, Washington, DC (United States). Div. of High Energy Physics; Ogilvie, M.C. [Washington Univ., St. Louis, MO (United States). Dept. of Physics


    We discuss the renormalization of the lattice formulation of the heavy quark effective theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration. (orig.).

  15. Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.


    We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

  16. Method of exact lung puncture

    Energy Technology Data Exchange (ETDEWEB)

    Voss, L.


    The accuracy can be improved, and the risk of complications can be reduced in the case of cytodiagnostic lung puncture, if one optimises the method whereby the puncture needle is inserted into the lesion. The author describes such a procedure incorporating the use of technical aids for marking the exact puncture point of the cannula. At the same time the procedure results in a reduction of radiation exposure of both doctor and patient.

  17. Absence of a consistent classical equation of motion for a mass-renormalized point charge. (United States)

    Yaghjian, Arthur D


    The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self-electromagnetic force on an extended charged sphere of radius a are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self-force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, a transition force must be included during each of these two transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solution to the equation of motion without the transition forces. Although the exact time dependence of each transition force is not known, the effect of each transition force on the solution to the equation of motion can be determined to within a single unknown constant, namely the change in velocity of the charge across the transition interval. For the extended charged sphere, the changes in velocity across the transition intervals can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, regardless of the values chosen for the changes in the velocity across the transition intervals, renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.

  18. Dissociation between exact and approximate addition in developmental dyslexia. (United States)

    Yang, Xiujie; Meng, Xiangzhi


    Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

  19. Turbulent mixing of a critical fluid: The non-perturbative renormalization

    Directory of Open Access Journals (Sweden)

    M. Hnatič


    Full Text Available Non-perturbative Renormalization Group (NPRG technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow, but there is a new nonequilibrium regime (universality class associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

  20. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N


    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  1. Weights of Exact Threshold Functions

    DEFF Research Database (Denmark)

    Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.


    We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case...... and the Boolean cube {0,1} n . In the process we construct new families of ill-conditioned matrices. We further stratify the problem (in the linear case) in terms of the dimension k of the affine subspace spanned by the solutions, and give upper and lower bounds in this case as well. Our bounds here in terms of k...

  2. Matrix product density operators: Renormalization fixed points and boundary theories

    Energy Technology Data Exchange (ETDEWEB)

    Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)


    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  3. Renormalization out of equilibrium in a superrenormalizable theory

    CERN Document Server

    Garny, Mathias


    We discuss the renormalization of the initial value problem in Nonequilibrium Quantum Field Theory within a simple, yet instructive, example and show how to obtain a renormalized time evolution for the two-point functions of a scalar field and its conjugate momentum at all times. The scheme we propose is applicable to systems that are initially far from equilibrium and compatible with non-secular approximation schemes which capture thermalization. It is based on Kadanoff-Baym equations for non-Gaussian initial states, complemented by usual vacuum counterterms. We explicitly demonstrate how various cutoff-dependent effects peculiar to nonequilibrium systems, including time-dependent divergences or initial-time singularities, are avoided by taking an initial non-Gaussian three-point vacuum correlation into account.

  4. The proton-proton scattering without Coulomb force renormalization

    Directory of Open Access Journals (Sweden)

    Glöckle W.


    Full Text Available We demonstrate numerically that proton-proton (pp scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS equation for an exponentially screened Coulomb potential. For the limit of large screening radii we confirm analytically predicted properties for off-shell, half-shell and on-shell elements of the Coulomb t-matrix.

  5. BPHZ renormalization in configuration space for the A4-model

    Directory of Open Access Journals (Sweden)

    Steffen Pottel


    Full Text Available Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

  6. Massive renormalization scheme and perturbation theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Blaizot, Jean-Paul, E-mail: [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)


    We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.

  7. Charge renormalization for effective interactions of colloids at water interfaces


    Frydel, D.; Dietrich, S.; Oettel, M.


    We analyze theoretically the electrostatic interaction of surface-charged colloids at water interfaces with special attention to the experimentally relevant case of large charge densities on the colloid-water interface. Whereas linear theory predicts an effective dipole potential the strength of which is proportional to the square of the product of charge density and screening length, nonlinear charge renormalization effects change this dependence to a weakly logarithmic one. These results ap...

  8. Renormalized spacetime is two-dimensional at the Planck scale

    CERN Document Server

    Padmanabhan, T; Kothawala, Dawood


    Quantum field theory distinguishes between the bare variables -- which we introduce in the Lagrangian -- and the renormalized variables which incorporate the effects of interactions. This suggests that the renormalized, physical, metric tensor of spacetime (and all the geometrical quantities derived from it) will also be different from the bare, classical, metric tensor in terms of which the bare gravitational Lagrangian is expressed. We provide a physical ansatz to relate the renormalized metric tensor to the bare metric tensor such that the spacetime acquires a zero-point-length $\\ell _{0}$ of the order of the Planck length $L_{P}$. This prescription leads to several remarkable consequences. In particular, the Euclidean volume $V_D(\\ell,\\ell _{0})$ in a $D$-dimensional spacetime of a region of size $\\ell $ scales as $V_D(\\ell, \\ell_{0}) \\propto \\ell _{0}^{D-2} \\ell^2$ when $\\ell \\sim \\ell _{0}$, while it reduces to the standard result $V_D(\\ell,\\ell _{0}) \\propto \\ell^D$ at large scales ($\\ell \\gg \\ell _{0}...

  9. One-loop renormalization of a gravity-scalar system

    Energy Technology Data Exchange (ETDEWEB)

    Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)


    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

  10. AESS: Accelerated Exact Stochastic Simulation (United States)

    Jenkins, David D.; Peterson, Gregory D.


    The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution

  11. A new exactly solvable spatially one-dimensional quantum superradiance fermi-medium model and properties of its quantum solitonic states

    Directory of Open Access Journals (Sweden)

    D. Blackmore


    Full Text Available A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with external electromagnetic field is proposed. The infinite hierarchy of quantuum conservation laws and many-particle Bethe eigenstates that model quantum solitonic impulse structures are constructed. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed.

  12. Renormalization of the Abelian–Higgs model in the Rξ and Unitary gauges and the physicality of its scalar potential

    Directory of Open Access Journals (Sweden)

    Nikos Irges


    Full Text Available We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and Rξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the Rξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the Rξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.

  13. Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)


    We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  14. Exact self-dual skyrmions (United States)

    Ferreira, L. A.; Shnir, Ya.


    We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.

  15. Exact self-dual skyrmions

    Directory of Open Access Journals (Sweden)

    L.A. Ferreira


    Full Text Available We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space–time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.

  16. An exactly solvable system from quantum optics

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J., E-mail: [J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra (Poland); Przybylska, Maria, E-mail: [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland); Stachowiak, Tomasz, E-mail: [Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw (Poland)


    We investigate a generalisation of the Rabi system in the Bargmann–Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given. - Highlights: • New exactly solvable system from quantum optics is found. • Normalisation condition for system in Bargmann representation is used. • Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.

  17. Exact law of live nature (United States)

    Azbel‧, Mark Ya.


    The exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal-environment interactions (metabolism, etc.) which are a must for life; it is universal for all animals, from single-cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such a law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kinds of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species-specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single-cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.

  18. Renormalization of modular invariant Coulomb gas and sine-Gordon theories, and the quantum Hall flow diagram (United States)

    Carpentier, David


    Using the renormalization group (RG) we study two-dimensional electromagnetic Coulomb gas and extended sine-Gordon theories invariant under the modular group SL(2,icons/Journals/Common/BbbZ" ALT="BbbZ" ALIGN="TOP"/>). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following the proposal for a SL(2,icons/Journals/Common/BbbZ" ALT="BbbZ" ALIGN="TOP"/>) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.

  19. Renormalized dynamics of the Dean-Kawasaki model (United States)

    Bidhoodi, Neeta; Das, Shankar P.


    We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

  20. (Non)-renormalization of the chiral vortical effect coefficient

    Energy Technology Data Exchange (ETDEWEB)

    Golkar, Siavash; Son, Dam T. [Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago,5640 South Ellis Ave., Chicago, IL 60637 (United States)


    We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D, dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula ∑{sub n=1}{sup ∞}n=−1/12. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large N limit.

  1. Renormalization and applications of baryon distribution amplitudes QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger


    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)

  2. Renormalization and applications of baryon distribution amplitudes in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger


    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)

  3. Entanglement renormalization, quantum error correction, and bulk causality

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)


    Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

  4. On the robustness of the primordial power spectrum in renormalized Higgs inflation (United States)

    Bezrukov, Fedor; Pauly, Martin; Rubio, Javier


    We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in critical Higgs inflation scenarios containing a quasi-inflection point along the inflationary trajectory. The interplay of radiative corrections with this quasi-inflection point may translate into a sizable modification of the inflationary observables.

  5. Analytic renormalized bipartite and tripartite quantum discords with quantum phase transition in XXZ spins chain (United States)

    Joya, Wajid; Khan, Salman; Khalid Khan, M.; Alam, Sher


    The behavior of bipartite quantum discord (BQD) and tripartite quantum discord (TQD) in the Heisenberg XXZ spins chain is investigated with the increasing size of the system using the approach of the quantum renormalization group method. Analytical relations for both BQD and TQD are obtained and the results are checked through numerical optimization. In the thermodynamics limit, both types of discord exhibit quantum phase transition (QPT). The boundary of QPT links the phases of saturated discord and zero discord. The first derivative of both discords becomes discontinuous at the critical point, which corresponds to the second-order phase transition. Qualitatively identical, the amount of saturated BQD strongly depends on the relative positions of spins inside a block. TQD can be a better candidate than BQD both for analyzing QPT and implementing quantum information tasks. The scaling behavior in the vicinity of the critical point is discussed.

  6. Exact Solutions in Modified Gravity Models

    Directory of Open Access Journals (Sweden)

    Valery V. Obukhov


    Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.

  7. Two-loop renormalization in the standard model, part I. Prolegomena

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)


    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

  8. Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain. (United States)

    Strečka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L


    The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.

  9. Exact holography of the mass-deformed M2-brane theory

    Energy Technology Data Exchange (ETDEWEB)

    Jang, Dongmin; Kim, Yoonbai; Kwon, O. Kab [Sungkyunkwan University, Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Suwon (Korea, Republic of); Tolla, D.D. [Sungkyunkwan University, Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Suwon (Korea, Republic of); Sungkyunkwan University, University College, Suwon (Korea, Republic of)


    We test the holographic relation between the vacuum expectation values of gauge invariant operators in N = 6 U{sub k}(N) x U{sub -k}(N) mass-deformed ABJM theory and the LLM geometries with Z{sub k} orbifold in 11-dimensional supergravity. To do so, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension Δ = 1, which is given by left angle O{sup (Δ=1)} right angle = N{sup (3)/(2)} f{sub (Δ=1)}, for large N and k = 1. Here the factor f{sub (Δ)} is independent of N. Our results involve an infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a non-trivial test of gauge/gravity duality away from the conformal fixed point. We extend our results to the case of k ≠ 1 for LLM geometries represented by rectangular-shaped Young diagrams. We also discuss the exact mapping of the gauge/gravity at finite N for classical supersymmetric vacuum solutions in field theory side and corresponding classical solutions in gravity side. (orig.)

  10. Quasi exact solution of the Rabi Hamiltonian

    CERN Document Server

    Koç, R; Tuetuencueler, H


    A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

  11. Quantum algorithm for exact Monte Carlo sampling


    Destainville, Nicolas; Georgeot, Bertrand; Giraud, Olivier


    We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact Monte Carlo sampling methods, and yields a polynomial gain compared to classical procedures.

  12. Exact, almost and delayed fault detection

    DEFF Research Database (Denmark)

    Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.


    Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....

  13. New exact wave solutions for Hirota equation

    Indian Academy of Sciences (India)

    ... integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.

  14. Exact results and open questions in first principle functional RG (United States)

    Le Doussal, Pierre


    Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension d) at finite temperature T > 0 are reviewed and reexamined in this much expanded version of Le Doussal (2006) [67]. The particle limit d = 0 provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity ν ˜ T-both being formally irrelevant. An outstanding question in FRG, i.e. how temperature regularizes the otherwise singular flow of T = 0 FRG, maps to the viscous layer regularization of inertial range Burgers turbulence (i.e. to the construction of the inviscid limit). Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. First, multi-loop FRG corrections are examined and the direct loop expansion at T > 0 is shown to fail already in d = 0, a hierarchy of ERG equations being then required (introduced in Balents and Le Doussal (2005) [36]). Next we prove that the FRG function R( u) and higher cumulants defined from the field theory can be obtained for any d from moments of a renormalized potential defined in an sliding harmonic well. This allows to measure the fixed point function R( u) in numerics and experiments. In d = 0 the beta function (of the inviscid limit) is obtained from first principles to four loop. For Sinai model (uncorrelated Burgers initial velocities) the ERG hierarchy can be solved and the exact function R( u) is obtained. Connections to exact solutions for the statistics of shocks in Burgers and to ballistic aggregation are detailed. A relation is established between the size distribution of shocks and the one for droplets. A droplet solution to the ERG functional hierarchy is found for any d, and the form of R( u) in the thermal boundary layer is related to droplet probabilities. These being known for the d = 0 Sinai model the function R( u) is obtained there at any T. Consistency of the ɛ=4-d expansion in one and two loop FRG is studied from first principles, and connected to

  15. Point-particle effective field theory I: classical renormalization and the inverse-square potential (United States)

    Burgess, C. P.; Hayman, Peter; Williams, M.; Zalavári, László


    Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.

  16. The Γ-Limit of the Two-Dimensional Ohta-Kawasaki Energy. Droplet Arrangement via the Renormalized Energy (United States)

    Goldman, Dorian; Muratov, Cyrill B.; Serfaty, Sylvia


    This is the second in a series of papers in which we derive a Γ-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the Γ-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order Γ-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Thus, without appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of Γ-equivalence, the obtained results also yield an expansion of the minimal energy and a characterization of the zero super-level sets of the minimizers for the original Ohta-Kawasaki energy. This leads to the expectation of seeing triangular lattices of droplets as energy minimizers.

  17. Resummation and renormalization in effective theories of particle physics

    CERN Document Server

    Jakovac, Antal


    Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...

  18. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman


    Full Text Available We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a “half-shift”: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  19. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory (United States)

    Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.


    We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  20. Emergent Space-Time via a Geometric Renormalization Method

    CERN Document Server

    Rastgoo, Saeed


    We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...

  1. Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization

    CERN Document Server

    Giudice, Gian Francesco


    We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.

  2. Anomalous contagion and renormalization in networks with nodal mobility (United States)

    Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.


    A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.

  3. Improved quasi parton distribution through Wilson line renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Jiunn-Wei [Department of Physics, Center for Theoretical Sciences, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 106, Taiwan (China); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Ji, Xiangdong [INPAC, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China); Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Zhang, Jian-Hui, E-mail: [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)


    Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a “mass” counterterm in the auxiliary z-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

  4. Renormalized stress-energy tensor for stationary black holes

    CERN Document Server

    Levi, Adam


    We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the $t$-splitting variant of the method, which was first presented for $\\left\\langle\\phi^{2}\\right\\rangle_{ren}$, to compute the RSET in a stationary, asymptotically-flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally-coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.

  5. Holographic Renormalization of general dilaton-axion gravity

    CERN Document Server

    Papadimitriou, Ioannis


    We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.

  6. Momentum-subtraction renormalization techniques in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.


    Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

  7. Assessing notions of denormalization and renormalization of smoking in light of e-cigarette regulation. (United States)

    Sæbø, Gunnar; Scheffels, Janne


    The rationale for 'denormalization' of smoking in tobacco policies has been challenged by the emergence of e-cigarettes and the need to regulate e-cigarette use and promotion. Our aim is to assess the research status on e-cigarettes' contribution to 'renormalization' of smoking and to clarify how renormalization of smoking can be appraised at the conceptual and empirical level. Combining conceptual analysis and narrative review, the paper brings out three dimensions of denormalization/renormalization of smoking ('unacceptability/acceptability'; 'invisibility/visibility'; 'phasing out behaviour/maintaining behaviour') and an inherent duality of the e-cigarette as a smoking-like device and a smoking alternative. These analytical dimensions are applied qualitatively to consider the literature identified by searching the Web of Science database for 'e-cigarettes AND renormalization' (and variants thereof). Theoretically, normative changes in smoking acceptability, increased visibility of e-cigarettes and use, and observations of actual use (prevalence, dual use, gateway) can all be applied to illustrate processes of renormalization. However, only acceptability measures and user measures can be said to be empirical tests of renormalization effects. Visibility measures are only based on logical assumptions of a possible renormalization; they are not in themselves indicative of any "real" renormalization effects and can just as well be understood as possible consequences of normalization of e-cigarettes. Just as a downward trend in smoking prevalence is the litmus test of whether denormalization policy works, stagnating or rising smoking prevalence should be the main empirical indicator of renormalization. Copyright © 2017 Elsevier B.V. All rights reserved.

  8. Renormalization of massive Feynman amplitudes and homogeneity (based on a joint work with Raymond Stora)

    Energy Technology Data Exchange (ETDEWEB)

    Nikolov, Nikolay M., E-mail:


    We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.

  9. Direct Observation of Electrostatically Driven Band Gap Renormalization in a Degenerate Perovskite Transparent Conducting Oxide

    Energy Technology Data Exchange (ETDEWEB)

    Lebens-Higgins, Z.; Scanlon, D. O.; Paik, H.; Sallis, S.; Nie, Y.; Uchida, M.; Quackenbush, N. F.; Wahila, M. J.; Sterbinsky, G. E.; Arena, Dario A.; Woicik, J. C.; Schlom, D. G.; Piper, L. F. J.


    We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO 3 , using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La - BaSnO 3 is driven purely by electrostatic interactions.

  10. Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Hong -Hao [Chongqing Univ., Chongqing (People' s Republic of China); Wu, Xing -Gang [Chongqing Univ., Chongqing (People' s Republic of China); Ma, Yang [Chongqing Univ., Chongqing (People' s Republic of China); Brodsky, Stanley J. [Stanford Univ., Stanford, CA (United States); Mojaza, Matin [KTH Royal Inst. of Technology and Stockholm Univ., Stockholm (Sweden)


    A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R

  11. Exact Tests for Hardy-Weinberg Proportions

    National Research Council Canada - National Science Library

    Engels, William R


    Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments...

  12. Fast Exact Euclidean Distance (FEED) Transformation

    NARCIS (Netherlands)

    Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.


    Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number

  13. Exact Test of Independence Using Mutual Information

    Directory of Open Access Journals (Sweden)

    Shawn D. Pethel


    Full Text Available Using a recently discovered method for producing random symbol sequences with prescribed transition counts, we present an exact null hypothesis significance test (NHST for mutual information between two random variables, the null hypothesis being that the mutual information is zero (i.e., independence. The exact tests reported in the literature assume that data samples for each variable are sequentially independent and identically distributed (iid. In general, time series data have dependencies (Markov structure that violate this condition. The algorithm given in this paper is the first exact significance test of mutual information that takes into account the Markov structure. When the Markov order is not known or indefinite, an exact test is used to determine an effective Markov order.

  14. Exact Algorithms for Solving Stochastic Games

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels


    Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

  15. Renormalization in the cauchy problem for the Korteweg-de Vries equation (United States)

    Zakharov, S. V.


    We consider the Cauchy problem for the Korteweg-de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. We construct an asymptotic solution of this problem by the renormalization method.

  16. Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation


    Zakharov, Sergei V.


    The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.

  17. Renormalizations in softly broken N = 1 theories: Slavnov-Taylor identities (United States)

    Kondrashuk, Igor


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N = 1 SYM. The result is in accordance with the previous results obtained at the level of the supergraph technique.

  18. Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities


    Kondrashuk, Igor


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N=1 SYM. The result is in accordance with the previous results obtained at the level of supergraph technique.

  19. Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities

    Energy Technology Data Exchange (ETDEWEB)

    Kondrashuk, Igor [SISSA-ISAS and INFN, Sezione di Trieste, Trieste (Italy)]. E-mail:


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N=1 SYM. The result is in accordance with the previous results obtained at the level of the supergraph technique. (author)

  20. Renormalization of domain-wall bilinear operators with short-distance current correlators (United States)

    Tomii, M.; Cossu, G.; Fahy, B.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Noaki, J.; Jlqcd Collaboration


    We determine the renormalization constants for flavor nonsinglet fermion bilinear operators of Möbius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the nonperturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to O (αs4). We employ 2 +1 -flavor lattice ensembles at three lattice spacings in the range 0.044-0.080 fm.

  1. All-order renormalization of propagator matrix for fermionic system with flavor mixing

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics


    We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

  2. Landscape of the exact energy functional

    CERN Document Server

    Cohen, Aron J


    One of the great challenges of electronic structure theory is the search for the exact functional of density functional theory (DFT). Its existence is undoubted but it is hard to even conceptualize it as it is a surface in a massively multidimensional space. However, the asymmetric two-site Hubbard model has a two-dimensional universe of density matrices and the exact functional simply becomes a function of two variables whose landscape can be calculated, visualized and explored. This one unique surface contains all the possible physics of any system in this universe. A walk on this landscape, moved to the angle of any one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. We show concrete examples of pure-state density matrices that are not v-representable due to the underlying non-convex nature of the exact functional. Using the Perdew, Parr, Levy and Balduz extension to fractional ensembles we calculate the exact functional for all numbers of electrons. The derivative discontinui...

  3. Planar quantum quenches: Computation of exact time-dependent correlation functions at large $N$

    CERN Document Server

    Cubero, Axel Cortés


    We study a quantum quench of an integrable quantum field theory in the planar infinite-$N$ limit. Unlike isovector-valued $O(N)$ models, matrix-valued field theories in the infinite-$N$ limit are not solvable by the Hartre-Fock approximation, and are nontrivial interacting theories. We study quenches with initial states that are color-charge neutral, correspond to integrability-preserving boundary conditions, and that lead to nontrivial correlation functions of operators. We compute exactly at infinite $N$, the time-dependent one- and two-point correlation functions of the energy-momentum tensor and renormalized field operator after this quench using known exact form factors. This computation can be done fully analytically, due the simplicity of the initial state and the form factors in the planar limit. We also show that this type of quench preserves factorizability at all times, allows for particle transmission from the pre-quench state, while still having nontrivial interacting post-quench dynamics.

  4. Exactly Embedded Wavefunction Methods for Characterizing Nitrogen Reduction Catalysis (United States)


    SUBTITLE Exactly Embedded Wavefunction Methods for Characterizing Nitrogen Reduction Catalysis 5a. CONTRACT NUMBER N/A 5b. GRANT NUMBER FA9550... catalysis , such as hydrogen and nitrogen reduction. In a significant methodological advance from the past year, we developed an accurate and...1-0288), the Miller group developed new electronic structure embedding methods for the investigation of small- molecular activation catalysis , such as

  5. A Visual Basic Software for Computing Fisher's Exact Probability


    Haseeb Ahmad Khan


    Fisher's exact test (FET) is an important statistical method for testing association between two groups. However, the computations involved in FET are extremely tedious and time consuming due to multi-step factorial calculations after the construction of numerous 2x2 tables depending on the smallest cell value. A Visual-Basic computer program, CalcFisher, has been developed to handle the complexities of FET resorting the techniques of looping subroutines and logarithmic conversions. The softw...

  6. Exact solutions in three-dimensional gravity

    CERN Document Server

    Garcia-Diaz, Alberto A


    A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

  7. Exact and approximate calculation of giant resonances

    Energy Technology Data Exchange (ETDEWEB)

    Vertse, T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Liotta, R.J. [Royal Inst. of Tech., Stockholm (Sweden); Maglione, E. [Padua Univ. (Italy). Ist. di Fisica


    Energies, sum rules and partial decay widths of giant resonances in {sup 208}Pb are calculated solving exactly the continuum RPA equations corresponding to a central Woods-Saxon potential. For comparison an approximate treatment of those quantities in terms of pole expansions of the Green function (Berggren and Mittag-Leffler) is also performed. It is found that the approximated results agree well with the exact ones. Comparison with experimental data is made and a search for physically meaningful resonances is carried out. ((orig.))

  8. Exact Asymptotics of Bivariate Scale Mixture Distributions


    Hashorva, Enkelejd


    Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour ...

  9. Exact tensor hypercontraction: a universal technique for the resolution of matrix elements of local finite-range N-body potentials in many-body quantum problems. (United States)

    Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J


    Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.

  10. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    Energy Technology Data Exchange (ETDEWEB)

    Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)


    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  11. Verbal Interference Suppresses Exact Numerical Representation (United States)

    Frank, Michael C.; Fedorenko, Evelina; Lai, Peter; Saxe, Rebecca; Gibson, Edward


    Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Piraha (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching…

  12. Python for Education: The Exact Cover Problem

    Directory of Open Access Journals (Sweden)


    Full Text Available

    Python implementation of Algorithm X by Knuth is presented.
    Algorithm X finds all solutions to the exact cover problem.
    The exemplary results for pentominoes, Latin squares and Sudoku
    are given.

  13. On exact solutions of the Bogoyavlenskii equation

    Indian Academy of Sciences (India)

    Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...

  14. Compiling Relational Bayesian Networks for Exact Inference

    DEFF Research Database (Denmark)

    Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan


    We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and ...

  15. Exact Optimum Design of Segmented Thermoelectric Generators

    Directory of Open Access Journals (Sweden)

    M. Zare


    Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.

  16. Exact solutions for the biadjoint scalar field

    Energy Technology Data Exchange (ETDEWEB)

    White, C.D., E-mail: [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland (United Kingdom); Centre for Research in String Theory, Queen Mary University of London, London E1 4NS (United Kingdom)


    Biadjoint scalar theories are novel field theories that arise in the study of non-abelian gauge and gravity amplitudes. In this short paper, we present exact nonperturbative solutions of the field equations, and compare their properties with monopole-like solutions in non-abelian gauge theory. Our results may pave the way for nonperturbative studies of the double copy.

  17. New exact wave solutions for Hirota equation

    Indian Academy of Sciences (India)

    Nonlinear partial differential equations (NPDEs) of mathematical physics are major sub- jects in physical science. With the development of soliton theory, many useful methods for obtaining exact solutions of NPDEs have been presented. Some of them are: the (G /G)- expansion method [1–4], the simplest equation method ...

  18. Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD (United States)

    Głazek, Stanisław D.; Gómez-Rocha, María; More, Jai; Serafin, Kamil


    In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.

  19. Scaling symmetry, renormalization, and time series modeling: the case of financial assets dynamics. (United States)

    Zamparo, Marco; Baldovin, Fulvio; Caraglio, Michele; Stella, Attilio L


    We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

  20. One-loop renormalization of the NMSSM in SloopS. II. The Higgs sector (United States)

    Bélanger, G.; Bizouard, V.; Boudjema, F.; Chalons, G.


    We present a full one-loop renormalization of the Higgs sector of the next-to-minimal-supersymmetric-Standard-Model (NMSSM) and its implementation within sloops, a code for the automated computations of one-loop processes in theories beyond the Standard Model. The present work is the sequel to the study we performed on the renormalization of the sectors of the NMSSM comprising neutralinos, charginos, and sfermions, thereby completing the full one-loop renormalization of the NMSSM. We have investigated several renormalization schemes based on alternative choices (on-shell or DR ¯ ) of the physical parameters. Special attention is paid to the issue of the mixing between physical fields. To weigh the impact of the different renormalization schemes, the partial widths for the decays of the Higgs bosons into supersymmetric particles are computed at one loop. In many decays large differences between the schemes are found. We discuss the origin of these differences. In particular, we study two contrasting scenarios. The first model is MSSM-like with a small value for the mixing between the doublet and singlet Higgs superfields while the second model has a moderate value for this mixing. We critically discuss the issue of the reconstruction of the underlying parameters and their counterterms in the case of a theory with a large number of parameters, such as the NMSSM, from a set of physical parameters. In the present study this set corresponds to the minimum set of masses for the implementation of the on-shell schemes.

  1. Model checking exact cost for attack scenarios

    DEFF Research Database (Denmark)

    Aslanyan, Zaruhi; Nielson, Flemming


    Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....

  2. Exact solution to fractional logistic equation (United States)

    West, Bruce J.


    The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.

  3. The maximal family of exactly solvable chaos

    CERN Document Server

    Umeno, K


    A new two-parameter family of ergordic transformations with non-uniform invariant measures on the unit interval (I=[0,1]) is found here. The family has a special property that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is also proven here that this family is the most generalized class of exactly solvable chaos on (I) including the Ulam=Neumann map (y=4x(1-x)). Unpredictably, by choosing certain parameters, the maximal class of exactly solvable chaos is found to describe the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction.

  4. Exact Relativistic Magnetized Haloes around Rotating Disks

    Directory of Open Access Journals (Sweden)

    Antonio C. Gutiérrez-Piñeres


    Full Text Available The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.

  5. Exact solutions for helical magnetohydrodynamic equilibria

    Energy Technology Data Exchange (ETDEWEB)

    Villata, M. (Istituto di Fisica Generale, Universita di Torino, Via Pietro Giuria 1, I-10125 Torino (Italy)); Tsinganos, K. (Department of Physics, University of Crete and Research Center of Crete, GR-71409, Heraklion, Crete (Greece))


    Three novel classes of exact solutions of the generalized Grad--Shafranov equation for helically symmetric magnetohydrodynamic (MHD) equilibria are presented. The first two classes may be applied to helical MHD equilibria for plasma confined between two coaxial cylinders, while the third one to the modeling of helicoidal magnetic fields and flows in several recently observed astrophysical jets. The same solutions can be also used for the testing of sophisticated numerical codes. It is also shown that all helically symmetric MHD equilibria can be treated by the same general method which is employed to generate exact MHD solutions for systems possessing an ignorable coordinate in a system of three orthogonal basis vectors, although in the case of helical symmetry an [ital orthogonal] ignorable coordinate does not exist, contrary to what happens in the well-known cases of axial and translational symmetries.

  6. Exact geodesic distances in FLRW spacetimes (United States)

    Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri


    Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

  7. Introduction to Hubbard model and exact diagonalization

    Directory of Open Access Journals (Sweden)

    S. Akbar Jafari


    Full Text Available  Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.

  8. Introduction to Hubbard model and exact diagonalization


    S. Akbar Jafari


     Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.

  9. Vaidya-like exact solutions with torsion

    CERN Document Server

    Blagojević, M


    Starting from the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend massive gravity, a new class of the Vaidya-like exact solutions with torsion is constructed in the three-dimensional Poincar\\'e gauge theory. A particular subclass of these solutions is shown to possess the asymptotic conformal symmetry. The related canonical energy contains a contribution stemming from torsion.

  10. New exact cosmologies on the brane (United States)

    Astashenok, Artyom V.; Yurov, Artyom V.; Chervon, Sergey V.; Shabanov, Evgeniy V.; Sami, Mohammad


    We develop a method for constructing exact cosmological solutions in brane world cosmology. New classes of cosmological solutions on Randall-Sandrum brane are obtained. The superpotential and Hubble parameter are represented in quadratures. These solutions have inflationary phases under general assumptions and also describe an exit from the inflationary phase without a fine tuning of the parameters. Another class solutions can describe the current phase of accelerated expansion with or without possible exit from it.

  11. Testing the renormalisation group theory of cooperative transitions at the lambda point of helium (United States)

    Lipa, J. A.; Li, Q.; Chui, T. C. P.; Marek, D.


    The status of high resolution tests of the renormalization group theory of cooperative phase transitions performed near the lambda point of helium is described. The prospects for performing improved tests in space are discussed.

  12. Exact tests for Hardy-Weinberg proportions. (United States)

    Engels, William R


    Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common chi(2)-test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided.

  13. Exact Eigenfunctions of a Chaotic System

    CERN Document Server

    Ausländer, O M


    The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic contin...

  14. On the exactness of soft theorems (United States)

    Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao


    Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.

  15. Carrier plasmon induced nonlinear band gap renormalization in two-dimensional semiconductors. (United States)

    Liang, Yufeng; Yang, Li


    In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. However, the physical origin of this generic effect remains obscure. We develop a new plasmon-pole theory that efficiently and accurately captures this coupling. Using monolayer MoS(2) and MoSe(2) as prototype two-dimensional (2D) semiconductors, we reveal a striking band gap renormalization above 400 meV and an unusual nonlinear evolution of their band gaps with doping. This prediction significantly differs from the linear behavior that is observed in one-dimensional structures. Notably, our predicted band gap renormalization for MoSe(2) is in excellent agreement with recent experimental results. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques.

  16. A Non-Renormalization Theorem in Gapped Quantum Field Theory


    Shacham, Tomer


    We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does no...

  17. A non-renormalization theorem in gapped quantum field theory (United States)

    Shacham, Tomer


    We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that at zero momentum, the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does not receive quantum corrections.

  18. Renormalized molecular levels in a Sc3N@C-80 molecular electronic device

    DEFF Research Database (Denmark)

    Larade, Brian; Taylor, Jeremy Philip; Zheng, Q. R.


    We address several general questions about quantum transport through molecular systems by an ab initio analysis of a scandium-nitrogen doped C-80 metallofullerene device. Charge transfer from the Sc3N is found to drastically change the current-voltage characteristics: the current through the Sc3N...... @ C-80 device is double that through a bare C-80 device. We provide strong evidence that transport in such molecular devices is mediated by molecular electronic states which have been renormalized by the device environment, such as the electrodes and external bias V-b. The renormalized molecular...

  19. Renormalization constants of the lattice energy momentum tensor using the gradient flow

    CERN Document Server

    Capponi, Francesco; Patella, Agostino; Rago, Antonio


    We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results.

  20. Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases (United States)

    Monthus, Cécile


    When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.

  1. Renormalization of gauge theories in the background-field approach arXiv

    CERN Document Server

    Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.

    Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. In other words, the renormalization procedure for these gauge theories is compatible with their gauge invariance. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. We illustrate our general approach with several explicit examples.

  2. TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study. (United States)

    Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus


    The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients - using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact - at 94.5% and SLING-IUFT - at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness.

  3. Exact formation of hairy planar black holes


    Fan, Zhong-Ying; Chen, Bin


    We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to AdS space-times. In particular, for a special case $\\mu=(n-2)/2$, we obtain new classes of exact dynamical solutions describing black holes formation. We find there are two classes of collapse solutions. The first class solutions describe the evolution start from AdS space-time with a naked singularity...

  4. Compiling Relational Bayesian Networks for Exact Inference

    DEFF Research Database (Denmark)

    Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark


    We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...

  5. Why one needs a functional renormalization group to survive in a ...

    Indian Academy of Sciences (India)

    We choose the disorder at the microscopic scale to be Gaussian, with correlations. V (x, u)V (x ,u ) := δd(x − x ) ... dimensional reduction implies that the disorder-averaged 2-point function at zero temperature is ..... [20] S Scheidl, Private communication about 2-loop calculations for the random manifold problem (2000–2004).

  6. Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation (United States)

    Ahn, Kyung H.


    The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

  7. Renormalization group and instantons in stochastic nonlinear dynamics, from self-organized criticality to thermonuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Volchenkov, D. [Bielefeld Univ., Center of Excellence Cognitive Interaction Technology (CITEC) (Germany)


    Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)

  8. Sigma model renormalization group flow, ``central charge'' action, and Perelman's entropy (United States)

    Tseytlin, A. A.


    Zamolodchikov’s c-theorem type argument (and also string theory effective action constructions) imply that the RG flow in 2d sigma model should be a gradient one to all loop orders. However, the monotonicity of the flow of the target-space metric is not obvious since the metric on the space of metric-dilaton couplings is indefinite. To leading (one-loop) order when the RG flow is simply the Ricci flow the monotonicity was proved by Perelman [G. Perelman, math.dg/0211159.] by constructing an “entropy” functional which is essentially the metric-dilaton action extremized with respect to the dilaton with a condition that the target-space volume is fixed. We discuss how to generalize the Perelman’s construction to all loop orders (i.e. all orders in α'). The resulting entropy is equal to minus the central charge at the fixed points, in agreement with the general claim of the c-theorem.

  9. Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization

    Energy Technology Data Exchange (ETDEWEB)

    Ohta, Nobuyoshi [Kinki University, Department of Physics, Higashi-Osaka, Osaka (Japan); Percacci, Roberto [International School for Advanced Studies, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Vacca, Gian Paolo [INFN, Sezione di Bologna, Bologna (Italy)


    We employ the exponential parametrization of the metric and a ''physical'' gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. (orig.)

  10. Conserved Quantities And Renormalization Group Flows In Two-dimensional Field Theory

    CERN Document Server

    Gerganov, B E


    Several problems in two-dimensional field theory are investigated. The concepts of classical and quantum integrability in two space-time dimensions are presented in the Introduction and a number of algebraic structures associated with integrable systems are described. Some results of conformal field theory (CFT) and perturbed conformal field theory are reviewed. In Chapter 2, the problem of interaction of two-level atoms in fibrillar geometry with electro-magnetic radiation is studied in perturbation theory. A new formalism is developed, representing the atomic spin operators with elementary fermions, and a resemblance between the structures of this model and quantum electrodynamics is established. Although the system studied is not itself integrable, it can be shown that the integrable quantum sine-Gordon model has some validity as an approximate theory. The following two chapters study the properties of several multi-field generalizations of the sine-Gordon model. The Bukhvostov-Lipatov model is studied in ...

  11. Development of a Renormalization Group Approach to Multi-Scale Plasma Physics Computation (United States)


    δ /∇ = / + − (1) in which 0ε is the permittivity of free space. We wish to derive the Debye length λ and its dependence on fluctuations ξ in...ϕ is the electrostatic potential. Also q and m are the electron charge and mass and 0ε is the free space electrical permittivity . The boundary...existing relationship with General Electric and Nissan. One potential method to enhance diesel engines is “vortex” or turbulent mixing of the fuel and

  12. Renormalization-group analysis of the cosmological constraint on the Higgs scalar mass

    NARCIS (Netherlands)

    Kiselev, V. V.; Timofeev, S. A.

    The standard Model Higgs scalar boson minimally coupled to gravity does not take part in the inflation of the early universe if its mass exceeds a threshold value, which is m (H) (min) = 142 GeV in the tree approximation for the potential of the scalar. Two-loop corrections modify this estimate,

  13. Experimental test of renormalization group theory on the uniaxial, dipolar coupled ferromagnet LiTbf4

    DEFF Research Database (Denmark)

    Als-Nielsen, Jens Aage


    The transverse correlation range ξ and the susceptibility in the critical region has been measured by neutron scattering. A special technique required to resolve the superdiverging longitudinal correlation range has been utilized. The results for ξ together with existing specific-heat data are in...

  14. Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram

    DEFF Research Database (Denmark)

    Codello, Alessandro; Tonero, Alberto


    We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2-scalar theories. The idea is to perform the path integral by weighting...

  15. Application of the algebraic RNG model for transition simulation. [renormalization group theory (United States)

    Lund, Thomas S.


    The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.

  16. Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence

    CERN Document Server

    Jenkins, Elizabeth E; Trott, Michael


    We calculate the order \\lambda, \\lambda^2 and \\lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \\lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.

  17. Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories

    Directory of Open Access Journals (Sweden)

    John Cardy


    Full Text Available We propose using smeared boundary states $e^{-\\tau H}|\\cal B\\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.

  18. Critical phenomena with renormalization group analysis of a hierarchical model of financial crashes


    Wu, Tiankuang Tim


    Financial market models are able to help the investors foresee the risk of a financial market crash and reduce the probability of its occurrence. Modelling in financial markets is categorized into microscopic models and macroscopic models. The microscopic models study the mechanisms behind the market and their behaviour. These models assist in an understanding of the causes of financial market crashes. Macroscopic models find the disciplines and rules from the historical macroscopic data for ...

  19. Conformal invariance and new exact solutions of the elastostatics equations (United States)

    Chirkunov, Yu. A.


    We fulfilled a group foliation of the system of n-dimensional (n ≥ 2) Lame equations of the classical static theory of elasticity with respect to the infinite subgroup contained in normal subgroup of main group of this system. It permitted us to move from the Lame equations to the equivalent unification of two first-order systems: automorphic and resolving. We obtained a general solution of the automorphic system. This solution is an n-dimensional analogue of the Kolosov-Muskhelishvili formula. We found the main Lie group of transformations of the resolving system of this group foliation. It turned out that in the two-dimensional and three-dimensional cases, which have a physical meaning, this system is conformally invariant, while the Lame equations admit only a group of similarities of the Euclidean space. This is a big success, since in the method of group foliation, resolving equations usually inherit Lie symmetries subgroup of the full symmetry group that was not used for the foliation. In the three-dimensional case for the solutions of the resolving system, we found the general form of the transformations similar to the Kelvin transformation. These transformations are the consequence of the conformal invariance of the resolving system. In the three-dimensional case with a help of the complex dependent and independent variables, the resolving system is written as a simple complex system. This allowed us to find non-trivial exact solutions of the Lame equations, which direct for the Lame equations practically impossible to obtain. For this complex system, all the essentially distinct invariant solutions of the maximal rank we have found in explicit form, or we reduced the finding of those solutions to the solving of the classical one-dimensional equations of the mathematical physics: the heat equation, the telegraph equation, the Tricomi equation, the generalized Darboux equation, and other equations. For the resolving system, we obtained double wave of a

  20. Entanglement and relaxation in exactly solvable models (United States)

    Lychkovskiy, O.


    A system put in contact with a large heat bath normally thermalizes. This means that the state of the system ρℐ( t) approaches an equilibrium state ρ{eq/ℐ}, the latter depending only on macroscopic characteristics of the bath (e.g. temperature), but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present contribution we discuss the recently proven general theorems about thermalization and demonstrate how they work in exactly solvable models. In particular, we review a necessary condition for the system initial state independence (ISI) of ρ{eq/ℐ}, which was proven in our previous work, and apply it for two exactly solvable models, the XX spin chain and a central spin model with a special interaction with the environment. In the latter case we are able to prove the absence of the system ISI. Also the Eigenstate Thermalization Hypothesis is discussed. It is pointed out that although it is supposed to be generically true in essentially not-integrable ( chaotic) quantum systems, it is how-ever also valid in the integrable XX model.

  1. Exact Solution for a Gravitational Wave Detector (United States)

    Rabounski, Dmitri; Borissova, Larissa


    The experimental statement on gravitational waves proceeds from the equation for deviating geodesic lines and the equation for deviating non-geodesics. Weber's result was not based upon an exact solution to the equations, but on an approximate analysis of what could be expected: he expected that a plane weak wave of the space metric may displace two resting particles with respect to each other. In this work, exact solutions are presented for the deviation equation of both free and spring-connected particles. The solutions show that a gravitational wave may displace particles in a two-particle system only if they are in motion with respect to each other or the local space (there is no effect if they are at rest). Thus, gravitational waves produce a parametric effect on a two-particle system. According to the solutions, an altered detector construction can be proposed such that it might interact with gravitational waves: 1) a horizontally suspended cylindrical pig, whose butt-ends have basic relative oscillations induced by a laboratory source; 2) a free-mass detector where suspended mirrors have laboratory induced basic oscillations relative to each other.

  2. Electron-Phonon Renormalization of Electronic Band Structures of C Allotropes and BN Polymorphs (United States)

    Tutchton, Roxanne M.; Marchbanks, Christopher; Wu, Zhigang

    The effect of lattice vibration on electronic band structures has been mostly neglected in first-principles calculations because the electron-phonon (e-ph) renormalization of quasi-particle energies is often small (Career Award (Grant No. DE-SC0006433). Computations were carried out at the Golden Energy Computing Organization at CSM and the National Energy Research Scientific Computing Center (NERSC).

  3. Phase behavior of charged colloids : many-body effects, charge renormalization and charge regulation

    NARCIS (Netherlands)

    Zoetekouw, Bastiaan


    The main topic of this thesis is Poisson–Boltzmann theory for suspensions of charged colloids in two of its approximations: cell-type approximations that explicitly take into account non-linear effects near the colloidal surfaces, such as charge renormalization, at the expense of neglecting any

  4. Setting the renormalization scale in QCD: The principle of maximum conformality

    DEFF Research Database (Denmark)

    Brodsky, S. J.; Di Giustino, L.


    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali...

  5. One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances

    Energy Technology Data Exchange (ETDEWEB)

    Rosell, Ignasi [Departament de FIsica Teorica, IFIC, CSIC - Universitat de Valencia, Edifici d' Instituts de Paterna, Apt. Correus 22085, E-46071 Valencia (Spain); Ruiz-FemenIa, Pedro [Theory Division, Max-Planck-Institut fuer Physik, Foehringer Ring 6, D-80805 Munich (Germany); Portoles, Jorge [Departament de FIsica Teorica, IFIC, CSIC - Universitat de Valencia, Edifici d' Instituts de Paterna, Apt. Correus 22085, E-46071 Valencia (Spain)


    We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its {beta}-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite.

  6. Existence of Renormalized Solutions for p(x-Parabolic Equation with three unbounded nonlinearities

    Directory of Open Access Journals (Sweden)

    Youssef Akdim


    Full Text Available In this article, we study the existence of renormalized solution for the nonlinear $p(x$-parabolic problem of the form:\\\\ $\\begin{cases} \\frac{\\partial b(x,u}{\\partial t} - div (a(x,t,u,\

  7. Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence

    NARCIS (Netherlands)

    Haro, S. de; Skenderis, K.; Solodukhin, S.N.


    We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity actionin a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We

  8. Conservation laws and exact solutions for nonlinear diffusion in anisotropic media (United States)

    Avdonina, Elena D.; Ibragimov, Nail H.


    Conservation laws and exact solutions of nonlinear differential equations describing diffusion phenomena in anisotropic media with external sources are constructed. The construction is based on the method of nonlinear self-adjointness. Numerous exact solutions are obtained by using the recent method of conservation laws. These solutions are different from group invariant solutions and can be useful for investigating diffusion phenomena in complex media, e.g. in oil industry.

  9. Interference-exact radiative transfer equation

    DEFF Research Database (Denmark)

    Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani


    Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices.......The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators. Fully describing the optical absorption, emission, and interference of light hence conventionally requires combining the full...

  10. Exact eigenfunctions and the open topological string (United States)

    Mariño, Marcos; Zakany, Szabolcs


    Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions. In this paper, we first develop methods in spectral theory to compute these eigenfunctions. We also provide an integral matrix representation which allows them to be studied in a ’t Hooft limit, where they are described by standard topological open string amplitudes. Based on these results, we propose a conjecture for the exact eigenfunctions, which involves both the WKB wavefunction and the standard topological string wavefunction. This conjecture can be made completely explicit in the maximally supersymmetric, or self-dual case, which we work out in detail for local \

  11. Exact and Efficient Sampling of Conditioned Walks (United States)

    Adorisio, Matteo; Pezzotta, Alberto; de Mulatier, Clélia; Micheletti, Cristian; Celani, Antonio


    A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.

  12. FLAG: Exact Fourier-Laguerre transform on the ball (United States)

    Leistedt, Boris; McEwen, Jason


    FLAG is a fast implementation of the Fourier-Laguerre Transform, a novel 3D transform exploiting an exact quadrature rule of the ball to construct an exact harmonic transform in 3D spherical coordinates. The angular part of the Fourier-Laguerre transform uses the MW sampling theorem and the exact spherical harmonic transform implemented in the SSHT code. The radial sampling scheme arises from an exact quadrature of the radial half-line using damped Laguerre polynomials. The radial transform can in fact be used to compute the spherical Bessel transform exactly, and the Fourier-Laguerre transform is thus closely related to the Fourier-Bessel transform.

  13. Exact Fit of Simple Finite Mixture Models

    Directory of Open Access Journals (Sweden)

    Dirk Tasche


    Full Text Available How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.

  14. STELLAR: fast and exact local alignments

    Directory of Open Access Journals (Sweden)

    Weese David


    Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at The source code is freely distributed with the SeqAn C++ library version 1.3 and later at

  15. Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

    Directory of Open Access Journals (Sweden)

    Hongwei Yang


    Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

  16. Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality. (United States)

    Andreev, Oleg


    We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.

  17. Exact Hypothesis Tests for Log-linear Models with exactLoglinTest

    Directory of Open Access Journals (Sweden)

    Brian Caffo


    Full Text Available This manuscript overviews exact testing of goodness of fit for log-linear models using the R package exactLoglinTest. This package evaluates model fit for Poisson log-linear models by conditioning on minimal sufficient statistics to remove nuisance parameters. A Monte Carlo algorithm is proposed to estimate P values from the resulting conditional distribution. In particular, this package implements a sequentially rounded normal approximation and importance sampling to approximate probabilities from the conditional distribution. Usually, this results in a high percentage of valid samples. However, in instances where this is not the case, a Metropolis Hastings algorithm can be implemented that makes more localized jumps within the reference set. The manuscript details how some conditional tests for binomial logit models can also be viewed as conditional Poisson log-linear models and hence can be performed via exactLoglinTest. A diverse battery of examples is considered to highlight use, features and extensions of the software. Notably, potential extensions to evaluating disclosure risk are also considered.

  18. Material and Doping Dependence of the Nodal and Anti-Nodal Dispersion Renormalizations in Single- and Multi-Layer Cuprates

    Energy Technology Data Exchange (ETDEWEB)

    Johnston, S.; /Waterloo U. /SLAC; Lee, W.S.; /Stanford U., Geballe Lab. /SLAC; Nowadnick, E.A.; /SLAC /Stanford U., Phys. Dept.; Moritz, B.; /SLAC /North Dakota U.; Shen, Z.-X.; /Stanford U., Geballe Lab. /SLAC /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.; Devereaux, T.P.; /Stanford U., Geballe Lab. /SLAC


    In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of CuO{sub 2} layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.

  19. Exactly solvable models for symmetry-enriched topological phases (United States)

    Cheng, Meng; Gu, Zheng-Cheng; Jiang, Shenghan; Qi, Yang


    We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary transformations. We argue that for onsite unitary symmetries, our construction realizes all SETs free of anomaly, as long as the underlying topological order itself can be realized with a commuting-projector Hamiltonian. We further extend the construction to antiunitary symmetries (e.g., time-reversal symmetry), mirror-reflection symmetries, and to anomalous SETs on the surface of three-dimensional symmetry-protected topological phases. Mathematically, our construction naturally leads to a generalization of group extensions of unitary fusion categories to antiunitary symmetries.

  20. Magnetism in atomically thin quasi two-dimensional materials: Renormalized spin wave theory (United States)

    Li, Zhenglu; Cao, Ting; Louie, Steven G.

    In this work, we apply renormalized spin wave theory to the magnetic behavior of atomically thin two-dimensional crystals. We find that magnon-magnon interaction plays an important role in renormalizing the magnetic transition temperature, and the magnetic behavior is largely dependent on the magnetic anisotropy and the thickness of the crystal in the two-dimensional limit. Our method is applicable to general magnetic crystals with input spin interaction parameters mapped out from either ab initio calculations or extracted from experiments. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, and by the National Science Foundation. Computational resources have been provided by NERSC and XSEDE.

  1. Flexoelectricity and thermal fluctuations of lipid bilayer membranes: Renormalization of flexoelectric, dielectric, and elastic properties (United States)

    Liu, L. P.; Sharma, P.


    Thermal fluctuations renormalize the bending elasticity of lipid bilayers. This well-studied effect is a cornerstone in the study of several membrane biophysical phenomena. Analogously, nearly all membranes are endowed with an electromechanical coupling called flexoelectricity that admits membrane polarization due to curvature changes. Flexoelectricity is found to be important in a number of biological functions, including hearing, ion transport, and in some situations where mechanotransduction is necessary. Very little is known about the interplay between thermal fluctuations and flexoelectricity. In this work, we explore how the apparent flexoelectricity is altered due to thermal fluctuations and, further, how the elastic and dielectric properties are renormalized due to flexoelectricity. We find that the apparent bending rigidity is softened by flexoelectricity and discuss the ramifications for interpreting existing experimental work.

  2. Noise spectrum of quantum transport through double quantum dots: Renormalization and non-Markovian effects

    Directory of Open Access Journals (Sweden)

    Pengqin Shi


    Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.

  3. Energy Renormalization for Coarse-Graining the Dynamics of a Model Glass-Forming Liquid. (United States)

    Xia, Wenjie; Song, Jake; Hansoge, Nitin K; Phelan, Frederick R; Keten, Sinan; Douglas, Jack F


    Coarse-grained modeling achieves the enhanced computational efficiency required to model glass-forming materials by integrating out "unessential" molecular degrees of freedom, but no effective temperature transferable coarse-graining method currently exists to capture dynamics. We address this fundamental problem through an energy-renormalization scheme, in conjunction with the localization model of relaxation relating the Debye-Waller factor ⟨u 2 ⟩ to the structural relaxation time τ. Taking ortho-terphenyl as a model small-molecule glass-forming liquid, we show that preserving ⟨u 2 ⟩ (at picosecond time scale) under coarse-graining by renormalizing the cohesive interaction strength allows for quantitative prediction of both short- and long-time dynamics covering the entire temperature range of glass formation. Our findings provide physical insights into the dynamics of cooled liquids and make progress for building temperature-transferable coarse-grained models that predict key properties of glass-forming materials.

  4. Renormalization effects and phonon density of states in high temperature superconductors

    Directory of Open Access Journals (Sweden)

    Vinod Ashokan


    Full Text Available Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS and agreements with experimental observations.

  5. On the perturbative renormalization of four-quark operators for new physics

    Energy Technology Data Exchange (ETDEWEB)

    Papinutto, M. [Roma Univ. (Italy). Dipt. di Fisica; INFN, Sezione di Roma (Italy); Pena, C. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Preti, D. [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC


    We discuss the renormalization properties of the full set of ΔF = 2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schroedinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all ΔF = 1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard MS and RI-MOM schemes. Large truncation effects are found for some of the operators considered. (orig.)

  6. On the perturbative renormalization of four-quark operators for new physics (United States)

    Papinutto, M.; Pena, C.; Preti, D.


    We discuss the renormalization properties of the full set of Δ F=2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schrödinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all Δ F=1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard {\\overline{MS}} and RI-MOM schemes. Large truncation effects are found for some of the operators considered.

  7. A renormalization approach to describe charge transport in quasiperiodic dangling backbone ladder (DBL)-DNA molecules

    Energy Technology Data Exchange (ETDEWEB)

    Sarmento, R.G. [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Fulco, U.L. [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Albuquerque, E.L., E-mail: [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Caetano, E.W.S. [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara, 60040-531 Fortaleza, CE (Brazil); Freire, V.N. [Departamento de Fisica, Universidade Federal do Ceara, 60455-760 Fortaleza, CE (Brazil)


    Highlights: → One-step renormalization approach to describe the DBL-DNA molecule. → Electronic tight-binding Hamiltonian model. → A quasiperiodic sequence to mimic the DNA nucleotides arrangement. → Electronic transmission spectra. → I-V characteristics. -- Abstract: We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.

  8. Terahertz Measurement Of The Quasiparticle Mass Renormalization In Lead And Chromium

    CERN Document Server

    Gilmore, M A


    We study the optical conductivity of lead and chromium as a function of frequency and temperature using terahertz time-domain spectroscopy (THz-TDS). The optical conductivity is interpreted in terms of the extended Drude model (EDM), where the optical scattering rate and renormalized mass of the carriers take on frequency as well as temperature dependence. Within the EDM framework, the theory of electron-phonon scattering yields expressions for the optical scattering rate and mass enhancement, dependent upon the transport-weighted Eliashberg spectral function. This thesis presents THz- TDS measurements of thin films of Pb and Cr. We compare results for the optical scattering rate and quasiparticle mass renormalization to theory and find a strong agreement.

  9. Exact sampling hardness of Ising spin models (United States)

    Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.


    We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

  10. A non-renormalization theorem for chiral primary 3-point functions

    CERN Document Server

    Baggio, Marco; Papadodimas, Kyriakos


    In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.

  11. A renormalization operator for 1D maps under quasi-periodic perturbations (United States)

    Jorba, À.; Rabassa, P.; Tatjer, J. C.


    This paper concerns the reducibility loss of (periodic) invariant curves of quasi-periodically forced one-dimensional maps and its relationship with the renormalization operator. Let gα be a one-parametric family of one-dimensional maps with a cascade of period doubling bifurcations. Between each of these bifurcations, there exists a parameter value αn such that gα_n has a superstable periodic orbit of period 2n. Consider a quasi-periodic perturbation (with only one frequency) of the one-dimensional family of maps, and let us call ε the perturbing parameter. For ε small enough, the superstable periodic orbits of the unperturbed map become attracting invariant curves (depending on α and ε) of the perturbed system. Under a suitable hypothesis, it is known that there exist two reducibility loss bifurcation curves around each parameter value (αn, 0), which can be locally expressed as (α_n^+(\\varepsilon), \\varepsilon) and (α_n^-(\\varepsilon), \\varepsilon) . We propose an extension of the classic one-dimensional (doubling) renormalization operator to the quasi-periodic case. We show that this extension is well defined and the operator is differentiable. Moreover, we show that the slopes of reducibility loss bifurcation \\frac{d}{d\\varepsilon} α_n^+/-(0) can be written in terms of the tangent map of the new quasi-periodic renormalization operator. In particular, our result applies to the families of quasi-periodic forced perturbations of the Logistic Map typically encountered in the literature. We also present a numerical study that demonstrates that the asymptotic behaviour of \\{\\frac{d}{d\\varepsilon} α_n^+/-(0)\\}n≥ 0 is governed by the dynamics of the proposed quasi-periodic renormalization operator.

  12. The Schwinger α-PARAMETRIC Representation of the Finite-Temperature Field Theory:. Renormalization II (United States)

    Benhamou, Mabrouk; Kassou-Ou-Ali, Ahmed

    We extend to finite-temperature field theories, involving charged scalar or nonvanishing spin particles, the α parametrization of field theories at zero temperature. This completes a previous work concerning the scalar theory. As there, a function θ, which contains all temperature dependence, appears in the α integrand. The function θ is an extension of the usual theta function. The implications of the α parametrization for the renormalization problem are discussed.

  13. Egalitarian Improvement to Democracy: Quark renormalization constants in N_f=2 QCD

    CERN Document Server

    Petrov, K


    We present our results on the non-perturbative evaluation of the renormalization constant for the quark field, $Z_q$, in Landau gauge within RI-MOM scheme. Using three lattice spacing we are able to isolate lattice artefacts of various origin, both perturbative and non-perturbative. In particular, the existence of the dimension-two gluon-condensate is discussed, and confirmed.

  14. Density-matrix renormalization study of the Hubbard model on a Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Lepetit, M.B.; Cousy, M.; Pastor, G.M. [Toulouse-3 Univ., 31 (France). Lab. de Physique Quantique


    The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization left angle S{sub z}(i) right angle, its fluctuations left angle S{sub z}(i){sup 2} right angle - left angle S{sub z}(i) right angle {sup 2} and various spin correlation functions left angle S{sub z}(i)S{sub z}(j) right angle - left angle S{sub z}(i) right angle left angle S{sub z}(j) right angle are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments left angle S{sub z}(i) right angle increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors [ left angle S{sub z}(0) right angle {approx_equal}- left angle S{sub z}(1) right angle ]. At large U/t, left angle S{sub z}(i) right angle is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ vertical stroke left angle S{sub z}(i) right angle vertical stroke {approx_equal}0.35 for U/t{yields}+{infinity}]. left angle S{sub z}(i){sup 2} right angle - left angle S{sub z}(i) right angle {sup 2} shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of left angle S{sub z}(i){sup 2} right angle with increasing U/t and the formation of important permanent moments left angle S{sub z}(i) right angle at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. (orig.)

  15. Exact third-order density perturbation and one-loop power spectrum in general dark energy models

    Directory of Open Access Journals (Sweden)

    Seokcheon Lee


    Full Text Available Under the standard perturbation theory (SPT, we obtain the fully consistent third-order density fluctuation and kernels for the general dark energy models without using the Einstein–de Sitter (EdS universe assumption for the first time. We also show that even though the temporal and spatial components of the SPT solutions cannot be separable, one can find the exact solutions to any order in general dark energy models. With these exact solutions, we obtain the less than % error correction of one-loop matter power spectrum compared to that obtained from the EdS assumption for k=0.1 hMpc−1 mode at z=0(1,1.5. Thus, the EdS assumption works very well at this scale. However, if one considers the correction for P13, the error is about 6 (9, 11% for the same mode at z=0(1,1.5. One absorbs P13 into the linear power spectrum in the renormalized perturbation theory (RPT and thus one should use the exact solution instead of the approximation one. The error on the resummed propagator N of RPT is about 14 (8, 6% at z=0(1,1.5 for k=0.4 hMpc−1. For k=1 hMpc−1, the error correction of the total matter power spectrum is about 3.6 (4.6, 4.5% at z=0(1,1.5. Upcoming observation is required to archive the sub-percent accuracy to provide the strong constraint on the dark energy and this consistent solution is prerequisite for the model comparison.

  16. Exact third-order density perturbation and one-loop power spectrum in general dark energy models

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seokcheon; Park, Changbom [School of Physics, Korea Institute for Advanced Study, Heogiro 85, Seoul 130-722 (Korea, Republic of); Biern, Sang Gyu [Department of Physics and Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of)


    Under the standard perturbation theory (SPT), we obtain the fully consistent third-order density fluctuation and kernels for the general dark energy models without using the Einstein–de Sitter (EdS) universe assumption for the first time. We also show that even though the temporal and spatial components of the SPT solutions cannot be separable, one can find the exact solutions to any order in general dark energy models. With these exact solutions, we obtain the less than % error correction of one-loop matter power spectrum compared to that obtained from the EdS assumption for k=0.1 hMpc{sup −1} mode at z=0(1,1.5). Thus, the EdS assumption works very well at this scale. However, if one considers the correction for P{sub 13}, the error is about 6 (9, 11)% for the same mode at z=0(1,1.5). One absorbs P{sub 13} into the linear power spectrum in the renormalized perturbation theory (RPT) and thus one should use the exact solution instead of the approximation one. The error on the resummed propagator N of RPT is about 14 (8, 6)% at z=0(1,1.5) for k=0.4 hMpc{sup −1}. For k=1 hMpc{sup −1}, the error correction of the total matter power spectrum is about 3.6 (4.6, 4.5)% at z=0(1,1.5). Upcoming observation is required to archive the sub-percent accuracy to provide the strong constraint on the dark energy and this consistent solution is prerequisite for the model comparison.

  17. Upper bounds on minimum cardinality of exact and approximate reducts

    KAUST Repository

    Chikalov, Igor


    In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

  18. Quasitraces on exact C*-algebras are traces

    DEFF Research Database (Denmark)

    Haagerup, Uffe


    It is shown that all 2-quasitraces on a unital exact C ∗   -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗   -algebra has a tracial state, and (2) if an AW ∗   -factor of type II 1   is generated (as an AW ∗   -algebra) by an exact C ∗   -subalgebra, then i...

  19. New exact travelling wave solutions of some complex nonlinear equations (United States)

    Bekir, Ahmet


    In this paper, we establish exact solutions for complex nonlinear equations. The tanh-coth and the sine-cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.

  20. Stratified exact tests for the weak causal null hypothesis in randomized trials with a binary outcome. (United States)

    Chiba, Yasutaka


    Fisher's exact test is commonly used to compare two groups when the outcome is binary in randomized trials. In the context of causal inference, this test explores the sharp causal null hypothesis (i.e. the causal effect of treatment is the same for all subjects), but not the weak causal null hypothesis (i.e. the causal risks are the same in the two groups). Therefore, in general, rejection of the null hypothesis by Fisher's exact test does not mean that the causal risk difference is not zero. Recently, Chiba (Journal of Biometrics and Biostatistics 2015; 6: 244) developed a new exact test for the weak causal null hypothesis when the outcome is binary in randomized trials; the new test is not based on any large sample theory and does not require any assumption. In this paper, we extend the new test; we create a version of the test applicable to a stratified analysis. The stratified exact test that we propose is general in nature and can be used in several approaches toward the estimation of treatment effects after adjusting for stratification factors. The stratified Fisher's exact test of Jung (Biometrical Journal 2014; 56: 129-140) tests the sharp causal null hypothesis. This test applies a crude estimator of the treatment effect and can be regarded as a special case of our proposed exact test. Our proposed stratified exact test can be straightforwardly extended to analysis of noninferiority trials and to construct the associated confidence interval. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.