Lee, Myoung-Jae; Jung, Young-Dae
2016-01-01
The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.
Lee, Myoung-Jae [Department of Physics and Research Institute for Natural Sciences, Hanyang University, Seoul 04763 (Korea, Republic of); Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States)
2016-01-15
The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.
Wave function and CKM renormalization
Espriu, Doménec
2002-01-01
In this presentation we clarify some aspects of the LSZ formalism and wave function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the CKM mixing matrix which is closely related to wave function renormalization. The effects due to the electroweak radiative corrections that are described in this work are small, but they will need to be considered when the precision in the measurement of the charged current sector couplings reaches the 1% level. The work presented here is done in collaboration with Julian Manzano and Pere Talavera.
Parameswaran, S A; Kimchi, Itamar; Turner, Ari M; Stamper-Kurn, D M; Vishwanath, Ashvin
2013-03-22
We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell--and thus fractional site filling. We discuss situations where no classical bosonic insulator, which is a product state of particles on independent sites, is admitted. Nevertheless, we show that it is possible to construct a quantum Mott insulator of bosons if a trivial band insulator of fermions is possible at the same filling. The ground state wave function is simply a permanent of exponentially localized Wannier orbitals. Such a Wannier permanent wave function is featureless in that it respects all lattice symmetries and is the unique ground state of a parent Hamiltonian that we construct. Motivated by the recent experimental demonstration of a kagome optical lattice of bosons, we study this lattice at 1/3 site filling. Previous approaches to this problem have invariably produced either broken-symmetry states or topological order. Surprisingly, we demonstrate that a featureless insulator is a possible alternative and is the exact ground state of a local Hamiltonian. We briefly comment on the experimental relevance of our results to ultracold atoms as well as to 1/3 magnetization plateaus for kagome spin models in an applied field.
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Unitary Networks from the Exact Renormalization of Wave Functionals
Fliss, Jackson R; Parrikar, Onkar
2016-01-01
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 $AdS_{d+1}$. 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 rece...
Partly occupied Wannier functions
Thygesen, Kristian Sommer; Hansen, Lars Bruno; Jacobsen, Karsten Wedel
2005-01-01
We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibondin......We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding...
Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization
Giudice, Gian Francesco
1998-01-01
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.
Renormalization group approach to a p-wave superconducting model
Continentino, Mucio A.; Deus, Fernanda [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, Urca 22290-180, Rio de Janeiro, RJ (Brazil); Caldas, Heron [Departamento de Ciências Naturais, Universidade Federal de São João Del Rei, 36301-000, São João Del Rei, MG (Brazil)
2014-04-01
We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.
Hieida, Yasuhiro; Okunishi, Kouichi; Akutsu, Yasuhiro
1997-02-01
The product-wave-function renormalization group method, a new numerical renormalization group scheme proposed recently, is applied to one-dimensional quantum spin chains in a magnetic field. We find the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.
Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation
Enberg, Rikard
2006-12-01
I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.
Renormalization of Long Wavelength Spin Waves in the 2d Ferromagnet Rb2CrCl4
Lindgård, Per-Anker; Als-Nielsen, Jens Aage; Hutchings, M. T.
1980-01-01
Rb2CrCl4 is a nearly 2d-ferromagnetic, optically transparent insulator isomorphous with K2CuF4. High resolution neutron scattering data for temperatures below Tc = 52.4 K of the low energy long wavelength spin waves are presented and a Hartree-Fock analysis yields Hamiltonian parameters and accou...... and accounts for the renormalization. No evidence of a Bose condensate is found. A spin canting angle θ ≈ 2° is predicted....
Capillary-wave models and the effective-average-action scheme of functional renormalization group.
Jakubczyk, P
2011-08-01
We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension d≥2. Exploiting the nonuniqueness of the renormalization-group cutoff scheme, we find, however, that the capillary parameter ω is a scheme-dependent quantity below d=3. For d=3 the parameter ω is perfectly robust against scheme variation.
Quantum Superlattices, Wannier Stark Ladders and the 'Resonance' technique
Papageorgiou, C D; Raptis, T E
2016-01-01
We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state problems. We develop the transformation theory mapping the wave equation to LTL and we apply the model to the case of a solid state periodic lattice. We extend the theory with an additional Wannier-Stark term and we show with results the flexibility and the strength of the technique. The advantages of the method for arbitrary potentials are also stressed.
Hellmann-Feynman forces within the DFT + U in Wannier functions basis.
Novoselov, D; Korotin, Dm M; Anisimov, V I
2015-08-19
The most general way to describe localized atomic-like electronic states in strongly correlated compounds is to use Wannier functions. In the present paper we continue development of widely-used DFT + U method with the Wannier function basis set and propose a technique to calculate Hubbard contribution to atomic forces. The technique was implemented as a part of plane-waves pseudopotential code Quantum-ESPRESSO and tested on two compounds: charge transfer insulator NiO with cubic crystal structure and correlated metal SrVO3 with perovskite structure.
de Lima, M M; Kosevich, Yu A; Santos, P V; Cantarero, A
2010-04-23
We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry.
Muradoglu, M S; Baghai-Wadji, A R; Ng, T W
2010-04-01
Wannier functions derived from Bloch functions have been identified as an efficient means of analyzing the properties of photonic crystals in which localized functions have now opened the door for 2D and 3D structures containing defects to be investigated. In this paper, based on the Maxwell equations in diagonalized form and utilizing Bloch waves we have obtained an equivalent system of algebraic equations in eigenform. By establishing and exploiting several distinct properties of the resulting eigenpairs, we demonstrate an ability to construct Wannier functions associated with the simplest one-dimensional photonic structure. More importantly, the numerical investigation of the inner- and intra-band orthonormality conditions as well as Hilbert space partitioning features shows a capability for multi-resolution analysis that will make all-optical signal processing devices with photonic crystal structures feasible.
Renormalization of fermion mixing
Schiopu, R.
2007-05-11
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
Lavrov, P. M.; Shapiro, I. L.
2012-09-01
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz
Evenbly, G.; Vidal, G.
2015-11-01
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e-β H for infinite β . This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β , produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.
Evenbly, G; Vidal, G
2015-11-13
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Kramers-Wannier duality applied to the boolean satifiability problem
Mitchell, Joe; Hsu, Benjamin; Galitski, Victor
2014-03-01
Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. This research was supported by NSF-CAREER award No. DMR-0847224 and Simons Foundation.
Renormalized. pi. NN coupling constant and the P-italic-wave phase shifts in the cloudy bag model
Pearce, B.C.; Afnan, I.R.
1986-09-01
Most applications of the cloudy bag model to ..pi..N scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P-italic/sub 11/ channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ..pi pi..N system that incorporate three-body unitarity.
Renormalized πNN coupling constant and the P-wave phase shifts in the cloudy bag model
Pearce, B. C.; Afnan, I. R.
1986-09-01
Most applications of the cloudy bag model to πN scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P11 channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ππN system that incorporate three-body unitarity.
Wannier-Bloch approach to localization in high harmonics generation in solids
Osika, Edyta N; Ortmann, Lisa; Suárez, Noslen; Pérez-Hernández, Jose Antonio; Szafran, Bartłomiej; Ciappina, Marcelo F; Sols, Fernando; Landsman, Alexandra S; Lewenstein, Maciej
2016-01-01
Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission...
Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields
De Nittis, Giuseppe
2011-01-01
n this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results [Pan07, Kuc09] to include periodic zero flux magnetic fields. The new notion of magnetic symmetry plays a crucial r\\^ole; to a large class of symmetries for a non-magnetic system, one can associate "magnetic" symmetries of the related magnetic system. Observing that the existence of an exponentially localized Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic time-reversal symmetry is sufficient to ensure the triviality of the Bloch bundle in spatial dimension d = 1, 2, 3. For d = 4, an exponentially localized Wannier basis exists provided that the trace per unit volume of a suitable function of the Fermi projection vanishes. For d > 4 and d \\leq 2m (stable rank regime) only the exponential localization of a subset of Wannier functions ...
Compactly supported Wannier functions and algebraic K -theory
Read, N.
2017-03-01
In a tight-binding lattice model with n orbitals (single-particle states) per site, Wannier functions are n -component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense span all states in a given energy band or set of bands; compactly supported Wannier functions are such functions that vanish outside a bounded region. They arise not only in band theory, but also in connection with tensor-network states for noninteracting fermion systems, and for flat-band Hamiltonians with strictly short-range hopping matrix elements. In earlier work, it was proved that for general complex band structures (vector bundles) or general complex Hamiltonians—that is, class A in the tenfold classification of Hamiltonians and band structures—a set of compactly supported Wannier functions can span the vector bundle only if the bundle is topologically trivial, in any dimension d of space, even when use of an overcomplete set of such functions is permitted. This implied that, for a free-fermion tensor network state with a nontrivial bundle in class A, any strictly short-range parent Hamiltonian must be gapless. Here, this result is extended to all ten symmetry classes of band structures without additional crystallographic symmetries, with the result that in general the nontrivial bundles that can arise from compactly supported Wannier-type functions are those that may possess, in each of d directions, the nontrivial winding that can occur in the same symmetry class in one dimension, but nothing else. The results are obtained from a very natural usage of algebraic K -theory, based on a ring of polynomials in e±i kx,e±i ky,..., which occur as entries in the Fourier-transformed Wannier functions.
Renormalization Scheme Dependence and Renormalization Group Summation
McKeon, D G C
2016-01-01
We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter mu cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher order radiative corrections is absorbed by the behaviour of the running coupling.
Gover, A Rod
2016-01-01
For any conformally compact manifold with hypersurface boundary we define a canonical renormalized volume functional and compute an explicit, holographic formula for the corresponding anomaly. For the special case of asymptotically Einstein manifolds, our method recovers the known results. The anomaly does not depend on any particular choice of regulator, but the coefficients of divergences do. We give explicit formulae for these divergences valid for any choice of regulating hypersurface; these should be relevant to recent studies of quantum corrections to entanglement entropies. The anomaly is expressed as a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. We show that the variation of these energy functionals is exactly the obstruction to solving a singular Yamabe type problem with boundary data along the...
Vidal, G
2007-11-30
We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.
Abram, M; Zegrodnik, M; Spałek, J
2017-09-13
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Abram, M.; Zegrodnik, M.; Spałek, J.
2017-09-01
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
External pumping of hybrid nanostructures in microcavity with Frenkel and Wannier-Mott excitons
Dubovskiy, O. A.; Agranovich, V. M.
2016-09-01
The exciton-exciton interaction in hybrid nanostructures with resonating Frenkel and Wannier-Mott excitons was investigated in many publications. In microcavity the hybrid nanostructures can be exposed to different types of optical pumping, the most common one being pumping through one of the microcavity side. However, not investigated and thus never been discussed the hybrid excitons generation by pumping of confined quantum wells from the side of empty microcavity without nanostructures in a wave guided configuration. Here, we consider the hybrid excitations in cavity with organic and inorganic quantum wells and with different types of pumping from external source. The frequency dependence for intensity of excitations in hybrid structure is also investigated. The results may be used for search of most effective fluorescence and relaxation processes. The same approach may be used when both quantum wells are organic or inorganic.
Renormalizing the NN interaction with multiple subtractions
Timoteo, V.S. [Faculdade de Tecnologia, Universidade Estadual de Campinas, 13484-332 Limeira, SP (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, Comando de Tecnologia Aeroespacial, 12228-900 Sao Jose dos Campos, SP (Brazil); Delfino, A. [Departamento de Fisica, Universidade Federal Fluminense, 24210-150 Niteroi, RJ (Brazil); Tomio, L. [Instituto de Fisica Teorica, Universidade Estadual Paulista, 01140-070 Sao Paulo, SP (Brazil); Szpigel, S.; Duraes, F.O. [Centro de Ciencias e Humanidades, Universidade Presbiteriana Mackenzie, 01302-907 Sao Paulo, SP (Brazil)
2010-02-15
The aim of this work is to show how to renormalize the nucleon-nucleon interaction at next-to-next-to-leading order using a systematic subtractive renormalization approach with multiple subtractions. As an example, we calculate the phase shifts for the partial waves with total angular momentum J=2. The intermediate driving terms at each recursive step as well as the renormalized T-matrix are also shown. We conclude that our method is reliable for singular potentials such as the two-pion exchange and derivative contact interactions.
Fermion field renormalization prescriptions
Zhou, Yong
2005-01-01
We discuss all possible fermion field renormalization prescriptions in conventional field renormalization meaning and mainly pay attention to the imaginary part of unstable fermion Field Renormalization Constants (FRC). We find that introducing the off-diagonal fermion FRC leads to the decay widths of physical processes $t\\to c Z$ and $b\\to s \\gamma$ gauge-parameter dependent. We also discuss the necessity of renormalizing the bare fields in conventional quantum field theory.
Renormalization: an advanced overview
Gurau, R.; Rivasseau, V.; Sfondrini, A.|info:eu-repo/dai/nl/330983083
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond
Renormalized action improvements
Zachos, C.
1984-01-01
Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references.
Vibrational Density Matrix Renormalization Group.
Baiardi, Alberto; Stein, Christopher J; Barone, Vincenzo; Reiher, Markus
2017-08-08
Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.
Gutzwiller renormalization group
Lanatà, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Wang, Cai-Zhuang; Ho, Kai-Ming; Kotliar, Gabriel
2016-01-01
We develop a variational scheme called the "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.
Localized Basis for Effective Lattice Hamiltonians Lattice Wannier Functions
Rabe, K M
1994-01-01
A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corres...
Automated quantum conductance calculations using maximally-localised Wannier functions
Shelley, Matthew; Mostofi, Arash A; Marzari, Nicola
2011-01-01
A robust, user-friendly, and automated method to determine quantum conductance in disordered quasi-one-dimensional systems is presented. The scheme relies upon an initial density- functional theory calculation in a specific geometry after which the ground-state eigenfunctions are transformed to a maximally-localised Wannier function (MLWF) basis. In this basis, our novel algorithms manipulate and partition the Hamiltonian for the calculation of coherent electronic transport properties within the Landauer-Buttiker formalism. Furthermore, we describe how short- ranged Hamiltonians in the MLWF basis can be combined to build model Hamiltonians of large (>10,000 atom) disordered systems without loss of accuracy. These automated algorithms have been implemented in the Wannier90 code[Mostofi et al, Comput. Phys. Commun. 178, 685 (2008)], which is interfaced to a number of electronic structure codes such as Quantum-ESPRESSO, AbInit, Wien2k, SIESTA and FLEUR. We apply our methods to an Al atomic chain with a Na defect...
Differential Renormalization, the Action Principle and Renormalization Group Calculations
Smirnov, V. A.
1994-01-01
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action principle in the framework of differential renormalization is discussed.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-08
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Renormalization: an advanced overview
Gurau, Razvan; Sfondrini, Alessandro
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.
Renormalization Scheme Dependence and the Renormalization Group Beta Function
Chishtie, F. A.; McKeon, D. G. C.
2016-01-01
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is related to a change in the mass scale $\\mu$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expan...
DLTS study of the Wannier-Stark effect in Ge/Si QD superlattices
Sobolev, Mikhail M.; Cirlin, Georgii E.; Tonkikh, Alexander A.
2007-12-01
Deep-level transient spectroscopy (DLTS) has been applied to study the emission of electrons from quantum states in a 20-layer quantum-dot superlattice (QDSL) of Ge in a Ge/Si p-n heterostructure. Changes in the DLTS spectra of this structure strongly depend on the applied bias Ur. There are three bias ranges corresponding to three modes of the Wannier-Stark effect: Wannier-Stark ladder mode, Wannier-Stark localization and non-resonant Zener tunneling. The DLTS peaks for all the three modes are associated with emission of electrons from deep-level defects into the Wannier-Stark localized states resulting from the splitting of the electron miniband of the Ge/Si QDSL.
DLTS study of the Wannier-Stark effect in Ge/Si QD superlattices
Sobolev, Mikhail M. [A.F. Ioffe Physical Technical Institute, 26 Polytechnicheskaya ul., 194021 St. Petersburg (Russian Federation)], E-mail: m.sobolev@mail.ioffe.ru; Cirlin, Georgii E.; Tonkikh, Alexander A. [A.F. Ioffe Physical Technical Institute, 26 Polytechnicheskaya ul., 194021 St. Petersburg (Russian Federation)
2007-12-15
Deep-level transient spectroscopy (DLTS) has been applied to study the emission of electrons from quantum states in a 20-layer quantum-dot superlattice (QDSL) of Ge in a Ge/Si p-n heterostructure. Changes in the DLTS spectra of this structure strongly depend on the applied bias U{sub r}. There are three bias ranges corresponding to three modes of the Wannier-Stark effect: Wannier-Stark ladder mode, Wannier-Stark localization and non-resonant Zener tunneling. The DLTS peaks for all the three modes are associated with emission of electrons from deep-level defects into the Wannier-Stark localized states resulting from the splitting of the electron miniband of the Ge/Si QDSL.
Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings.
Wilkinson, P B
2002-05-01
The formation of photonic Bloch oscillations and Wannier-Stark ladders is demonstrated in an exponentially chirped one-dimensional Bragg grating. The photonic Bloch oscillations are investigated using Hamiltonian optics, and direct analogies are made with electron dynamics in periodic potentials. The results of transfer matrix calculations are presented, which show the existence of a photonic Wannier-Stark ladder that should be detectable in experiments.
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.
Renormalization for Philosophers
Butterfield, Jeremy
2014-01-01
We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas, and great successes, of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction (Section 4). One theme will be a contrast between two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization (from 1970 onwards) explains...
Ekkehard Krüger
2015-05-01
Full Text Available The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates.
The renormalization; La normalisation
Rivasseau, V. [Paris-6 Univ., Lab. de Physique Theorique, 91 - Orsay (France); Gallavotti, G. [Universita di Roma, La Sapienza, Fisica, Roma (Italy); Zinn-Justin, J. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique Theorique, 91- Gif sur Yvette (France); Connes, A. [College de France, 75 - Paris (France)]|[Institut des Hautes Etudes Scientifiques - I.H.E.S., 91 - Bures sur Yvette (France); Knecht, M. [Centre de Physique Theorique, CNRS-Luminy, 13 - Marseille (France); Mansoulie, B. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique des Particules, 91- Gif sur Yvette (France)
2002-07-01
This document gathers 6 articles. In the first article the author reviews the theory of perturbative renormalization, discusses its limitations and gives a brief introduction to the powerful point of view of the renormalization group, which is necessary to go beyond perturbation theory and to define renormalization in a constructive way. The second article is dedicated to renormalization group methods by illustrating them with examples. The third article describes the implementation of renormalization ideas in quantum field theory. The mathematical aspects of renormalization are given in the fourth article where the link between renormalization and the Riemann-Hilbert problem is highlighted. The fifth article gives an overview of the main features of the theoretical calculations that have been done in order to obtain accurate predictions for the anomalous magnetic moments of the electron and of the muon within the standard model. The challenge is to make theory match the unprecedented accuracy of the last experimental measurements. The last article presents how ''physics beyond the standard model'' will be revealed at the large hadron collider (LHC) at CERN. This accelerator will be the first to explore the 1 TeV energy range directly. Supersymmetry, extra-dimensions and Higgs boson will be the different challenges. It is not surprising that all theories put forward today to subtend the electro-weak breaking mechanism, predict measurable or even spectacular signals at LHC. (A.C.)
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Free-fermion entanglement spectrum through Wannier interpolation
Lee, Ching Hua; Ye, Peng
2015-02-01
Quantum entanglement plays a ubiquitous role in theoretical physics, from the characterization of novel phases of matter to understanding the efficacy of numerical algorithms. As such, there have been extensive studies on the entanglement spectrum (ES) of free-fermion systems, particularly in the relation between its spectral flow and topological charge pumping. However, far less has been studied about the spacing between adjacent entanglement eigenenergies, which affects the truncation error in numerical computations involving matrix product states or projected entangled pair states. In this paper, we shall hence derive asymptotic bounds for the ES spacings through an interpolation argument that utilizes known results on Wannier function decay. For translationally invariant systems, the entanglement energies are shown to decay at a rate monotonically related to the complex gap between the filled and occupied bands. This interpolation also demonstrates the one-to-one correspondence between the ES and the edge states. Our results also provide asymptotic bounds for the eigenvalue distribution of certain types of block Toeplitz matrices common in physics, even for those not arising from entanglement calculations.
Exact exchange with non-orthogonal generalized Wannier functions
Mountjoy, Jeff; Todd, Michelle; Mosey, Nicholas J.
2017-03-01
The evaluation of exact exchange (EXX) is an important component of quantum chemical calculations performed with ab initio and hybrid density functional methods. While evaluating exact exchange is routine in molecular quantum chemical calculations performed with localized basis sets, the non-local nature of the exchange operator presents a major impediment to the efficient use of exact exchange in calculations that employ planewave basis sets. Non-orthogonal generalized Wannier functions (NGWFs) corresponding to planewave expansions of localized basis functions are an alternative form of basis set that can be used in quantum chemical calculations. The periodic nature of these functions renders them suitable for calculations of periodic systems, while the contraction of sets of planewaves into individual basis functions reduces the number of variational parameters, permitting the construction and direct diagonalization of the Fock matrix. The present study examines how NGWFs corresponding to Fourier series representations of conventional atom-centered basis sets can be used to evaluate exact exchange in periodic systems. Specifically, an approach for constructing the exchange operator with NGWFs is presented and used to perform Hartree-Fock calculations with a series of molecules in periodically repeated simulation cells. The results demonstrate that the NGWF approach is significantly faster than the EXX method, which is a standard approach for evaluating exact exchange in periodic systems.
Singular Renormalization Group Equations
Minoru, HIRAYAMA; Department of Physics, Toyama University
1984-01-01
The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.
Renormalization of supersymmetric theories
Pierce, D.M.
1998-06-01
The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M{sub W} and sin{sup 2}{theta}{sup eff}. He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses.
woptic: optical conductivity with Wannier functions and adaptive k-mesh refinement
Assmann, E; Kuneš, J; Toschi, A; Blaha, P; Held, K
2015-01-01
We present an algorithm for the adaptive tetrahedral integration over the Brillouin zone of crystalline materials, and apply it to compute the optical conductivity, dc conductivity, and thermopower. For these quantities, whose contributions are often localized in small portions of the Brillouin zone, adaptive integration is especially relevant. Our implementation, the woptic package, is tied into the wien2wannier framework and allows including a many-body self energy, e.g. from dynamical mean-field theory (DMFT). Wannier functions and dipole matrix elements are computed with the DFT package Wien2k and Wannier90. For illustration, we show DFT results for fcc-Al and DMFT results for the correlated metal SrVO$_3$.
Carvalho, Vanuildo S de [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Freire, Hermann, E-mail: hfreire@mit.edu [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 2139 (United States)
2014-09-15
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.
HS Jebeli
2012-12-01
Full Text Available Calculation of Hall coefficient in semiclassical approach requires the first and the second derivatives of the energy bands at the Fermi level. We use the Maximally Localized Wannier Function technique to determine the required band derivatives and calculate the ordinary Hall conductivity and ordinary Hall coefficient in Al,Cu, Pd, Li, Au, Ag and Pb cubic metals.
Hilbert space renormalization for the many-electron problem.
Li, Zhendong; Chan, Garnet Kin-Lic
2016-02-28
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.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Compressive Spectral Renormalization Method
Bayindir, Cihan
2016-01-01
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.
Lavrov, Peter M
2010-01-01
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST symmetry after renormalization is preserved. The advantage of the Sp(2)-method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)- scalars.
Lavrov, Peter M., E-mail: lavrov@tspu.edu.r [Department of Mathematical Analysis, Tomsk State Pedagogical University, Kievskaya St. 60, Tomsk 634061 (Russian Federation)
2011-08-11
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge-invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST-symmetry after renormalization is preserved. The advantage of the Sp(2) method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)-scalars.
Renormalizing Entanglement Distillation.
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens
2016-01-15
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Holographic renormalization and supersymmetry
Genolini, Pietro Benetti; Cassani, Davide; Martelli, Dario; Sparks, James
2017-02-01
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.
Renormalization conditions and non-diagrammatic approach to renormalizations
Faizullaev, B. A.; Garnov, S. A.
1996-01-01
The representation of the bare parameters of Lagrangian in terms of total vertex Green's functions is used to obtain the general form of renormalization conditions. In the framework of this approach renormalizations can be carried out without treatment to Feynman diagrams.
Using Wannier functions to improve solid band gap predictions in density functional theory.
Ma, Jie; Wang, Lin-Wang
2016-04-26
Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.
Using Wannier functions to improve solid band gap predictions in density functional theory
Ma, Jie; Wang, Lin-Wang
2016-04-01
Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.
Renormalization on noncommutative torus
D'Ascanio, D; Vassilevich, D V
2016-01-01
We study a self-interacting scalar $\\varphi^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the nonlocal counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points towards the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $\\theta$.
Renormalization of composite operators
Polonyi, J
2001-01-01
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\\phi^3$ theory in dimension $d=6$.
Battle, G A
1999-01-01
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
Renormalization on noncommutative torus
D' Ascanio, D.; Pisani, P. [Universidad Nacional de La Plata, Instituto de Fisica La Plata-CONICET, La Plata (Argentina); Vassilevich, D.V. [Universidade Federal do ABC, CMCC, Santo Andre, SP (Brazil); Tomsk State University, Department of Physics, Tomsk (Russian Federation)
2016-04-15
We study a self-interacting scalar φ{sup 4} theory on the d-dimensional noncommutative torus. We determine, for the particular cases d = 2 and d = 4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ. (orig.)
Renormalization on noncommutative torus
D'Ascanio, D.; Pisani, P.; Vassilevich, D. V.
2016-04-01
We study a self-interacting scalar \\varphi ^4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.
An efficient approach to calculating Wannier states and extension to inhomogeneous systems
Bissbort, Ulf; Hofstetter, Walter [ITP, Goethe-Universitaet Frankfurt (Germany)
2013-07-01
Wannier states are a fundamental and central constituent to the construction of many-body models, as they are restricted to the single-particle Hilbert subspace of the respective band, while minimizing the spatial spread. Although simple in their initial definition as discrete Fourier transforms of the Bloch states, their actual computation amounts to a non-trivial high-dimensional minimization problem of the spatial variance as a complex phases of the single-particle Bloch state. Various involved techniques have been devised to efficiently treat this minimization problem, which quickly becomes numerically demanding for all but the simplest lattice geometries. We present an alternative approach, which allows for an efficient numerical calculation of the maximally localized Wannier states and entirely circumvents the pitfalls associated with the minimization technique, such as getting stuck in local minima. The computational effort scales favorably with increasing dimensions and lattice geometries in comparison to the minimization technique. Furthermore it allows for the first clear and unambiguous definition of Wannier states in inhomogeneous systems.
Renormalization group for evolving networks.
Dorogovtsev, S N
2003-04-01
We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that the critical behavior of percolation on the growing networks differs from that in uncorrelated networks.
Inflation, Renormalization, and CMB Anisotropies
Agullo, I; Olmo, Gonzalo J; Parker, Leonard
2010-01-01
In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.
Renormalization group circuits for gapless states
Swingle, Brian; McGreevy, John; Xu, Shenglong
2016-05-01
We show that a large class of gapless states are renormalization group fixed points in the sense that they can be grown scale by scale using local unitaries. This class of examples includes some theories with a dynamical exponent different from one, but does not include conformal field theories. The key property of the states we consider is that the ground-state wave function is related to the statistical weight of a local statistical model. We give several examples of our construction in the context of Ising magnetism.
Parker, Shane M.; Shiozaki, Toru [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States)
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Active space decomposition with multiple sites: Density matrix renormalization group algorithm
Parker, Shane M
2014-01-01
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few {\\mu}Eh or less) with M = 128 in both cases, which is in contrast to conventional ab initio density matrix renormalization group.
Parker, Shane M; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE(h) or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Fifty years of the renormalization group
Shirkov, D V
2001-01-01
Renormalization was the breakthrough that made quantum field theory respectable in the late 1940s. Since then, renormalization procedures, particularly the renormalization group method, have remained a touchstone for new theoretical developments. This work relates the history of the renormalization group. (17 refs).
Renormalizing an initial state
Collins, Hael; Vardanyan, Tereza
2014-01-01
The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.
Practical Algebraic Renormalization
Grassi, P A; Steinhauser, M
1999-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustra...
Renormalized Volumes with Boundary
Gover, A Rod
2016-01-01
We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant (Q-curvature, transgression)-type pairs for hypersurfaces with boundary. For the special case of anomalies coming from the volume enclosed by a minimal hypersurface ending on the boundary of a Poincare--Einstein structure, this result recovers Branson's Q-curvature and corresponding transgression. When the singular metric solves a boundary version of the constant scalar curvature Yamabe problem, the anomaly gives generalized Willmore energy functionals for hypersurfaces with boundary. Our approach ...
Gies, Holger; Jaeckel, Joerg
2004-09-01
We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral-symmetry-breaking (χSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the χSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.
Renormalization Group Tutorial
Bell, Thomas L.
2004-01-01
Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.
Tensor Network Renormalization.
Evenbly, G; Vidal, G
2015-10-30
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.
Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
Wu, Xing-Gang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin
2014-01-01
A valid prediction from quantum field theory for a physical observable should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since truncated perturbation series do not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $\\beta$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the "Principle of Minimum Sensitivity" (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a deta...
Entanglement renormalization for quantum fields in real space.
Haegeman, Jutho; Osborne, Tobias J; Verschelde, Henri; Verstraete, Frank
2013-03-08
We show how to construct renormalization group (RG) flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization ansatz to continuum theories. The variational class of wave functions arising from this RG flow are translation invariant and exhibits an entropy-area law. We illustrate the construction for a free nonrelativistic boson model, and argue that the full power of the construction should emerge in the case of interacting theories.
Suijlekom, W.D. van
2008-01-01
We study the structure of renormalization Hopf algebras of gauge theories. We identify certain Hopf subalgebras in them, whose character groups are semidirect products of invertible formal power series with formal diffeomorphisms. This can be understood physically as wave function renormalization and renormalization of the coupling constants, respectively. After taking into account the Slavnov-Taylor identities for the couplings as generators of a Hopf ideal, we find Hopf subalgebras in the c...
The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach
Synatschke-Czerwonka, Franziska; Fischbacher, Thomas; Bergner, Georg
2010-01-01
We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called F...
Renormalization automated by Hopf algebra
Broadhurst, D J
1999-01-01
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a finite renormalized expression for any Feynman diagram. We thus verify a representation of the operator product expansion, which generalizes Chen's lemma for iterated integrals. The subset of diagrams whose forest structure entails a unique primitive subdivergence provides a representation of the Hopf algebra ${\\cal H}_R$ of undecorated rooted trees. Our undecorated Hopf algebra program is designed to process the 24,213,878 BPHZ contributions to the renormalization of 7,813 diagrams, with up to 12 loops. We consider 10 models, each in 9 renormalization schemes. The two simplest models reveal a notable feature of the subalgebra of Connes and Moscovici, corresponding to the commutative part of the Hopf ...
Chaotic renormalization-group trajectories
Damgaard, Poul H.; Thorleifsson, G.
1991-01-01
, or in regions where the renormalization-group flow becomes chaotic. We present some explicit examples of these phenomena for the case of a Lie group valued spin-model analyzed by means of a variational real-space renormalization group. By directly computing the free energy of these models around the parameter......Under certain conditions, the renormalization-group flow of models in statistical mechanics can change dramatically under just very small changes of given external parameters. This can typically occur close to bifurcations of fixed points, close to the complete disappearance of fixed points...... regions in which such nontrivial modifications of the renormalization-group flow occur, we can extract the physical consequences of these phenomena....
Differential renormalization of gauge theories
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
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
Holographic renormalization in teleparallel gravity
Krssak, Martin [Universidade Estadual Paulista, Instituto de Fisica Teorica, Sao Paulo, SP (Brazil)
2017-01-15
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.)
Renormalization and resolution of singularities
Bergbauer, Christoph; Brunetti, Romeo; Kreimer, Dirk
2009-01-01
Since the seminal work of Epstein and Glaser it is well established that perturbative renormalization of ultraviolet divergences in position space amounts to extension of distributions onto diagonals. For a general Feynman graph the relevant diagonals form a nontrivial arrangement of linear subspaces. One may therefore ask if renormalization becomes simpler if one resolves this arrangement to a normal crossing divisor. In this paper we study the extension problem of distributions onto the won...
Linear scaling calculation of maximally localized Wannier functions with atomic basis set.
Xiang, H J; Li, Zhenyu; Liang, W Z; Yang, Jinlong; Hou, J G; Zhu, Qingshi
2006-06-21
We have developed a linear scaling algorithm for calculating maximally localized Wannier functions (MLWFs) using atomic orbital basis. An O(N) ground state calculation is carried out to get the density matrix (DM). Through a projection of the DM onto atomic orbitals and a subsequent O(N) orthogonalization, we obtain initial orthogonal localized orbitals. These orbitals can be maximally localized in linear scaling by simple Jacobi sweeps. Our O(N) method is validated by applying it to water molecule and wurtzite ZnO. The linear scaling behavior of the new method is demonstrated by computing the MLWFs of boron nitride nanotubes.
The analytic renormalization group
Frank Ferrari
2016-08-01
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.
Cluster functional renormalization group
Reuther, Johannes; Thomale, Ronny
2014-01-01
Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a free expansion point of the action, the flow of the RG parameter Λ allows us to trace the evolution of the effective one- and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-1/2 bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.
The analytic renormalization group
Ferrari, Frank
2016-08-01
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 = 2 πk / 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.
Dziedzic, J; Hill, Q; Skylaris, C-K
2013-12-07
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
Poncé, S.; Margine, E. R.; Verdi, C.; Giustino, F.
2016-12-01
The EPW (Electron-Phonon coupling using Wannier functions) software is a Fortran90 code that uses density-functional perturbation theory and maximally localized Wannier functions for computing electron-phonon couplings and related properties in solids accurately and efficiently. The EPW v4 program can be used to compute electron and phonon self-energies, linewidths, electron-phonon scattering rates, electron-phonon coupling strengths, transport spectral functions, electronic velocities, resistivity, anisotropic superconducting gaps and spectral functions within the Migdal-Eliashberg theory. The code now supports spin-orbit coupling, time-reversal symmetry in non-centrosymmetric crystals, polar materials, and k and q-point parallelization. Considerable effort was dedicated to optimization and parallelization, achieving almost a ten times speedup with respect to previous releases. A computer test farm was implemented to ensure stability and portability of the code on the most popular compilers and architectures. Since April 2016, version 4 of the EPW code is fully integrated in and distributed with the Quantum ESPRESSO package, and can be downloaded through QE-forge at http://qe-forge.org/gf/project/q-e.
First-principles calculation of nonlinear optical responses by Wannier interpolation
Wang, Chong; Liu, Xiaoyu; Kang, Lei; Gu, Bing-Lin; Xu, Yong; Duan, Wenhui
2017-09-01
Various nonlinear optical (NLO) responses, like shift current and second harmonic generation (SHG), are revealed to be closely related to topological quantities involving the Berry connection and Berry curvature. First-principles prediction of NLO responses is of great importance to fundamental research and device design, but efficient computational methods are still lacking. The main challenge is that the calculations require a very dense k -point sampling that is computationally expensive and a proper treatment of the gauge problem for topological quantities. Here we present a Wannier interpolation method for first-principles calculation of NLO responses, which overcomes the challenge. This method interpolates physical quantities accurately for any desired k point with little computational cost and constructs a smooth gauge by the perturbation theory. To demonstrate the method, we study shift current of monolayer GeS and WS2 as well as SHG of bulk GaAs, getting good agreements with previous results. We show that the traditional sum rule method converges slowly with the number of bands, whereas the perturbation way does not. Moreover, our method is easily adapted to build tight-binding models for the following theoretical investigations. Last but not least, the method is compatible with most first-principles approaches, including density functional theory and beyond. With these advantages, Wannier interpolation is a promising method for first-principles studies of NLO phenomena.
Averaging and renormalization for the Korteveg–deVries–Burgers equation
Chorin, Alexandre J.
2003-01-01
We consider traveling wave solutions of the Korteveg–deVries–Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an “eddy” (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out. PMID:12913126
Averaging and renormalization for the Korteveg-deVries-Burgers equation.
Chorin, Alexandre J
2003-08-19
We consider traveling wave solutions of the Korteveg-deVries-Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an "eddy" (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out.
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
Local renormalization method for random systems
Gittsovich O.; Hubener R.; Rico E.; Briegel H.J.
2010-01-01
In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contractor renormalization (CORE). We analyze the performance of the method on the 2D random transverse field Ising model (RTFIM).
Heat Kernel Renormalization on Manifolds with Boundary
Albert, Benjamin I.
2016-01-01
In the monograph Renormalization and Effective Field Theory, Costello gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. In this paper, we extend Costello's renormalization procedure to a class of manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Renormalization of QED with planar binary trees
Brouder, Christian; Frabetti, Alessandra
2000-01-01
The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.
Renormalization group theory impact on experimental magnetism
Köbler, Ulrich
2010-01-01
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...
Lecture Notes on Holographic Renormalization
Skenderis, K
2002-01-01
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime.
Landau levels in 2D materials using Wannier Hamiltonians obtained by first principles
Lado, J. L.; Fernández-Rossier, J.
2016-09-01
We present a method to calculate the Landau levels and the corresponding edge states of two dimensional (2D) crystals using as a starting point their electronic structure as obtained from standard density functional theory (DFT). The DFT Hamiltonian is represented in the basis of maximally localized Wannier functions. This defines a tight-binding Hamiltonian for the bulk that can be used to describe other structures, such as ribbons, provided that atomic scale details of the edges are ignored. The effect of the orbital magnetic field is described using the Peierls substitution in the hopping matrix elements. Implementing this approach in a ribbon geometry, we obtain both the Landau levels and the dispersive edge states for a series of 2D crystals, including graphene, Boron Nitride, MoS2, Black Phosphorous, Indium Selenide and MoO3. Our procedure can readily be used in any other 2D crystal, and provides an alternative to effective mass descriptions.
Surface-modified Wannier-Stark states in a 1D optical lattice
Maury, A; Gorza, M -P; Lambrecht, A; Guérout, R
2016-01-01
We study the energy spectrum of atoms trapped in a vertical 1D optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our model includes the long-range Casimir-Polder potential together with a short-range Lennard-Jones potential, which are considered non-perturbatively with respect to the optical lattice potential. We find an intricate energy spectrum which contains a pair of loosely-bound states localized close to the surface in addition to a surface-modified Wannier-Stark ladder at long distances. Atomic interferometry involving those loosely-bound atom-surface states is proposed to probe the adsorption dynamics of atoms on mirrors.
Wannier-Stark localization and terahertz electroluminescence of natural SiC superlattice
Sankin, V. I.; Andrianov, A. V.; Petrov, A. G.; Zakhar' in, A. O. [A.F. Ioffe Physical Technical Institute, 194021 St. Petersburg (Russian Federation)
2013-12-04
We report on efficient terahertz electroluminescence in the region of 1.5-2 THz from high electric field biased 6H-SiC n{sup +}−n{sup −}−n{sup +} structures with a natural superlattice at 7 K. The properties of the terahertz emission allow it to be attributed to spontaneous radiation resulting from electron Bloch oscillations in SiC natural superlattice. The use of the unique object, namely, natural superlattice of SiC allowed us to demonstrate a whole series of remarkable effects of Wannier-Stark localization and to get the intensive terahertz emission under steady-state electrical excitation of Bloch oscillations.
Giustino, Feliciano
2008-03-01
The interaction between electrons and phonons is central to many phenomena, including electrical and thermal transport and superconductivity. Recently the electron-phonon (e-ph) interaction has been the focus of intense research efforts in the physics of high-temperature superconductivity and nanoscale transport. Despite the continued interest in the e-ph problem, first-principles calculations remain challenging due to the large computational effort required to describe e-ph scattering processes in the proximity of the Fermi surface. In this talk I will present a method based on Wannier functions which greatly reduces the computational cost of e-ph calculations [1,2]. The underlying idea is to exploit the spatial localization of electrons and phonons in the maximally localized Wannier representation. After describing the method I will review recent applications to materials of current interest. I will discuss how the e-ph interaction affects the dynamics of Dirac fermions in graphene [3], the origin of superconductivity in boron-doped diamond [1], and the relation between Fermi surface topology and superconductivity in super-hard carbides. I will conclude this presentation by discussing the role of phonons in the angle-resolved photoemission spectra of cuprates [4]. [1] F. Giustino, J.R. Yates, I. Souza, M.L. Cohen, and S.G. Louie, Phys. Rev. Lett. 98, 047005 (2007). [2] F. Giustino, M.L. Cohen, and S.G. Louie, Phys. Rev. B 76, 165108 (2007). [3] C.-H. Park, F. Giustino, M.L. Cohen, and S.G. Louie, Phys. Rev. Lett. 99, 086804 (2007). [4] F. Giustino, M.L. Cohen, and S.G. Louie, http://arXiv:0710.2146.
Sukhomlinov, Sergey V.; Smirnov, Konstantin S.
2012-11-01
The interatomic C6 dispersion coefficients in crystalline and amorphous SiO2 and ZrO2 structures were obtained with the approach proposed by Silvestrelli (2008 Phys. Rev. Lett. 100 053002) and based on the use of maximally localized Wannier functions (MLWFs) for partitioning the electron density. Localization of Wannier functions close to the nuclei in oxide systems makes it possible to assign the MLWFs to the atoms in an unambiguous way and then to compute the C6 coefficients in an atom pairwise manner. A modification of the method is suggested in which the MLWFs are condensed to effective orbitals centred on the atoms and parameters of these effective orbitals are used for computing the interatomic dispersion coefficients. The obtained values of the dispersion coefficients were found to vary not only from one oxide to another, but also between different modifications of the same compound. The oxygen-oxygen coefficient {C}_{6}^{{OO}} reveals the largest variation and its value in ZrO2 structures is twice as large as that in SiO2 ones. Atomic characteristics obtained in the frame of the effective orbital method, such as the self-atom dispersion coefficient, and the oxide ion polarizability were found to correlate with the metal-oxygen bond length and the oxygen coordination number in the systems. This behaviour is attributed to the confinement of electrons by the electrostatic potential. The values of the coefficient and of the polarizability were related to charges of the oxygen atoms. In all studied systems the oxygen atoms having larger absolute values of charge were found to be less polarizable because of a stronger confinement effect. The obtained results can be used in the development of polarizable force fields for the atomistic modelling of oxide materials.
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Holographic Renormalization in Dense Medium
Chanyong Park
2014-01-01
describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space.
Concepts of renormalization in physics.
Alexandre, Jean
2005-01-01
A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, and then show how similar ideas appear in particle physics. This short review is written for non-particle physicists and/or students aiming at studying particle physics.
Renormalization group flows and anomalies
Komargodski, Zohar
2015-01-01
This chapter reviews various aspects of renormalization group flows and anomalies. The chapter considers specific Euclidean two-dimensional theories. Namely, the theories are invariant under translations and rotations in the two space directions. Here the chapter studies theories where, if possible, certain equations hold in fact also at coincident points. In other words, the chapter looks at theories where there is no local gravitational anomaly.
Renormalization of Dirac's Polarized Vacuum
Lewin, Mathieu
2010-01-01
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\\Lambda$. We then discuss the limit $\\Lambda\\to\\infty$ in detail, by resorting to charge renormalization.
Sleep and Synaptic Renormalization: A Computational Study
Olcese, Umberto; Esser, Steve K.
2010-01-01
Recent evidence indicates that net synaptic strength in cortical and other networks increases during wakefulness and returns to a baseline level during sleep. These homeostatic changes in synaptic strength are accompanied by corresponding changes in sleep slow wave activity (SWA) and in neuronal firing rates and synchrony. Other evidence indicates that sleep is associated with an initial reactivation of learned firing patterns that decreases over time. Finally, sleep can enhance performance of learned tasks, aid memory consolidation, and desaturate the ability to learn. Using a large-scale model of the corticothalamic system equipped with a spike-timing dependent learning rule, in agreement with experimental results, we demonstrate a net increase in synaptic strength in the waking mode associated with an increase in neuronal firing rates and synchrony. In the sleep mode, net synaptic strength decreases accompanied by a decline in SWA. We show that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength. Moreover, when the model “learns” a sequence of activation during waking, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time. Finally, sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios, increased resistance to interference, and desaturation of learning capabilities. Although the specific mechanisms implemented in the model cannot capture the variety and complexity of biological substrates, and will need modifications in line with future evidence, the present simulations provide a unified, parsimonious account for diverse experimental findings coming from molecular, electrophysiological, and behavioral approaches. PMID:20926617
Improved Lattice Renormalization Group Techniques
Petropoulos, Gregory; Hasenfratz, Anna; Schaich, David
2013-01-01
We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.
Simple approach to renormalize the Cabibbo-Kabayashi-Maskawa matrix
Kniehl, B.A.; Sirlin, A. [Max-Planck-Institut fuer Physik, Muenchen (Germany)
2006-08-15
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix at the one-loop level. After explaining how to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, the mass counterterms are chosen to cancel all divergent sm contributions, and also their finite parts subject to hermiticity constraints. The proof of gauge independence and finiteness of the remaining one-loop corrections to W{yields} q{sub i}+ anti q{sub j} reduces to the single-generation case. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which is gauge independent and preserves unitarity. (orig.)
Renormalization group analysis of graphene with a supercritical Coulomb impurity
Nishida, Yusuke
2016-01-01
We develop a field theoretical approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.
Renormalization group analysis of graphene with a supercritical Coulomb impurity
Nishida, Yusuke
2016-08-01
We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial-wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power-law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.
Complex networks renormalization: flows and fixed points.
Radicchi, Filippo; Ramasco, José J; Barrat, Alain; Fortunato, Santo
2008-10-03
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.
Constraining differential renormalization in abelian gauge theories
del Águila, F; Tapia, R M; Pérez-Victoria, M
1998-01-01
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.
Quark Confinement and the Renormalization Group
Ogilvie, Michael C
2010-01-01
Recent approaches to quark confinement are reviewed, with an emphasis on their connection to renormalization group methods. Basic concepts related to confinement are introduced: the string tension, Wilson loops and Polyakov lines, string breaking, string tension scaling laws, center symmetry breaking, and the deconfinement transition at non-zero temperature. Current topics discussed include confinement on $R^3\\times S^1$, the real-space renormalization group, the functional renormalization group, and the Schwinger-Dyson equation approach to confinement.
Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials
Gresch, Dominik; Autès, Gabriel; Yazyev, Oleg V.; Troyer, Matthias; Vanderbilt, David; Bernevig, B. Andrei; Soluyanov, Alexey A.
2017-02-01
The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k .p models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, Z2, and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.
All-order renormalization of propagator matrix for fermionic system with flavor mixing
Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2013-08-15
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.
All-order renormalization of the propagator matrix for fermionic systems with flavor mixing.
Kniehl, Bernd A
2014-02-21
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 and their expansions through two loops 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.
Zhou, YE; Vahala, George
1993-01-01
The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.
Renormalization of Extended QCD$_2$
Fukaya, Hidenori
2015-01-01
Extended QCD (XQCD) proposed by Kaplan [1] is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low energy hadronic models. We analyze the renormalization group flow of two-dimensional (X)QCD, which is solvable in the limit of large number of colors Nc, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low energy region.
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)
2013-08-01
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).
Renormalization of dimension 6 gluon operators
HyungJoo Kim
2015-09-01
Full Text Available We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.
Improved system identification with Renormalization Group.
Wang, Qing-Guo; Yu, Chao; Zhang, Yong
2014-09-01
This paper proposes an improved system identification method with Renormalization Group. Renormalization Group is applied to a fine data set to obtain a coarse data set. The least squares algorithm is performed on the coarse data set. The theoretical analysis under certain conditions shows that the parameter estimation error could be reduced. The proposed method is illustrated with examples.
Renormalization of Lepton Mixing for Majorana Neutrinos
Broncano, A; Jenkins, E; Jenkins, Elizabeth
2005-01-01
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
Renormalization of lepton mixing for Majorana neutrinos
Broncano, A. [Departamento de Fisica Teorica, C-XI, and IFT, C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)]. E-mail: alicia.broncano@uam.es; Gavela, M.B. [Departamento de Fisica Teorica, C-XI, and IFT, C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)]. E-mail: gavela@delta.ft.uam.es; Jenkins, Elizabeth [Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)]. E-mail: ejenkins@ucsd.edu
2005-01-17
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
An alternative to exact renormalization equations
Alexandre, Jean
2005-01-01
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective action, and recovers usual renormalization results.
Wavelet view on renormalization group
Altaisky, M V
2016-01-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier described in {\\em Phys.Rev.D} 81(2010)125003, 88(2013)025015, is finite by construction. The space of scale-dependent functions $\\{ \\phi_a(x) \\}$ is more relevant to physical reality than the space of square-integrable functions $\\mathrm{L}^2(R^d)$, because, due to the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than point. The effective action $\\Gamma_{(A)}$ of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet -- an "aperture function" of a measuring device used to produce the snapshot of a field $\\phi$ at the point $x$ with the resolution $a$. The standard RG results for $\\phi^4$ model are reproduced.
Renormalized Wick expansion for a modified PQCD
de Oca, Alejandro Cabo Montes
2007-01-01
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 counter-terms are allowed in this mass less 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 to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows 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 $m_q$ and $m_g$ 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...
Renormalized Wick expansion for a modified PQCD
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)
2008-05-15
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.)
Density matrix renormalization group numerical study of the kagome antiferromagnet.
Jiang, H C; Weng, Z Y; Sheng, D N
2008-09-12
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
Method of renormalization potential for one model of Hartree-Fock-Slater type
Zasorin, Y V
2002-01-01
A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential
Estevez, J Octavio; Arriaga, Jesús; Mendez-Blas, Antonio; Reyes-Ayona, Edgar; Escorcia, José; Agarwal, Vivechana
2012-07-23
: Theoretical demonstration and experimental evidence of photon Bloch oscillations and Wannier-Stark ladders (WSLs) in dual-periodical (DP) multilayers, based on porous silicon, are presented. An introduction of the linear gradient in refractive indices in DP structure, which is composed by stacking two different periodic substructures N times, resulted in the appearance of WSLs. Theoretical time-resolved reflection spectrum shows the photon Bloch oscillations with a period of 130 fs. Depending on the values of the structural parameters, one can observe the WSLs in the near infrared or visible region which may allow the generation of terahertz radiation with a potential applications in several fields like imaging.
Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective
Zhou, Ye; McComb, W. David; Vahala, George
1997-01-01
The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.
Renormalization algorithm with graph enhancement
Hübener, R; Hartmann, L; Dür, W; Plenio, M B; Eisert, J
2011-01-01
We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states (PEPS). We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with tensor tree states can greatly improve the accuracy of the description of ground states and time evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.
Renormalization group analysis of turbulence
Smith, Leslie M.
1989-01-01
The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.
Multilogarithmic velocity renormalization in graphene
Sharma, Anand; Kopietz, Peter
2016-06-01
We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene. Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff scheme, we calculate the quasiparticle velocity, v (k ) , and the quasiparticle residue, Z , with frequency-dependent polarization. One of our most striking results is that v (k ) ∝ln[Ck(α ) /k ] where the momentum- and interaction-dependent cutoff scale Ck(α ) vanishes logarithmically for k →0 . Here k is measured with respect to one of the charge neutrality (Dirac) points and α =2.2 is the strength of dimensionless bare interaction. Moreover, we also demonstrate that the so-obtained multilogarithmic singularity is reconcilable with the perturbative expansion of v (k ) in powers of the bare interaction.
Gauge invariance and holographic renormalization
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Renormalization of two-dimensional quantum electrodynamics
Casana S, Rodolfo; Dias, Sebastiao A
1997-12-01
The Schwinger model, when quantized in a gauge non-invariant way exhibits a dependence on a parameter {alpha} (the Jackiw-Rajaraman parameter) in a way which is analogous to the case involving chiral fermions (the chiral Schwinger model). For all values of a {alpha}1, there are divergences in the fermionic Green`s functions. We propose a regularization of the generating functional Z [{eta}, {eta}, J] and we use it to renormalize the theory to one loop level, in a semi-perturbative sense. At the end of the renormalization procedure we find an implicit dependence of {alpha} on the renormalization scale {mu}. (author) 26 refs.
Mass Renormalization in String Theory: General States
Pius, Roji; Sen, Ashoke
2014-01-01
In a previous paper we described a procedure for computing the renormalized masses and S-matrix elements in bosonic string theory for a special class of massive states which do not mix with unphysical states under renormalization. In this paper we extend this result to general states in bosonic string theory, and argue that only the squares of renormalized physical masses appear as the locations of the poles of the S-matrix of other physical states. We also discuss generalizations to Neveu-Schwarz sector states in heterotic and superstring theories.
Aspects of Galileon non-renormalization
Goon, Garrett [Department of Applied Mathematics and Theoretical Physics, Cambridge University,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Hinterbichler, Kurt [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario, N2L 2Y5 (Canada); Joyce, Austin [Enrico Fermi Institute and Kavli Institute for Cosmological Physics, University of Chicago,S. Ellis Avenue, Chicago, IL 60637 (United States); Trodden, Mark [Center for Particle Cosmology, Department of Physics and Astronomy,University of Pennsylvania,S. 33rd Street, Philadelphia, PA 19104 (United States)
2016-11-18
We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and P(X) theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. However, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.
Real-space renormalization yields finite correlations.
Barthel, Thomas; Kliesch, Martin; Eisert, Jens
2010-07-02
Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law.
Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
Gallavotti, G.
1985-04-01
A self-contained analysis is given of the simplest quantum fields from the renormalization group point of view: multiscale decomposition, general renormalization theory, resummations of renormalized series via equations of the Callan-Symanzik type, asymptotic freedom, and proof of ultraviolet stability for sine-Gordon fields in two dimensions and for other super-renormalizable scalar fields. Renormalization in four dimensions (Hepp's theorem and the De Calan--Rivasseau nexclamation bound) is presented and applications are made to the Coulomb gases in two dimensions and to the convergence of the planar graph expansions in four-dimensional field theories (t' Hooft--Rivasseau theorem).
Exact Renormalization of Massless QED2
Casana, R; Casana, Rodolfo; Dias, Sebastiao Alves
2001-01-01
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Exact Renormalization of Massless QED2
Casana, Rodolfo; Dias, Sebastião Alves
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Efimov physics from a renormalization group perspective
Hammer, Hans-Werner; Platter, Lucas
2011-01-01
We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.
Efimov physics from a renormalization group perspective.
Hammer, Hans-Werner; Platter, Lucas
2011-07-13
We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.
Lectures on the functional renormalization group method
Polonyi, J
2001-01-01
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed poin...
Improved Monte Carlo Renormalization Group Method
Gupta, R.; Wilson, K. G.; Umrigar, C.
1985-01-01
An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.
Towards Holographic Renormalization of Fake Supergravity
Borodatchenkova, Natalia; Mueck, Wolfgang
2008-01-01
A step is made towards generalizing the method of holographic renormalization to backgrounds which are not asymptotically AdS, corresponding to a dual gauge theory which has logarithmically running couplings even in the ultraviolet. A prime example is the background of Klebanov-Strassler (KS). In particular, a recipe is given how to calculate renormalized two-point functions for the operators dual to the bulk scalars. The recipe makes use of gauge-invariant variables for the fluctuations around the background and works for any bulk theory of the fake supergravity type. It elegantly incorporates the renormalization scheme dependence of local terms in the correlators. Before applying the method to the KS theory, it is verified that known results in asymptotically AdS backgrounds are reproduced. Finally, some comments on the calculation of renormalized vacuum expectation values are made.
Sector-dependent versus standard renormalization of Pauli-Villars-regulated light-front QED
Chabysheva, S S
2009-01-01
We consider quantum electrodynamics quantized on the light front in Feynman gauge and regulated in the ultraviolet by the inclusion of massive, negative-metric Pauli--Villars (PV) particles in the Lagrangian. The eigenstate of the electron is approximated by a Fock-state expansion truncated to include one photon. The Fock-state wave functions are computed from the fundamental Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic moment. Two methods of renormalization are considered: a sector-dependent renormalization, where the bare parameters of the Lagrangian are allowed to depend on the Fock sectors between which the particular Hamiltonian term acts, and a standard renormalization, where the bare parameters are the same for all sectors. Both methods are shown to require some care with respect to ultraviolet divergences; neither method can allow all PV masses to be taken to infinity. In addition, the sector-dependent approach suffers from an infrared divergence that requires a nonzero ...
Renormalization-group improved inflationary scenarios
Pozdeeva, E O
2016-01-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
Renormalization-group improved inflationary scenarios
Pozdeeva, E. O.; Vernov, S. Yu.
2017-03-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
Relativistic causality and position space renormalization
Ivan Todorov
2016-01-01
The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (t...
Renormalization in Periodically Driven Quantum Dots.
Eissing, A K; Meden, V; Kennes, D M
2016-01-15
We report on strong renormalization encountered in periodically driven interacting quantum dots in the nonadiabatic regime. Correlations between lead and dot electrons enhance or suppress the amplitude of driving depending on the sign of the interaction. Employing a newly developed flexible renormalization-group-based approach for periodic driving to an interacting resonant level we show analytically that the magnitude of this effect follows a power law. Our setup can act as a non-Markovian, single-parameter quantum pump.
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Higher loop renormalization of fermion bilinear operators
Skouroupathis, A
2007-01-01
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\\bar\\psi\\Gamma\\psi$, where $\\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_\\psi$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. A longer write-up of the present work, including the conversion of our results to the MSbar scheme and a generalization to arbitrary fermion representations, can be found in arXiv:0707.2906 .
Euclidean Epstein-Glaser renormalization
Keller, Kai J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2009-03-15
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.)
Oono, Y.; Freed, Karl F.
1981-07-01
A conformation space renormalization group is developed to describe polymer excluded volume in single polymer chains. The theory proceeds in ordinary space in terms of position variables and the contour variable along the chain, and it considers polymers of fixed chain length. The theory is motivated along two lines. The first presents the renormalization group transformation as the means for extracting the macroscopic long wavelength quantities from the theory. An alternative viewpoint shows how the renormalization group transformation follows as a natural consequence of an attempt to correctly treat the presence of a cut-off length scale. It is demonstrated that the current configuration space renormalization method has a one-to-one correspondence with the Wilson-Fisher field theory formulation, so our method is valid to all orders in ɛ = 4-d where d is the spatial dimensionality. This stands in contrast to previous attempts at a configuration space renormalization approach which are limited to first order in ɛ because they arbitrarily assign monomers to renormalized ''blobs.'' In the current theory the real space chain conformations dictate the coarse graining transformation. The calculations are presented to lowest order in ɛ to enable the development of techniques necessary for the treatment of dynamics in Part II. The theory is presented both in terms of the simple delta function interaction as well as using realistic-type interaction potentials. This illustrates the renormalization of the interactions, the emergence of renormalized many-body interactions, and the complexity of the theta point.
van Enter, A C; Fernández, R
1999-05-01
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram.
Enter, Aernout C.D. van; Fernández, Roberto
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the
Dynamic renormalization in the framework of nonequilibrium thermodynamics.
Ottinger, Hans Christian
2009-02-01
We show how the dynamic renormalization of nonequilibrium systems can be carried out within the general framework of nonequilibrium thermodynamics. Whereas the renormalization of Hamiltonians is well known from equilibrium thermodynamics, the renormalization of dissipative brackets, or friction matrices, is the main new feature for nonequilibrium systems. Renormalization is a reduction rather than a coarse-graining technique; that is, no new dissipative processes arise in the dynamic renormalization procedure. The general ideas are illustrated for dilute polymer solutions where, in renormalizing bead-spring chain models, dissipative hydrodynamic interactions between different smaller beads contribute to the friction coefficient of a single larger bead.
First principles calculations for liquids and solids using maximally localized Wannier functions
Swartz, Charles W., VI
The field of condensed matter computational physics has seen an explosion of applicability over the last 50+ years. Since the very first calculations with ENIAC and MANIAC the field has continued to pushed the boundaries of what is possible; from the first large-scale molecular dynamics simulation, to the implementation of Density Functional Theory and large scale Car-Parrinello molecular dynamics, to million-core turbulence calculations by Standford. These milestones represent not only technological advances but theoretical breakthroughs and algorithmic improvements as well. The work in this thesis was completed in the hopes of furthering such advancement, even by a small fraction. Here we will focus mainly on the calculation of electronic and structural properties of solids and liquids, where we shall implement a wide range of novel approaches that are both computational efficient and physically enlightening. To this end we routinely will work with maximally localized Wannier functions (MLWFs) which have recently seen a revival in mainstream scientific literature. MLWFs present us with interesting opportunity to calculate a localized orbital within the planewave formalism of atomistic simulations. Such a localization will prove to be invaluable in the construction of layer-based superlattice models, linear scaling hybrid functional schemes and model quasiparticle calculations. In the first application of MLWF we will look at modeling functional piezoelectricity in superlattices. Based on the locality principle of insulating superlattices, we apply the method of Wu et al to the piezoelectric strains of individual layers under iifixed displacement field. For a superlattice of arbitrary stacking sequence an accurate model is acquired for predicting piezoelectricity. By applying the model in the superlattices where ferroelectric and antiferrodistortive modes are in competition, functional piezoelectricity can be achieved. A strong nonlinear effect is observed and can
Contractor renormalization group and the Haldane conjecture
Weinstein, Marvin
2001-05-01
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.
Kammerlander, David; Botti, Silvana; Marques, Miguel A. L.; Marini, Andrea; Attaccalite, Claudio
2012-09-01
The Bethe-Salpeter equation is a widely used approach to describe optical excitations in bulk semiconductors. It leads to spectra that are in very good agreement with experiment, but the price to pay for such accuracy is a very high computational burden. One of the main bottlenecks is the large number of k points required to obtain converged spectra. In order to circumvent this problem we propose a strategy to solve the Bethe-Salpeter equation based on a double-grid technique coupled to a Wannier interpolation of the Kohn-Sham band structure. This strategy is then benchmarked for a particularly difficult case, the calculation of the absorption spectrum of GaAs, and for the well-studied case of Si. The considerable gains observed in these cases fully validate our approach, and open the way for the application of the Bethe-Salpeter equation to large and complex systems.
Renormalization group independence of Cosmological Attractors
Fumagalli, Jacopo
2017-06-01
The large class of inflationary models known as α- and ξ-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters (ns , r) are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular ξ-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Perturbatively improving RI-MOM renormalization constants
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Foundations and Applications of Entanglement Renormalization
Evenbly, Glen
2011-01-01
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence of the difficultly of the so-called many-body problem, many exotic quantum phenomena involving extended systems, such as high temperature superconductivity, remain not well understood on a theoretical level. Entanglement renormalization is a recently proposed numerical method for the simulation of many-body systems which draws together ideas from the renormalization group and from the field of quantum information. By taking due care of the quantum entanglement of a system, entanglement renormalization has the potential to go beyond the limitations of previous numerical methods and to provide new insight to quantum collective phenomena. This thesis comprises a significant portion of the research development of ER following its initial proposal. This includes exploratory stud...
Renormalized vacuum polarization of rotating black holes
Ferreira, Hugo R C
2015-01-01
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.
Perturbatively improving RI-MOM renormalization constants
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Wilsonian renormalization, differential equations and Hopf algebras
Thomas, Krajewski
2008-01-01
In this paper, we present an algebraic formalism inspired by Butcher's B-series in numerical analysis and the Connes-Kreimer approach to perturbative renormalization. We first define power series of non linear operators and propose several applications, among which the perturbative solution of a fixed point equation using the non linear geometric series. Then, following Polchinski, we show how perturbative renormalization works for a non linear perturbation of a linear differential equation that governs the flow of effective actions. Finally, we define a general Hopf algebra of Feynman diagrams adapted to iterations of background field effective action computations. As a simple combinatorial illustration, we show how these techniques can be used to recover the universality of the Tutte polynomial and its relation to the $q$-state Potts model. As a more sophisticated example, we use ordered diagrams with decorations and external structures to solve the Polchinski's exact renormalization group equation. Finally...
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wu, Xing-Gang [Chongqing Univ. (China); SLAC National Accelerator Lab., Menlo Park, CA (United States)
2012-08-07
In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {β^{R}_{i}}-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.
Durães F.O.
2010-04-01
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.
Alleviating the window problem in large volume renormalization schemes
Korcyl, Piotr
2017-01-01
We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$ ensembles generated at 5 different lattice spacings. We show that in the advocated strategy results for the renormalization constants are to a large extend independent of the specific lattice direction used to define the renormalization condition. Hence, ver...
Loop Optimization for Tensor Network Renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-01
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.
Relativistic causality and position space renormalization
Todorov, Ivan
2016-11-01
The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior) in the case of the massless φ4 theory and display the dilation and the conformal anomaly.
Renormalization Group independence of Cosmological Attractors
Fumagalli, Jacopo
2016-01-01
The large class of inflationary models known as $\\alpha$- and $\\xi$-attractors give identical predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Renormalization of Wilson operators in Minkowski space
Andra, A
1996-01-01
We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge renormalization does not work in a simple graph-by-graph way; but does work when certain graphs are added together. We also verify that, in a simple example of a smooth loop in Minkowski space, the existence of pairs of points which are light-like separated does not cause any extra divergences.
Novel formulations of CKM matrix renormalization
Kniehl, B A
2009-01-01
We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.
Exact Renormalization Group for Point Interactions
Eröncel, Cem
2014-01-01
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble non-abelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Automating Renormalization of Quantum Field Theories
Kennedy, A D; Rippon, T
2007-01-01
We give an overview of state-of-the-art multi-loop Feynman diagram computations, and explain how we use symbolic manipulation to generate renormalized integrals that are then evaluated numerically. We explain how we automate BPHZ renormalization using "henges" and "sectors", and give a brief description of the symbolic tensor and Dirac gamma-matrix manipulation that is required. We shall compare the use of general computer algebra systems such as Maple with domain-specific languages such as FORM, highlighting in particular memory management issues.
Random vibrational networks and the renormalization group.
Hastings, M B
2003-04-11
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results.
Relativistic causality and position space renormalization
Ivan Todorov
2016-11-01
Full Text Available The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with “quantum periods” and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior in the case of the massless φ4 theory and display the dilation and the conformal anomaly.
Information geometry and the renormalization group.
Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata
2015-11-01
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.
Loop Optimization for Tensor Network Renormalization.
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-17
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.
EXACT RENORMALIZATION GROUP FOR POINT INTERACTIONS
Osman Teoman Turgut Teoman Turgut
2014-04-01
Full Text Available Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble nonabelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Perturbative renormalization of the electric field correlator
Christensen, C
2016-01-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
C. Christensen
2016-04-01
Full Text Available The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3 gauge theory, finding a ∼12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
Christensen, C.; Laine, M.
2016-04-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ∼ 12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Hypercuboidal renormalization in spin foam quantum gravity
Bahr, Benjamin; Steinhaus, Sebastian
2017-06-01
In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.
Renormalized dissipation in plasmas with finite collisionality
Parker, S.E. [Princeton Plasma Physics Lab., NJ (United States); Carati, D. [Universite Libre de Bruxelles (Belgium). Service de Physique Statistique
1995-05-01
A nonlinear truncation procedure for Fourier-Hermite expansion of Boltzmann-type plasma equations is presented which eliminates fine velocity scale, taking into account its effect on coarser scales. The truncated system is then transformed back to (x, v) space which results in a renormalized Boltzmann equation. The resulting equation may allow for coarser velocity space resolution in kinetic simulations while reducing to the original Boltzmann equation when fine velocity scales are resolved. To illustrate the procedure, renormalized equations are derived for one dimensional electrostatic plasmas in which collisions are modeled by the Lenard-Bernstein operator.
Supersymmetric O(N) models in d=3 with functional renormalization group (FRG) methods
Hellwig, Tobias; Heilmann, Marianne; Wipf, Andreas [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Lithim, Daniel F. [Department of Physics and Astronomy, University of Sussex, BN1 9QH, Brighton (United Kingdom)
2013-07-01
While a lot of results concerning scalar O(N) models are known, much less is known for supersymmetric O(N) models. The 1/N expansions were examined in some earlier works with the help of the Hartree-Fock approximation. In this talk results for all N are presented. These results were obtained by using FRG methods and a manifest supersymmetric regulator. For finite N fixed point solutions and critical exponents are obtained. We comment on effects of different truncations in the effective average action. Starting point is the LPA approximation. In a second step a wave function renormalization is included and deviations from LPA solution are discussed. This is done for a field dependent and field independent form of the wave function renormalization. This knowledge could also prove to be helpful for further FRG studies of supersymmetric theories.
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal
2016-01-01
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal; Andersen, Jens O.
2017-02-01
In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in 1 +1 dimensions in the large-Nc limit and in the 3 +1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Enhancement of field renormalization in scalar theories via functional renormalization group
Zappalà, Dario
2012-01-01
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, to determine the effective potential and the renormalization function of the field in the broken phase. The flow equations of these quantities are derived from a reduction of the full flow of the effective action onto a set of equations for the n-point vertices of the theory. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.
Bonini, M; Marchesini, G
1993-01-01
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the ``relevant'' vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.
Bonini, M.; D'Attanasio, M.; Marchesini, G.
1993-11-01
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the "relevant" vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)
2006-12-15
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.)
Composite operators in lattice QCD nonperturbative renormalization
Göckeler, M; Oelrich, H; Perlt, H; Petters, D; Rakow, P; Schäfer, A; Schierholz, G; Schiller, A
1999-01-01
We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
Renormalization Group Equations for the CKM matrix
Kielanowski, P; Montes de Oca Y, J H
2008-01-01
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs extension and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle $\\alpha$ of the unitarity triangle. For the special case of the Standard Model and its extensions with $v_{1}\\approx v_{2}$ we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters $\\bar{\\rho}=(1-{1/2}\\lambda^{2})\\rho$ and $\\bar{\\eta}=(1-{1/2}\\lambda^{2})\\eta$ are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix mi...
Finite volume renormalization scheme for fermionic operators
Monahan, Christopher; Orginos, Kostas [JLAB
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
RENORMALIZED ENERGY WITH VORTICES PINNING EFFECT
Ding Shijin
2000-01-01
This paper is a continuation of the previous paper in the Journal of Partial Differential Equations [1]. We derive in this paper the renormalized energy to further determine the locations of vortices in some case for the variational problem related to the superconducting thin films having variable thickness.
Complete renormalization of QCD at five loops
Luthe, Thomas; Maier, Andreas; Marquard, Peter; Schröder, York
2017-03-01
We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.
Renormalization and effective actions for general relativity
Neugebohrn, F.
2007-05-15
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.)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many t...
Korytar, Richard; Pruneda, Miguel; Ordejon, Pablo; Lorente, Nicolas [Centre d' Investigacio en Nanociencia i Nanotecnologia (CSIC-ICN), Campus de la UAB, E-08193 Bellaterra (Spain); Junquera, Javier, E-mail: rkorytar@cin2.e [Departamento de Ciencias de la Tierra y Fisica de la Materia Condensada, Universidad de Cantabria, E-39005 Santander (Spain)
2010-09-29
We have adapted the maximally localized Wannier function approach of Souza et al (2002 Phys. Rev. B 65 035109) to the density functional theory based SIESTA code (Soler et al 2002 J. Phys.: Condens. Mater. 14 2745) and applied it to the study of Co substitutional impurities in bulk copper as well as to the Cu(111) surface. In the Co impurity case, we have reduced the problem to the Co d-electrons and the Cu sp-band, permitting us to obtain an Anderson-like Hamiltonian from well defined density functional parameters in a fully orthonormal basis set. In order to test the quality of the Wannier approach to surfaces, we have studied the electronic structure of the Cu(111) surface by again transforming the density functional problem into the Wannier representation. An excellent description of the Shockley surface state is attained, permitting us to be confident in the application of this method to future studies of magnetic adsorbates in the presence of an extended surface state.
Functional renormalization group study of fluctuation effects in fermionic superfluids
Eberlein, Andreas
2013-03-22
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
Renormalization of Magnetic Excitations in Praseodymium
Lindgård, Per-Anker
1975-01-01
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...... and the ratio between the exchange interaction and d is very close to unity. However, zero-point motion prevents the system from ordering.......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...
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
Information loss along the renormalization flow
Beny, Cedric; Osborne, Tobias [Leibniz Universitaet Hannover (Germany)
2013-07-01
Our ability to probe the real world is always limited by experimental constraints such as the precision of our instruments. It is remarkable that the resulting imperfect data nevertheless contains regularities which can be understood in terms of effective laws. The renormalization group (RG) aims to formalize the relationship between effective theories summarizing the behaviour of a single system probed at different length scales. An important feature of the RG is its tendency to converge to few universal effective field theories at large scale. We explicitly model the change of resolution at which a quantum lattice system is probed as a completely positive semigroup on density operators, i.e., a family of quantum channels, and derive from it a renormalization ''group'' on effective theories. This formalism suggests a family of finite distinguishability metrics which contract under the RG, hence identifying the information that is lost on the way to universal RG fixed points.
Poissonian renormalizations, exponentials, and power laws
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Holographic renormalization and the electroweak precision parameters
Round, Mark
2010-09-01
We study the effects of holographic renormalization on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS5 geometry containing a bulk scalar and SU(2)×SU(2) gauge fields. The scalar field obtains a vacuum expectation value (VEV) which represents a condensate that triggers electroweak symmetry breaking. Fermion fields are constrained to live on the UV brane and do not propagate in the bulk. The two-point functions are holographically renormalized through the addition of boundary counterterms. Measurable quantities are then expressed in terms of well-defined physical parameters, free from any spurious dependence on the UV cutoff. A complete study of the precision parameters is carried out and bounds on physical quantities derived. The large-N scaling of results is discussed.
ENCORE: An extended contractor renormalization algorithm.
Albuquerque, A Fabricio; Katzgraber, Helmut G; Troyer, Matthias
2009-04-01
Contractor renormalization (CORE) is a real-space renormalization-group method to derive effective Hamiltionians for microscopic models. The original CORE method is based on a real-space decomposition of the lattice into small blocks and the effective degrees of freedom on the lattice are tensor products of those on the small blocks. We present an extension of the CORE method that overcomes this restriction. Our generalization allows the application of CORE to derive arbitrary effective models whose Hilbert space is not just a tensor product of local degrees of freedom. The method is especially well suited to search for microscopic models to emulate low-energy exotic models and can guide the design of quantum devices.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Accurate renormalization group analyses in neutrino sector
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)
2014-08-15
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.
Heisenberg's wave packet reconsidered
Grabbe, J. Orlin
2005-01-01
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing Heisenberg's restrictions leads to a more general formulation of the uncertainty principle. This reformulation shows quantum uncertainty can exist at a macroscopic level. These modifications also give rise to a new form of Schrodinger's wave equation as the...
Biswas, P K; Gogonea, V
2005-10-22
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.
Disordered Holographic Systems I: Functional Renormalization
Adams, Allan
2011-01-01
We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance or marginality of quenched disorder holds.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
Renormalized versions of the massless Thirring model
Casana, R
2003-01-01
We present a non-perturbative study of the (1+1)-dimensional massless Thirring model by using path integral methods. The model presents two features, one of them has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. We make a detailed analysis of their UV divergence structure, a non-perturbative regularization and renormalization processes are proposed.
Dense nucleonic matter and the renormalization group
Drews, Matthias; Klein, Bertram; Weise, Wolfram
2013-01-01
Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.
Dense nucleonic matter and the renormalization group
Drews Matthias
2014-03-01
Full Text Available Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.
Field renormalization in photonic crystal waveguides
Colman, Pierre
2015-01-01
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....
Renormalization of QCD under longitudinal rescaling
Xiao, Jing
2009-01-01
The form of the quantum Yang-Mills action, under a longitudinal rescaling is determined using a Wilsonian renormalization group. The high-energy limit, is the extreme limit of such a rescaling. We compute the anomalous dimensions and discuss the validity of the high-energy limit. This thesis is an expanded version of joint work with P. Orland, which appeared in arXiv:0901.2955.
A Hopf algebra deformation approach to renormalization
Ionescu, L M; Ionescu, Lucian M.; Marsalli, Michael
2003-01-01
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and double Lie algebras/Lie bialgebras, via r-matrices. It is suggested that the QFTs obtained via deformation quantization and renormalization correspond to each other in the sense of Kontsevich/Cattaneo-Felder.
Zero Point Energy of Renormalized Wilson Loops
Hidaka, Yoshimasa; Pisarski, Robert D.
2009-01-01
The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero wh...
Quark confinement and the renormalization group.
Ogilvie, Michael C
2011-07-13
Recent approaches to quark confinement are reviewed, with an emphasis on their connection to renormalization group (RG) methods. Basic concepts related to confinement are introduced: the string tension, Wilson loops and Polyakov lines, string breaking, string tension scaling laws, centre symmetry breaking and the deconfinement transition at non-zero temperature. Current topics discussed include confinement on R(3)×S(1), the real-space RG, the functional RG and the Schwinger-Dyson equation approach to confinement.
Renormalization group and linear integral equations
Klein, W.
1983-04-01
We develop a position-space renormalization-group transformation which can be employed to study general linear integral equations. In this Brief Report we employ our method to study one class of such equations pertinent to the equilibrium properties of fluids. The results of applying our method are in excellent agreement with known numerical calculations where they can be compared. We also obtain information about the singular behavior of this type of equation which could not be obtained numerically.
Integrable Renormalization II: the general case
Ebrahimi-Fard, K; Kreimer, D; Ebrahimi-Fard, Kurusch; Guo, Li; Kreimer, Dirk
2004-01-01
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decomposition of renormalization theory is derived by using the Rota-Baxter double construction, respectively Atkinson's theorem. We also outline the extension to the Hopf algebra of Feynman graphs via decorated rooted trees.
Renormalization persistency of tensor force in nuclei
Tsunoda, Naofumi; Tsukiyama, Koshiroh; Hjorth-Jensen, Morten
2011-01-01
In this work we analyze the tensor-force component of effective interactions appropriate for nuclear shell-model studies, with particular emphasis on the monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions such as AV8' and $\\chi$N$^3$LO are tailored to shell-model studies by employing $V_{low k}$ techniques to handle the short-range repulsion of the $NN$ interactions and by applying many-body perturbation theory to incorporate in-medium effects. We show, via numerical studies of effective interactions for the $sd$ and $pf$ shells, that the tensor-force contribution to the monopole term of the effective interaction is barely changed by these renormalization procedures, resulting in almost the same monopole term as the one of the bare $NN$ interactions. We propose to call this feature {\\it Renormalization Persistency} of the tensor force, as it is a remarkable property of the renormalization and should have many interesting consequences in nuclear systems. For higher multipole terms,...
A shape dynamical approach to holographic renormalization
Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2015-01-01
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)
Holographic entanglement renormalization of topological insulators
Wen, Xueda; Cho, Gil Young; Lopes, Pedro L. S.; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei
2016-08-01
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multiscale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the renormalization group to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. That is, if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales.
Face aftereffects involve local repulsion, not renormalization.
Storrs, Katherine R; Arnold, Derek H
2015-01-01
After looking at a photograph of someone for a protracted period (adaptation), a previously neutral-looking face can take on an opposite appearance in terms of gender, identity, and other attributes-but what happens to the appearance of other faces? Face aftereffects have repeatedly been ascribed to perceptual renormalization. Renormalization predicts that the adapting face and more extreme versions of it should appear more neutral after adaptation (e.g., if the adaptor was male, it and hyper-masculine faces should look more feminine). Other aftereffects, such as tilt and spatial frequency, are locally repulsive, exaggerating differences between adapting and test stimuli. This predicts that the adapting face should be little changed in appearance after adaptation, while more extreme versions of it should look even more extreme (e.g., if the adaptor was male, it should look unchanged, while hyper-masculine faces should look even more masculine). Existing reports do not provide clear evidence for either pattern. We overcame this by using a spatial comparison task to measure the appearance of stimuli presented in differently adapted retinal locations. In behaviorally matched experiments we compared aftereffect patterns after adapting to tilt, facial identity, and facial gender. In all three experiments data matched the predictions of a locally repulsive, but not a renormalizing, aftereffect. These data are consistent with the existence of similar encoding strategies for tilt, facial identity, and facial gender.
Renormalization group flows and continual Lie algebras
Bakas, Ioannis
2003-01-01
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...
Renormalization, Hopf algebras and Mellin transforms
Panzer, Erik
2014-01-01
This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like to point out properties of the kinematic subtraction scheme which is also widely used in physics (under the names of MOM or BPHZ). In particular we relate renormalized Feynman rules $\\phi_R$ in this scheme to the universal property of the Hopf algebra $H_R$ of rooted trees, exhibiting a refined renormalization group equation which is equivalent to $\\phi_R: H_R \\rightarrow K[x]$ being a morphism of Hopf algebras to the polynomials in one indeterminate. Upon introduction of analytic regularization this results in efficient combinatorial recursions to calculate $\\phi_R$ in terms of the Mellin transform. We find that different Feynman rules are related by a distinguished class of Hopf algebra automorphisms of $H_R$ that arise naturally from Hochschild cohomology. Also we recall...
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...
Renormalization of multiple infinities and the renormalization group in string loops
Russo, J.; Tseytlin, A. A.
1990-08-01
There is a widespread belief that string loop massles divergences may be absorbed into a renormalization of σ-model couplings (space-time metric and dilaton). The crucial property for this idea to be consistently implemented to arbitrary order in string loops should be the renormalizability of the generating functional for string amplitudes. We make several non-trivial checks of the renormalizability by explicit calculations at genus 1, 2 and 3. The renormalizability becomes non-trivial at the log 2ɛ order. We show that the log 2 ɛ counterterms are universal (e.g. the same counterterms provide finiteness both of two-loop scattering amplitudes and of the three-loop partition function) and are related to the log ɛ counterterms (β-functions) in the standard way dictated by the renormalization group. This checks the consistency of the Fischler-Susskind mechanism and implies that the renormalization group acts properly at the string loop level.
Hilbert space renormalization for the many-electron problem
Li, Zhendong
2015-01-01
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 wav...
Gauge and Scheme Dependence of Mixing Matrix Renormalization
Pilaftsis, Apostolos
2002-01-01
We revisit the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized ${\\bar {\\rm MS}}$ scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultra-violet safe and has a pure dispersive form. Employing the unitarity properties of the theory, we can successfully utilize the afore-mentioned scheme-dependent relation to preserve basic global or local symmetries of the bare Lagrangian through the entire process of renormalization. As an immediate application of our study, we derive the gauge-independent renormalization-group equations of mixing matrices in a minimal extension of the Standard Model with isosinglet neutrinos.
Renormalization in general theories with inter-generation mixing
Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Sirlin, Alberto [New York Univ., NY (United States). Dept. of Physics
2011-11-15
We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)
An algebraic Birkhoff decomposition for the continuous renormalization group
Girelli, F; Martinetti, P
2004-01-01
This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited.
Improved Epstein–Glaser renormalization in x-space versus differential renormalization
Gracia-Bondía, José M. [Department of Theoretical Physics, Universidad de Zaragoza, 50009 Zaragoza (Spain); BIFI Research Center, Universidad de Zaragoza, 50018 Zaragoza (Spain); Department of Physics, Universidad de Costa Rica, San José 11501 (Costa Rica); Gutiérrez, Heidy [Department of Physics, Universidad de Costa Rica, San José 11501 (Costa Rica); Várilly, Joseph C., E-mail: joseph.varilly@ucr.ac.cr [Department of Mathematics, Universidad de Costa Rica, San José 11501 (Costa Rica)
2014-09-15
Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
Improved Epstein–Glaser renormalization in x-space versus differential renormalization
José M. Gracia-Bondía
2014-09-01
Full Text Available Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
Enhancement of field renormalization in scalar theories via functional renormalization group
Zappalà, Dario
2012-01-01
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-per...
Summation of Higher Order Effects using the Renormalization Group Equation
Elias, V; Sherry, T N
2004-01-01
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is payed to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed, and is used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling and the effective potential in massless scalar electrodynamics.
Applications of noncovariant gauges in the algebraic renormalization procedure
Boresch, A; Schweda, Manfred
1998-01-01
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
One Loop Renormalization of the Littlest Higgs Model
Grinstein, Benjamin; Uttayarat, Patipan
2011-01-01
In Little Higgs models a collective symmetry prevents the Higgs from acquiring a quadratically divergent mass at one loop. This collective symmetry is broken by weakly gauged interactions. Terms, like Yukawa couplings, that display collective symmetry in the bare Lagrangian are generically renormalized into a sum of terms that do not respect the collective symmetry except possibly at one renormalization point where the couplings are related so that the symmetry is restored. We study here the one loop renormalization of a prototypical example, the Littlest Higgs Model. Some features of the renormalization of this model are novel, unfamiliar form similar chiral Lagrangian studies.
Gauge and Scheme Dependence of Mixing Matrix Renormalization
Pilaftsis, Apostolos
2002-01-01
We revisit the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized ${\\bar {\\rm MS}}$ scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultra-violet safe and has a pure dispersive for...
Renormalization of Hierarchically Interacting Isotropic Diffusions
den Hollander, F.; Swart, J. M.
1998-10-01
We study a renormalization transformation arising in an infinite system of interacting diffusions. The components of the system are labeled by the N-dimensional hierarchical lattice ( N≥2) and take values in the closure of a compact convex set bar D subset {R}^d (d ≥slant 1). Each component starts at some θ ∈ D and is subject to two motions: (1) an isotropic diffusion according to a local diffusion rate g: bar D to [0,infty ] chosen from an appropriate class; (2) a linear drift toward an average of the surrounding components weighted according to their hierarchical distance. In the local mean-field limit N→∞, block averages of diffusions within a hierarchical distance k, on an appropriate time scale, are expected to perform a diffusion with local diffusion rate F ( k) g, where F^{(k)} g = (F_{c_k } circ ... circ F_{c_1 } ) g is the kth iterate of renormalization transformations F c ( c>0) applied to g. Here the c k measure the strength of the interaction at hierarchical distance k. We identify F c and study its orbit ( F ( k) g) k≥0. We show that there exists a "fixed shape" g* such that lim k→∞ σk F ( k) g = g* for all g, where the σ k are normalizing constants. In terms of the infinite system, this property means that there is complete universal behavior on large space-time scales. Our results extend earlier work for d = 1 and bar D = [0,1], resp. [0, ∞). The renormalization transformation F c is defined in terms of the ergodic measure of a d-dimensional diffusion. In d = 1 this diffusion allows a Yamada-Watanabe-type coupling, its ergodic measure is reversible, and the renormalization transformation F c is given by an explicit formula. All this breaks down in d≥2, which complicates the analysis considerably and forces us to new methods. Part of our results depend on a certain martingale problem being well-posed.
Functional renormalization group approach to neutron matter
Matthias Drews
2014-11-01
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.
Analytic continuation of functional renormalization group equations
Floerchinger, Stefan
2012-01-01
Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N) symmetry we discuss the analytic structure of the flowing action and show how it is possible to derive and solve flow equations for real-time properties such as propagator residues and particle decay widths. The formalism conserves space-time symmetries such as Lorentz or Galilei invariance and allows for improved, self-consistent approximations in terms of derivative expansions in Minkowski space.
Renormalization group formulation of large eddy simulation
Yakhot, V.; Orszag, S. A.
1985-01-01
Renormalization group (RNG) methods are applied to eliminate small scales and construct a subgrid scale (SSM) transport eddy model for transition phenomena. The RNG and SSM procedures are shown to provide a more accurate description of viscosity near the wall than does the Smagorinski approach and also generate farfield turbulence viscosity values which agree well with those of previous researchers. The elimination of small scales causes the simultaneous appearance of a random force and eddy viscosity. The RNG method permits taking these into account, along with other phenomena (such as rotation) for large-eddy simulations.
The exact renormalization group and approximation solutions
Morris, T R
1994-01-01
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\\lambda \\varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
Perturbative and nonperturbative renormalization in lattice QCD
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)
2010-03-15
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.)
Monolithic integration on InP of a Wannier Stark modulator with a strained MQW DFB 1.55-micron laser
Allovon, Michel; Fouchet, Sylvie; Harmand, Jean-Christophe; Ougazzaden, Abdallah; Rose, Benoit; Gloukhian, Andre; Devaux, Fabrice
1995-02-01
We present the technical approach and the preliminary device results on the first integration of a Wannier Stark (WS) electroabsorption (EA) modulator with a DFB laser on InP. The WS modulator active layer consists of a lattice matched InGaAs-InAlAs superlattice (SL) grown by solid source MBE (Molecular Beam Epitaxy). It is butt-coupled to a laser grown by AP-MOVPE whose active layer includes a strained InGaAsP-InGaAsP MQW stack. Device results cover static performances of integrated lasers and modulators, and measurements of high frequency characteristics (small signal bandwidth and 10 Gb/s eye diagram).
Goldberger-treiman relation in the renormalized sigma model
Strubbe, H.J.
1972-01-01
The regularization and renormalization of the full sigma model is worked out explicitly in the tree and one-loop approximation. Various renormalized quantities relevant for chiral symmetry breaking are listed. The numerically calculated Goldberger-Treiman relation is also compared with experiment.
Feynman graph solution to Wilson's exact renormalization group
Sonoda, H
2003-01-01
We introduce a new prescription for renormalizing Feynman diagrams. The prescription is similar to BPHZ, but it is mass independent, and works in the massless limit as the MS scheme with dimensional regularization. The prescription gives a diagrammatic solution to Wilson's exact renormalization group differential equation.
A comment on the relationship between differential and dimensional renormalization
Dunne, G; Dunne, Gerald; Rius, Nuria
1992-01-01
We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension.
Renormalization group theory of the three dimensional dilute Bose gas
Bijlsma, M.; Stoof, H.T.C.
1996-01-01
We study the three-dimensional atomic Bose gas using renormalization group techniques. Using our knowledge of the microscopic details of the interatomic interaction, we determine the correct initial values of our renormalization group equations and thus obtain also information on nonuniversal
Functional renormalization group approach to the Kraichnan model.
Pagani, Carlo
2015-09-01
We study the anomalous scaling of the structure functions of a scalar field advected by a random Gaussian velocity field, the Kraichnan model, by means of functional renormalization group techniques. We analyze the symmetries of the model and derive the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion.
The Yang-Mills gradient flow and renormalization
Ramos, Alberto
2015-01-01
In this proceedings contribution we will review the main ideas behind the many recent works that apply the gradient flow to the determination of the renormalized coupling and the renormalization of composite operators. We will pay special attention to the continuum extrapolation of flow quantities.
Simple on-shell renormalization framework for the Cabibbo-Kobayashi-Maskawa matrix
Kniehl, B.A.; Sirlin, A. [Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut
2006-12-15
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust non-diagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W{yields}q{sub i}+ anti q{sub j} reduces to that in the unmixed, single-generation case. Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate. (orig.)
Lopez-Aguilar, F.; Costa-Quintana, J. (Dept. de Fisica, Grupo de Electromagnetismo, Univ. Autonoma de Barcelona, Bellaterra, E-08193 Barcelona (ES))
1992-07-10
In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method.
Two-Loop Renormalization in the Standard Model
Actis, S; Passarino, G; Passera, M
2006-01-01
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.
Holographic Entanglement Renormalization of Topological Insulators
Wen, Xueda; Lopes, Pedro L S; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei
2016-01-01
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA do...
Ultrasoft renormalization of the potentials in vNRQCD
Stahlhofen, Maximilian Horst
2009-02-18
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.)
Density functionals and dimensional renormalization for an exactly solvable model
Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.
1993-07-01
We treat an analytically solvable version of the ``Hooke's Law'' model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functionals pertain to the ``intermediate'' density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.
Nearest neighbor interaction in the Path Integral Renormalization Group method
de Silva, Wasanthi; Clay, R. Torsten
2014-03-01
The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.
The impact of renormalization group theory on magnetism
Köbler, U.; Hoser, A.
2007-11-01
The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ɛ that is independent of spin structure and lattice symmetry. Normally the Tɛ function holds up to ~0.85Tc where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the Tɛ function are demonstrated for the spontaneous magnetization and for the heat capacity.
Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
Carrozza, Sylvain; Rivasseau, Vincent
2013-01-01
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.
Pižorn, Iztok; Verstraete, Frank
2012-02-10
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows us to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.
Improved Epstein–Glaser renormalization in x -space versus differential renormalization
Gracia-Bondía, José M.; Heidy Gutiérrez; Várilly, Joseph C.
2014-01-01
Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential reno...
Renormalization of QED near Decoupling Temperature
Masood, Samina S
2014-01-01
We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron selfmass, {\\delta}m/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.
Spin Connection and Renormalization of Teleparallel Action
Krššák, Martin
2015-01-01
In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are always contaminated by spurious contributions coming from the inertial effects. Since these contributions can be removed only quasi-locally, one usually ends up with a quasi-local notion of energy and momentum. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action, being thus possible to obtain local notions of energy and momentum. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values.
Fermionic functional integrals and the renormalization group
Feldman, Joel; Trubowitz, Eugene
2002-01-01
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...
Holographic interpretations of the renormalization group
Balasubramanian, Vijay; Lawrence, Albion
2012-01-01
In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $\\Delta \
Linear integral equations and renormalization group
Klein, W.; Haymet, A. D. J.
1984-08-01
A formulation of the position-space renormalization-group (RG) technique is used to analyze the singular behavior of solutions to a number of integral equations used in the theory of the liquid state. In particular, we examine the truncated Kirkwood-Salsburg equation, the Ornstein-Zernike equation, and a simple nonlinear equation used in the mean-field theory of liquids. We discuss the differences in applying the position-space RG to lattice systems and to fluids, and the need for an explicit free-energy rescaling assumption in our formulation of the RG for integral equations. Our analysis provides one natural way to define a "fractal" dimension at a phase transition.
Charge renormalization in nominally apolar colloidal dispersions.
Evans, Daniel J; Hollingsworth, Andrew D; Grier, David G
2016-04-01
We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.
Development of renormalization group analysis of turbulence
Smith, L. M.
1990-01-01
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
VLES Modelling with the Renormalization Group
Chris De Langhe; Bart Merci; Koen Lodefier; Erik Dick
2003-01-01
In a Very-Large-Eddy Simulation (VLES), the filterwidth-wavenumber can be outside the inertial range, and simple subgrid models have to be replaced by more complicated ('RANS-like') models which can describe the transport of the biggest eddies. One could approach this by using a RANS model in these regions, and modify the lengthscale in the model for the LES-regions[1～3]. The problem with these approaches is that these models are specifically calibrated for RANS computations, and therefore not suitable to describe inertial range quantities. We investigated the construction of subgrid viscosity and transport equations without any calibrated constants, but these are calculated directly form the Navier-Stokes equation by means of a Renormalization Group (RG)procedure. This leads to filterwidth dependent transport equations and effective viscosity with the right limiting behaviour (DNS and RANS limits).
Spin connection and renormalization of teleparallel action
Krššák, Martin, E-mail: krssak@ift.unesp.br; Pereira, J. G., E-mail: jpereira@ift.unesp.br [Instituto de Física Teórica, Universidade Estadual Paulista, R. Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP (Brazil)
2015-10-31
In general relativity, inertia and gravitation are both included in the Levi–Civita connection. As a consequence, the gravitational action, as well as the corresponding energy–momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.
Development of renormalization group analysis of turbulence
Smith, L. M.
1990-01-01
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
Integrable Renormalization I: the Ladder Case
Ebrahimi-Fard, K; Kreimer, D; Ebrahimi-Fard, Kurusch; Guo, Li; Kreimer, Dirk
2004-01-01
In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf algebra characters, i.e. for Feynman rules. In this work we would like to show that this Birkhoff factorization finds its natural formulation in terms of a classical r-matrix, coming from a Rota-Baxter structure underlying the target space of the regularized Hopf algebra characters. Working in the rooted tree Hopf algebra, the simple case of the Hopf subalgebra of ladder trees is treated in detail. The extension to the general case, i.e. the full Hopf algebra of rooted trees or Feynman graphs is briefly outlined.
On the Renormalization of Heavy Quark Effective Field Theory
Kilian, W
1994-01-01
The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach correctly reproduces the infrared behaviour of full QCD. Choosing a renormalization scheme in the full theory fixes the renormalization scheme in the effective theory except for the scale of the heavy quark field. Explicit formulae are given for the effective Lagrangian, and one--loop matching renormalization constants are computed for the operators of order $1/m$. Finally, the multiparticle sector of HqEFT is considered.
Ward identities and Wilson renormalization group for QED
Bonini, M; Marchesini, G
1994-01-01
We analyze a formulation of QED based on the Wilson renormalization group. Although the ``effective Lagrangian'' used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's functions correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski's renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponding counterterms are generated in the process of fixing the physical conditions.
Ward identities and Wilson renormalization group for QED
Bonini, M.; D'Attanasio, M.; Marchesini, G.
1994-04-01
We analyze a formulation of QED based on the Wilson renormalization group. Although the "effective lagrangian" used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's function correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponing counter-terms are generated in the process of fixing the physical conditions.
Renormalization group improved Higgs inflation with a running kinetic term
Takahashi, Fuminobu; Takahashi, Ryo
2016-09-01
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.
Dynamical real space renormalization group applied to sandpile models.
Ivashkevich, E V; Povolotsky, A M; Vespignani, A; Zapperi, S
1999-08-01
A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.
Asymmetric charge renormalization for nanoparticles in aqueous media.
González-Mozuelos, P; de la Cruz, M Olvera
2009-03-01
The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.
Basis invariant measure of CP-violation and renormalization
A. Hohenegger
2015-10-01
Full Text Available We analyze, in the context of a simple toy model, for which renormalization schemes the CP-properties of bare Lagrangian and its finite part coincide. We show that this is the case for the minimal subtraction and on-shell schemes. The CP-properties of the theory can then be characterized by CP-odd basis invariants expressed in terms of renormalized masses and couplings. For the minimal subtraction scheme we furthermore show that in CP-conserving theories the CP-odd basis invariants are zero at any scale but are not renormalization group invariant in CP-violating ones.
Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.
Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin
2015-12-01
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice
Zener tunneling of light waves in an optical superlattice.
Ghulinyan, Mher; Oton, Claudio J; Gaburro, Zeno; Pavesi, Lorenzo; Toninelli, Costanza; Wiersma, Diederik S
2005-04-01
We report on the observation of Zener tunneling of light waves in spectral and time-resolved transmission measurements, performed on an optical superlattice made of porous silicon. The structure was designed to have two photonic minibands, spaced by a narrow frequency gap. A gradient in the refractive index was introduced to create two optical Wannier-Stark ladders and, at a critical value of the optical gradient, tunneling between energy bands was observed in the form of an enhanced transmission peak and a characteristic time dependence of the transmission.
Renormalization and power counting of chiral nuclear forces
Long, Bingwei [JLAB
2013-08-01
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.
Reductive renormalization of the phase-field crystal equation.
Oono, Y; Shiwa, Y
2012-12-01
It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods. Reductive renormalization was proposed to make this unification practically accessible; actually, this reductive perturbation is far simpler than most reduction methods, such as the rather standard scaling expansion. However, a rather cryptic exposition of the method seems to have been the cause of some trouble. Here, an explicit demonstration of the consistency of the reductive renormalization-group procedure is given for partial differentiation equations (of a certain type, including time-evolution semigroup type equations). Then, the procedure is applied to the reduction of a phase-field crystal equation to illustrate the streamlined reduction method. We conjecture that if the original system is structurally stable, the reductive renormalization-group result and that of the original equation are diffeomorphic.
Dimensional regularization and renormalization of non-commutative QFT
Gurau, R
2007-01-01
Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized $\\Phi^{\\star 4}_4$ model on the Moyal space.
The Role of Renormalization Group in Fundamental Theoretical Physics
Shirkov, Dmitri V.
1997-01-01
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of fundamental physics.
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
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.
Renormalization of Polyakov loops in fundamental and higher representations
Kaczmarek, O; Hübner, K
2007-01-01
We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal entent of the lattice and find that both prescriptions are equivalent, resulting in renormalization constants that depend on the bare coupling. Furthermore these renormalization constants show Casimir scaling for higher representations of the Polyakov loops. The analysis of Polyakov loops in different representations of the color SU(3) group indicates that a simple perturbative inspired relation in terms of the quadratic Casimir operator is realized to a good approximation at temperatures $T \\gsim T_c$ for renormalized as well as bare loops. In contrast to a vanishing Polyakov loop in representations with non-zero triality in the confined phase, the adjoint loops are small but non-zero even for temperatures below the critical one. The adjoint quark-antiquark pairs exhibit screening. This behavior can be related to the bindin...
Screening of heterogeneous surfaces: charge renormalization of Janus particles.
Boon, N; Carvajal Gallardo, E; Zheng, S; Eggen, E; Dijkstra, M; van Roij, R
2010-03-17
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.
Renormalization of the energy-momentum tensor on the lattice
Pepe, Michele
2015-01-01
We present the calculation of the non-perturbative renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. That computation is carried out in the framework of shifted boundary conditions, where a thermal quantum field theory is formulated in a moving reference frame. The non-perturbative renormalization factors are then used to measure the Equation of State of the SU(3) Yang-Mills theory. Preliminary numerical results are presented and discussed.
Cohomology and Renormalization of BFYM Theory in three Dimensions
Accardi, A; Martellini, M; Zeni, M; Accardi, Alberto; Belli, Andrea; Martellini, Maurizio; Zeni, Mauro
1997-01-01
The first order formalism for 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of cohomology and renormalization for both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources.
Theory of temperature dependent phonon-renormalized properties
Monserrat, Bartomeu; Conduit, G. J.; Needs, R. J.
2013-01-01
We present a general harmonic theory for the temperature dependence of phonon-renormalized properties of solids. Firstly, we formulate a perturbation theory in phonon-phonon interactions to calculate the phonon renormalization of physical quantities. Secondly, we propose two new schemes for extrapolating phonon zero-point corrections from temperature dependent data that improve the accuracy by an order of magnitude compared to previous approaches. Finally, we consider the low-temperature limi...
Supergravity corrections to $(g-2)_l$ in differential renormalization
del Águila, F; Muñoz-Tàpia, R; Pérez-Victoria, M
1997-01-01
The method of differential renormalization is extended to the calculati= on of the one-loop graviton and gravitino corrections to $(g-2)_l$ in unbroken supergravity. Rewriting the singular contributions of all the diagrams in= terms of only one singular function, U(1) gauge invariance and supersymmetry ar= e preserved. We compare this calculation with previous ones which made use = of momentum space regularization (renormalization) methods.
The local renormalization of super-Yang-Mills theories
Gillioz, Marc
2016-01-01
We show how to consistently renormalize $\\mathcal{N} = 1$ and $\\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
Renormalization theory in four dimensional scalar fields. Pt. 1
Gallavotti, G.; Nicolo, F.
1985-08-01
We present a renormalization group appraoch to the renormalization thoery of PHI/sub 4//sup 4/ using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the Schwinger functions. The main aim of this paper is to show how one can in this way obtain the n-bounds.
Aspects of renormalization in finite-density field theory
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
2015-05-26
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.
Investigation of renormalization effects in high temperature cuprate superconductors
Zabolotnyy, Volodymyr B.
2008-04-16
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.)
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
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, will be discussed in p...
Technical fine-tuning problem in renormalized perturbation theory
Foda, O.E.
1983-01-01
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.
4-wave dynamics in kinetic wave turbulence
Chibbaro, Sergio; Rondoni, Lamberto
2016-01-01
A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function $Z$ is obtained within an "interaction representation" and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for $Z$. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the $N$-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency.
Ma Lei; Huang Ai-Qun; Li Jun
2011-01-01
This paper studies the normal state properties of itinerant electrons in a toy model, which is constructed according to the model for coexisting ferromagnetism and superconductivity proposed by Suhl [Suhl H 2001 Phys. Rev. Lett. 87 167007]. In this theory with ferromagnetic ordering based on localized spins, the exchange interaction J between conduction electrons and localized spin is taken as the pairing glue for s-wave superconductivity. It shows that this J term will first renormalize the normal state single conduction electron structures substantially. It finds dramatically enhanced or suppressed magnetization of itinerant electrons for positive or negative J. Singlet Cooper pairing can be ruled out due to strong spin polarisation in the J > 0 case while a narrow window for s-wave superconductivity is opened around some ferromagnetic J.
Karachevtseva, L.; Goltviansky, Yu.; Sapelnikova, O.; Lytvynenko, O.; Stronska, O.; Bo, Wang; Kartel, M.
2016-12-01
Opportunities to enhance the properties of structured surfaces were demonstrated on 2D macroporous silicon structures with SiO2 coatings. We investigated the IR light absorption oscillations in macroporous silicon structures with SiO2 coatings 0-800 nm thick. The Wannier-Stark electro-optical effect due to strong electric field on Si-SiO2boundary and an additional electric field of quasi-guided optical modes were taken into account. The photonic modes and band gaps were also considered as peculiarities in absorbance spectra of macroporous silicon structures with a thick SiO2 coating. The photonic modes do not coincide with the quasi-guided modes in the silicon matrix and do not appear in absorption spectra of 2D macroporous silicon structures with surface nanocrystals.
ARPES and NMTO Wannier Orbital Theory of Li{sub 0.9}Mo{sub 6}O{sub 17}
Dudy, L. [Physikalisches Institut, Universitaet Wuerzburg, D- 97074 Wuerzburg (Germany); Allen, J.W. [University of Michigan, Ann Arbor, MI (United States); Denlinger, J.D. [Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA (United States); He, J. [Clemson University, Clemson, SC (United States); Greenblatt, M. [Rutgers University, Piscataway, NJ (United States); Haverkort, M.W. [Max-Planck-Institut fuer Chemische Physik fester Stoffe, Dresden (Germany); Andersen, O.K.; Nohara, Y. [Max-Planck-Institut fuer Festkoerperphysik, Stuttgart (Germany)
2015-07-01
Li{sub 0.9}Mo{sub 6}O{sub 17} displays theoretically interesting metallic quasi-one dimensional (1D) behavior that is unusually robust against 3D crossover with decreasing temperature, and is characterized by a large value of anomalous exponent α∼ 0.6. We present very high resolution, low temperature (T=6K-30K) angle resolved photoemission spectroscopy (ARPES) of its band structure and Fermi surface (FS), analyzed with N-th order muffin tin orbital (NMTO) Wannier function band theory. We confirm a previous conclusion that LDA band theory is unusually successful, implying a small Hubbard U, and find in ARPES the dispersion and FS warping and splitting expected for predicted small and long range hoppings (t {sub perpendicular} {sub to} ∼ 10-15 meV) between chains.
Naka, Akiyoshi; Hirakawa, Kazuhiko; Unuma, Takeya
2016-11-01
We investigate the phase and terahertz (THz) gain of Bloch oscillations in GaAs-based superlattices at various temperatures of T = 80-298 K by using THz emission spectroscopy under bias electric fields. The transient current is found to start from its maximum nearly as damped cos ωB t (ωB/2π: Bloch frequency) throughout this temperature range, having only a small initial phase even for kT > ħωB (k: Boltzmann constant) and dephasing time shortening with increasing temperature. A spectral analysis indicates inversionless THz gain that originates from the capacitive nature of a Wannier-Stark ladder system with broadened energy levels at room temperature.
Renormalization of aperiodic model lattices: spectral properties
Kroon, L
2003-01-01
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...
General Covariance from the Quantum Renormalization Group
Shyam, Vasudev
2016-01-01
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...
Renormalization group approach to superfluid neutron matter
Hebeler, K.
2007-06-06
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.)
Theories of Matter: Infinities and Renormalization
Kadanoff, Leo P
2010-01-01
This paper looks at the theory underlying the science of materials from the perspectives of physics, the history of science, and the philosophy of science. We are particularly concerned with the development of understanding of the thermodynamic phases of matter. The question is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) rise from a pot of heated water. The nature of the phases is brought into the sharpest focus in phase transitions: abrupt changes from one phase to another and hence changes from one behavior to another. This article starts with the development of mean field theory as a basis for a partial understanding of phase transition phenomena. It then goes on to the limitations of mean field theory and the development of very different supplementary understanding through the renormalization group concept. Throughout, the behavior at the phase transition is illuminated by an "extende...
Renormalization of QED Near Decoupling Temperature
Samina S. Masood
2014-01-01
Full Text Available We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron self-mass, δm/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.
Exact renormalization group and Sine Gordon theory
Oak, Prafulla; Sathiapalan, B.
2017-07-01
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional ϕ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating c-functions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.
Renormalization of oscillator lattices with disorder.
Ostborn, Per
2009-05-01
A real-space renormalization transformation is constructed for lattices of nonidentical oscillators with dynamics of the general form dvarphi_{k}/dt=omega_{k}+g summation operator_{l}f_{lk}(varphi_{l},varphi_{k}) . The transformation acts on ensembles of such lattices. Critical properties corresponding to a second-order phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, second-order phase transitions with the predicted properties are observed as g increases in two structurally different two-dimensional oscillator models. One model has smooth coupling f_{lk}(varphi_{l},varphi_{k})=phi(varphi_{l}-varphi_{k}) , where phi(x) is nonodd. The other model is pulse coupled, with f_{lk}(varphi_{l},varphi_{k})=delta(varphi_{l})phi(varphi_{k}) . Lower bounds for the critical dimensions for different types of coupling are obtained. For nonodd coupling, macroscopic synchronization cannot be ruled out for any dimension D> or =1 , whereas in the case of odd coupling, the well-known result that it can be ruled out for D<3 is regained.
Polarizable Embedding Density Matrix Renormalization Group.
Hedegård, Erik D; Reiher, Markus
2016-09-13
The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.
Functional renormalization group methods in quantum chromodynamics
Braun, J.
2006-12-18
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.)
Holographic renormalization as a canonical transformation
Papadimitriou, Ioannis
2010-01-01
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...
Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei
2016-01-01
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...
Stanescu, Tudor D.; Das Sarma, Sankar
2017-07-01
A minimal model for the hybrid superconductor-semiconductor nanowire Majorana platform is developed that fully captures the effects of the low-energy renormalization of the nanowire modes arising from the presence of the parent superconductor. In this model, the parent superconductor is an active component that participates explicitly in the low-energy physics, not just a passive partner that only provides proximity-induced Cooper pairs for the nanowire. This treatment on an equal footing of the superconductor and the semiconductor has become necessary in view of recent experiments, which do not allow a consistent interpretation based just on the bare semiconductor properties. The general theory involves the evaluation of the exact semiconductor Green's function that includes a dynamical self-energy correction arising from the tunnel-coupled superconductor. Using a tight-binding description, the nanowire Green's function is obtained in various relevant parameter regimes, with the parent superconductor being treated within the BCS-BdG prescription. General conditions for the emergence of topological superconductivity are worked out for single-band as well as multiband nanowires and detailed numerical results are given for both infinite and finite wire cases. The topological quantum phase diagrams are provided numerically and the Majorana bound states are obtained along with their oscillatory energy-splitting behaviors due to wave function overlap in finite wires. Renormalization effects are shown to be both qualitatively and quantitatively important in modifying the low-energy spectrum of the nanowire. The results of the theory are found to be in good qualitative agreement with Majorana nanowire experiments, leading to the conclusion that the proximity-induced low-energy renormalization of the nanowire modes by the parent superconductor is of fundamental importance in superconductor-semiconductor hybrid structures, except perhaps in the uninteresting limit of
Holographic dynamics from multiscale entanglement renormalization ansatz
Chua, Victor; Passias, Vasilios; Tiwari, Apoorv; Ryu, Shinsei
2017-05-01
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 repurposed 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 gapped paramagnetic phase of the transverse field Ising model, we demonstrate the holographic duality between excited states induced by single spin-flips (Ising "magnons") acting on the ground state and single ancilla qubit spin flips. The single ancillae qubit excitation is shown to be stable in the bulk under real-time evolution and hence defines a stable holographic quasiparticle, which we have named the "hologron." Their bulk 2D Hamiltonian, energy spectrum, and dynamics within the MERA network are studied numerically. The "dictionary" between the bulk and boundary is determined and realizes many features of the holographic correspondence in a non-CFT limit of the boundary theory. As an added spin-off, this dictionary together with the extension to multihologron sectors gives us a systematic way to construct quantitatively accurate low-energy effective Hamiltonians.
Renormalization group and the deep structure of the proton
Petermann, Andreas
1979-01-01
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...
Renormalized scattering series for frequency-domain waveform modelling of strong velocity contrasts
Jakobsen, M.; Wu, R. S.
2016-08-01
An improved description of scattering and inverse scattering processes in reflection seismology may be obtained on the basis of a scattering series solution to the Helmoltz equation, which allows one to separately model primary and multiple reflections. However, the popular scattering series of Born is of limited seismic modelling value, since it is only guaranteed to converge if the global contrast is relatively small. For frequency-domain waveform modelling of realistic contrasts, some kind of renormalization may be required. The concept of renormalization is normally associated with quantum field theory, where it is absolutely essential for the treatment of infinities in connection with observable quantities. However, the renormalization program is also highly relevant for classical systems, especially when there are interaction effects that act across different length scales. In the scattering series of De Wolf, a renormalization of the Green's functions is achieved by a split of the scattering potential operator into fore- and backscattering parts; which leads to an effective reorganization and partially re-summation of the different terms in the Born series, so that their order better reflects the physics of reflection seismology. It has been demonstrated that the leading (single return) term in the De Wolf series (DWS) gives much more accurate results than the corresponding Born approximation, especially for models with high contrasts that lead to a large accumulation of phase changes in the forward direction. However, the higher order terms in the DWS that are associated with internal multiples have not been studied numerically before. In this paper, we report from a systematic numerical investigation of the convergence properties of the DWS which is based on two new operator representations of the DWS. The first operator representation is relatively similar to the original scattering potential formulation, but more global and explicit in nature. The second
Renormalization Scheme Dependence in a QCD Cross Section
Chishtie, Farrukh
2015-01-01
From the perturbatively computed contributions to the $e^+e^- \\rightarrow$ hadrons cross section $R_{e^{+}e^{-}}$, we are able to determine the sum of all leading-log (LL), next-to-leading-log (NLL) etc. contributions to $R_{e^{+}e^{-}}$ up to four loop order (ie, the N$^3$LL contributions) by using the renormalization group equation. We then sum all logarithmic contributions, giving the result for $R_{e^{+}e^{-}}$ in terms of the log-independent contribution and the RG $\\beta$-function. Two renormalization schemes are then considered, both of which lead to an expression for $R_{e^{+}e^{-}}$ in terms of scheme-independent parameters. Both schemes result in expressions for $R_{e^{+}e^{-}}$ that are independent of the renormalization scale parameter $\\mu$. They are then compared with purely perturbative results and RG-summed N$^{3}$LL results.
Non-perturbative renormalization of three-quark operators
Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)
2008-10-15
High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS scheme at {mu}=2 GeV. (orig.)
Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
Valderrama, Manuel Pavon
2016-01-01
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 ...
Renormalization group analysis of the gluon mass equation
Aguilar, A C; Papavassiliou, J
2014-01-01
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, whose deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various p...
Renormalization Group Equation for Low Momentum Effective Nuclear Interactions
Bogner, S K; Kuo, T T S; Brown, G E
2001-01-01
We consider two nonperturbative methods originally used to derive shell model effective interactions in nuclei. These methods have been applied to the two nucleon sector to obtain an energy independent effective interaction V_{low k}, which preserves the low momentum half-on-shell T matrix and the deuteron pole, with a sharp cutoff imposed on all intermediate state momenta. We show that V_{low k} scales with the cutoff precisely as one expects from renormalization group arguments. This result is a step towards reformulating traditional model space many-body calculations in the language of effective field theories and the renormalization group. The numerical scaling properties of V_{low k} are observed to be in excellent agreement with our exact renormalization group equation.
Renormalization of position space amplitudes in a massless QFT
Todorov, Ivan
2017-03-01
Ultraviolet renormalization of position space massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree is determined by the degree of divergence while their order—the highest power of logarithm in the dilation anomaly—is given by the number of (sub)divergences. In the present paper we review these results and observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformally invariant theory internal integration is also proven to preserve the order of associate homogeneity. The renormalized 4-point amplitudes in the φ4 theory (in four space-time dimensions) are written as (non-analytic) translation invariant functions of four complex variables with calculable conformal anomaly. Our conclusion concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless φ4 theory agrees with the old result of Lowenstein and Zimmermann [23].
The Renormalization of the Electroweak Standard Model to All Orders
Kraus, E
1998-01-01
We give the renormalization of the standard model of electroweak interactions to all orders of perturbation theory by using the method of algebraic renormalization, which is based on general properties of renormalized perturbation theory and not on a specific regularization scheme. The Green functions of the standard model are uniquely constructed to all orders, if one defines the model by the Slavnov-Taylor identity, Ward-identities of rigid symmetry and a specific form of the abelian local gauge Ward-identity, which continues the Gell-Mann Nishijima relation to higher orders. Special attention is directed to the mass diagonalization of massless and massive neutral vectors and ghosts. For obtaining off-shell infrared finite expressions it is required to take into account higher order corrections into the functional symmetry operators. It is shown, that the normalization conditions of the on-shell schemes are in agreement with the most general symmetry transformations allowed by the algebraic constraints.
Emergent geometry from field theory: Wilson's renormalization group revisited
Kim, Ki-Seok; Park, Chanyong
2016-06-01
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low-energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdSd +2 /CFTd +1 duality conjecture. We claim that the AdS3 /CFT2 duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large-Ns limit, where Ns is the number of fermion flavors.
Bandgap renormalization in single-wall carbon nanotubes.
Zhu, Chunhui; Liu, Yujie; Xu, Jieying; Nie, Zhonghui; Li, Yao; Xu, Yongbing; Zhang, Rong; Wang, Fengqiu
2017-09-11
Single-wall carbon nanotubes (SWNTs) have been extensively explored as an ultrafast nonlinear optical material. However, due to the numerous electronic and morphological arrangements, a simple and self-contained physical model that can unambiguously account for the rich photocarrier dynamics in SWNTs is still absent. Here, by performing broadband degenerate and non-degenerate pump-probe experiments on SWNTs of different chiralities and morphologies, we reveal strong evidences for the existence of bandgap renormalization in SWNTs. In particularly, it is found that the broadband transient response of SWNTs can be well explained by the combined effects of Pauli blocking and bandgap renormalization, and the distinct dynamics is further influenced by the different sensitivity of degenerate and non-degenerate measurements to these two concurrent effects. Furthermore, we attribute optical-phonon bath thermalization as an underlying mechanism for the observed bandgap renormalization. Our findings provide new guidelines for interpreting the broadband optical response of carbon nanotubes.
Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion.
Růžička, Štěpán; Allen, Michael P
2015-08-11
Experiments done on polydisperse particles of cadmium selenide have recently shown that the particles form spherical isolated clusters with low polydispersity of cluster size. The computer simulation model of Xia et al. ( Nat. Nanotechnol. 2011 , 6 , 580 ) explaining this behavior used a short-range van der Waals attraction combined with a variable long-range screened electrostatic repulsion, depending linearly on the volume of the clusters. In this work, we term this dependence "linear renormalization" of the repulsive term, and we use advanced Monte Carlo simulations to investigate the kinetically slowed down phase separation in a similar but simpler model. We show that amorphous drops do not dissolve and crystallinity evolves very slowly under linear renormalization, and we confirm that low polydispersity of cluster size can also be achieved using this model. The results indicate that the linear renormalization generally leads to monodisperse clusters.
The ab-initio density matrix renormalization group in practice.
Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Renormalization group approach to scalar quantum electrodynamics on de Sitter
González, Francisco Fabián
2016-01-01
We consider the quantum loop effects in scalar electrodynamics on de Sitter space by making use of the functional renormalization group approach. We first integrate out the photon field, which can be done exactly to leading (zeroth) order in the gradients of the scalar field, thereby making this method suitable for investigating the dynamics of the infrared sector of the theory. Assuming that the scalar remains light we then apply the functional renormalization group methods to the resulting effective scalar theory and focus on investigating the effective potential, which is the leading order contribution in the gradient expansion of the effective action. We find symmetry restoration at a critical renormalization scale $\\kappa=\\kappa_{\\rm cr}$ much below the Hubble scale $H$. When compared with the results of Serreau and Guilleux [arXiv:1306.3846 [hep-th], arXiv:1506.06183 [hep-th
Systematic renormalization at all orders in the DiffRen and improved Epstein-Glaser schemes
Gracia-Bondía, José M
2015-01-01
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
Renormalization group theory of the critical properties of the interacting bose fluid
Creswick, Richard J.; Wiegel, F.W.
1982-01-01
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.
V. Bacsó
2015-12-01
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.
1999-01-01
In this paper we apply the renormalization-group (RG) inspired resummation method to the one-loop effective potential at finite temperature evaluated in the massive scalar 04 model renormalized at zero-temperature, and study whether ourresummation procedure a la RG uccessfully resum the dominant correction terms apperaed in the perturbative caluculation in the T = 0 renormalization scheme or not.Our findings are i) that if we start from the theory renormalized at T = 0, then the condition tha...
Patel, Niravkumar D.; Nocera, Alberto; Alvarez, Gonzalo; Arita, Ryotaro; Moreo, Adriana; Dagotto, Elbio
2016-08-01
The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe2S3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015), 10.1038/nmat4351] opens a broad avenue of research, because it represents the first report of pairing tendencies in a quasi-one-dimensional iron-based high-critical-temperature superconductor. Similarly, as in the case of the cuprates, ladders and chains can be far more accurately studied using many-body techniques and model Hamiltonians than their layered counterparts, particularly if several orbitals are active. In this publication, we derive a two-orbital Hubbard model from first principles that describes individual ladders of BaFe2S3 . The model is studied with the density matrix renormalization group. These first reported results are exciting for two reasons: (i) at half-filling, ferromagnetic order emerges as the dominant magnetic pattern along the rungs of the ladder, and antiferromagnetic order along the legs, in excellent agreement with neutron experiments; and (ii) with hole doping, pairs form in the strong coupling regime, as found by studying the binding energy of two holes doped on the half-filled system. In addition, orbital selective Mott phase characteristics develop with doping, with only one Wannier orbital receiving the hole carriers while the other remains half-filled. These results suggest that the analysis of models for iron-based two-leg ladders could clarify the origin of pairing tendencies and other exotic properties of iron-based high-critical-temperature superconductors in general.
Dynamics and applicability of the similarity renormalization group
Launey, K D; Dytrych, T; Draayer, J P [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Popa, G, E-mail: kristina@baton.phys.lsu.edu [Department of Physics and Astronomy, Ohio University, Zanesville, OH 43701 (United States)
2012-01-13
The similarity renormalization group (SRG) concept (or flow equations methodology) is studied with a view toward the renormalization of nucleon-nucleon interactions for ab initio shell-model calculations. For a general flow, we give quantitative measures, in the framework of spectral distribution theory, for the strength of the SRG-induced higher order (many-body) terms of an evolved interaction. Specifically, we show that there is a hierarchy among the terms, with those of the lowest particle rank being the most important. This feature is crucial for maintaining the unitarity of SRG transformations and key to the method's applicability. (paper)
Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
Klebanov, Igor R; Pufu, Silviu S; Safdi, Benjamin R
2012-01-01
The renormalized entanglement entropy (REE) across a circle of radius R has been proposed as a c-function in Poincar\\'e invariant (2+1)-dimensional field theory. A proof has been presented of its monotonic behavior as a function of R, based on the strong subadditivity of entanglement entropy. However, this proof does not directly establish stationarity of REE at conformal fixed points of the renormalization group. In this note we study the REE for the free massive scalar field theory near the UV fixed point described by a massless scalar. Our numerical calculation indicates that the REE is not stationary at the UV fixed point.
1-loop renormalization of QED{sub 2}
Casana S, Rodolfo; Dias, Sebastiao A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1997-12-31
The Schwinger model, when quantized in a gauge non-invariant way exhibits a dependence on a parameter a (the Jackiw-Rajaraman parameter) in a way which is analogous to the case involving chiral fermions (the chiral Schwinger model). For all values of a {ne} 1, there are divergences in the fermionic Green`s functions. We propose a regularization of the generating functional Z({eta},{eta}-bar, J) and we use it to re normalize the theory to one loop level, in a semi-perturbative sense. At the end of the renormalization procedure we find an implicit dependence of a on the renormalization scale {mu}. (author) 9 refs.
Four loop renormalization of the Gross-Neveu model
Gracey, J A; Schroder, Y
2016-01-01
We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.
Real-space renormalization yields finitely correlated states
Barthel, Thomas; Eisert, Jens
2010-01-01
Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one dimension, MERA states can be efficiently mapped to finitely-correlated states, also known as projected entangled pair states (PEPS), with a bond dimension independent of the system size. Hence, MERA states form an efficiently contractible class of PEPS and obey an area law for the entanglement entropy. It is shown further that there exist other efficiently contractible schemes violating the area law.
Perturbative n-Loop Renormalization by an Implicit Regularization Technique
Gobira, S R
2001-01-01
We construct a regularization independent procedure for implementing perturbative renormalization. An algebraic identity at the level of the internal lines of the diagrams is used which allows for the identification of counterterms in a purely algebraic way. Order by order in a perturbative expansion we automatically obtain in the process, finite contributions, local and nonlocal divergences. The notorious complications of overlapping divergences never enter and the corresponding counterterms arise automatically on the same footing as any other counterterm. The result of the present mathematical procedure is a considerable algebraic simplification which clarifies the connection between renormalization and counterterms in the Lagrangian.
Renormalized position space amplitudes in a massless QFT
Todorov, Ivan
2015-01-01
Ultraviolet renormalization of massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree coincides with the degree of divergence while their order - the highest power of the logarithm in the dilation anomaly - is given by the number of (sub)divergences. We observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformal invariant theory internal integration is also proven to preserve the order of associate homogeneity. Our conclusions concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless $\\varphi^4$ theory agrees with the old result of Lowenstein and Zimmermann [LZ].
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, Robert; Barton, J. Michael
1990-01-01
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
Background field functional renormalization group for absorbing state phase transitions.
Buchhold, Michael; Diehl, Sebastian
2016-07-01
We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.
From infinite to two dimensions through the functional renormalization group.
Taranto, C; Andergassen, S; Bauer, J; Held, K; Katanin, A; Metzner, W; Rohringer, G; Toschi, A
2014-05-16
We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling.
The renormalization scale-setting problem in QCD
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)
2013-09-01
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
Effective Charge on Polymer Colloids Obtained Using a Renormalization Model.
Quesada-Pérez; Callejas-Fernández; Hidalgo-Álvarez
1998-10-01
Static light scattering has been used to study the electrostatic interaction between colloidal particles. Experiments were carried out using a latex with a very small diameter, allowing structure determination at high particle concentration. The obtained effective charge characterizing this interaction is found to be smaller than the bare charge determined from titration. A renormalization model connecting both values has been used. The agreement between the renormalized charge and that obtained from scattering data seems to point out that this model operates well. Copyright 1998 Academic Press.
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
Chen, Xia; Kulik, Alexey M.
2012-01-01
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Renormalizing the Lippmann-Schwinger equation for the one pion exchange potential
Eiras, D; Eiras, Dolors; Soto, Joan
2003-01-01
We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.
Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus
2017-02-14
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
Hu, Weifeng; Chan, Garnet Kin-Lic
2015-07-14
We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection.
Real Space Renormalization of Majorana Fermions in Quantum Nano-Wire Superconductors
Jafari, R.; Langari, A.; Akbari, Alireza; Kim, Ki-Seok
2017-02-01
We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As an example we focus on the Kitaev chain to investigate the topological quantum phase transition (TQPT) in the one-dimensional spinless p-wave superconductor. Studying the behaviour of local compressibility and ground-state fidelity, show that the TQPT is signalled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point are used as proper indicators for the TQPT, which signals the appearance of Majorana fermions. Finally, we present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the TQPT, which reveals two different scaling behaviors as we approach the critical point and thermodynamic limit.
Second-Order Self-Consistent-Field Density-Matrix Renormalization Group.
Ma, Yingjin; Knecht, Stefan; Keller, Sebastian; Reiher, Markus
2017-06-13
We present a matrix-product state (MPS)-based quadratically convergent density-matrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (J. Chem. Phys. 1985, 82, 5053), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and superconfiguration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz. Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure.
Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling
Longcope, D. W.; Sudan, R. N.
1991-01-01
The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
Second-Order Self-Consistent-Field Density-Matrix Renormalization Group
Ma, Yingjin; Keller, Sebastian; Reiher, Markus
2016-01-01
We present a matrix-product state (MPS)-based quadratically convergent density-matrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (JCP 82, 5053, (1985)), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second-order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and super-configuration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz. Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure
Freitag, Leon; Angeli, Celestino; Reiher, Markus
2016-01-01
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess in a study of a heme model the accuracy of the strongly- and partially-contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
Men'shenin, V. V.
2013-06-01
A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn2O5 multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.
Lorentz space estimates for the Coulombian renormalized energy
Serfaty, Sylvia
2011-01-01
In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier-Serfaty \\cite{ss1,ss3}. To derive the estimates, we use a technique that we introduced in \\cite{st}, which couples the "ball construction method" to estimates in the Lorentz space $L^{2,\\infty}$.
Renormings concerning exposed points and non-smoothness
GARCíA-PACHECO; Francisco; Javier
2009-01-01
Intuitively, non-smooth points might look like exposed points. However, in this paper we show that real Banach spaces having dimension greater than or equal to three can be equivalently renormed to obtain non-smooth points which are also non-exposed.
Renormalization of four-fermion operators for higher twist calculations
Capitani, S; Horsley, R; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
1999-01-01
The evaluation of the higher twist contributions to Deep Inelastic Scattering amplitudes involves a non trivial choice of operator bases for the higher orders of the OPE expansion of the two hadronic currents. In this talk we discuss the perturbative renormalization of the four-fermion operators that appear in the above bases.
Screening of heterogeneous surfaces: Charge renormalization of Janus particles
Boon, N.; Carvajal Gallardo, E.; Zheng, S.; Eggen, E.; Dijkstra, M.; Van Roij, R.
2010-01-01
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadru
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
Rota-Baxter algebras and the Hopf algebra of renormalization
Ebrahimi-Fard, K.
2006-06-15
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.)
Renorms and topological linear contractions on Hilbert spaces
施茂祥; 谭炳均; 陈国强
1999-01-01
Properties of and the relationships between (topological) proper contractions, (topological) strict contractions and (topological) contractions are investigated, Explicit renorms are constructed so that all operators in a (finite or countable) family or a semigroup simultaneously become proper contractions or strict contractions. Some results are obtained for operator weighted shifts or operator weighted continuous shifts to be topological strict contractions.
Running with rugby balls: bulk renormalization of codimension-2 branes
Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.
2013-01-01
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.
Inverse Symmetry Breaking and the Exact Renormalization Group
Pietroni, M; Tetradis, N
1997-01-01
We discuss the question of inverse symmetry breaking at non-zero temperature using the exact renormalization group. We study a two-scalar theory and concentrate on the nature of the phase transition during which the symmetry is broken. We also examine the persistence of symmetry breaking at temperatures higher than the critical one.
On Newton-Cartan local renormalization group and anomalies
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)
2016-11-28
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.
Computing the effective action with the functional renormalization group
Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław
2016-01-01
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.......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 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...
On Newton-Cartan local renormalization group and anomalies
Auzzi, Roberto; Filippini, Francesco; Nardelli, Giuseppe
2016-01-01
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.
Anisotropic bond percolation by position-space renormalization group
de Oliveira, Paulo Murilo
1982-02-01
We present a position-space renormalization-group procedure for the anisotropic bond-percolation problem in a square lattice. We use a kind of cell which preserves the geometrical features of the whole lattice, including duality. In this manner, the whole phase diagram and the dimensionality crossover exponent (both are exactly known) are reproduced for any scaling factor.
Renormalization group approach to the interacting bose fluid
Wiegel, F.W.
1978-01-01
It is pointed out that the method of functional integration provides a very convenient starting point for the renormalization group approach to the interacting Bose gas. Using such methods we show in a general and non-perturbative way that the critical exponents of the Bose gas are identical to
RENORMALIZATION FACTOR AND ODD-OMEGA GAP SINGLET SUPERCONDUCTIVITY
DOLGOV, OV; LOSYAKOV, VV
1994-01-01
Abrahams et al. [Phys. Rev. B 47 (1993) 513] have considered the possibility of a nonzero critical temperature of the superconductor transition to the state with odd-omega pp function and shown that the condition for it is the following inequality for the renormalization factor. Z (k, omega(n)) <1.
Renormalization group flows in gauge-gravity duality
Murugan, Arvind
2016-01-01
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
Renormalization constants for 2-twist operators in twisted mass QCD
Alexandrou, C; Korzec, T; Panagopoulos, H; Stylianou, F
2010-01-01
Perturbative and non-perturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the non-perturbative evaluation of the one-derivative twist-2 vector and axial vector operators. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing $a$ corresponding to $\\beta=3.9, 4.05, 4.20$. Subtraction of ${\\cal O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to ${\\cal O}(a^2)$. The renormalization conditions are defined in the RI$'$-MOM scheme, for both perturbative and non-perturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set...
Charge renormalization of nanoparticles immersed in a molecular electrolyte.
Arenas-Gómez, B L; González-Mozuelos, P
2010-01-07
The renormalization of the electric charge of nanoparticles (small colloids) at infinite dilution immersed in a supporting electrolyte containing molecular ions is studied here using a simple model. The nanoparticles are represented by charged spheres of finite diameter, the anions are assumed to be pointlike, and the cations are modeled as two identical charged points connected by a rigid rod. The static structure of this model system is determined using the reference interaction site model equations with suitable closure relations and the renormalized charges are analyzed employing the dressed interactions site theory approach. It is found that for a wide range of ionic strengths these renormalized charges are clearly dependent on the length of the cations for nanoparticles with negative bare charge, but this dependence is practically negligible for nanoparticles with positive bare charges. In the limit of zero cation length and small nanoparticle charges the standard Derjaguin-Landau-Verwey-Overbeek model renormalization is recovered. A brief account of the structural and thermodynamic properties of the model molecular electrolyte is also provided.
Simple perturbative renormalization scheme for supersymmetric gauge theories
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-06-30
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..)/sup -/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.
Renormalization Group Flows, Cycles, and c-Theorem Folklore
Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.
2012-03-01
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.
Holographic torus entanglement and its renormalization group flow
Bueno, Pablo; Witczak-Krempa, William
2017-03-01
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.
Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange
Higa, R; Valderrama, M Pavon; Arriola, E Ruiz
2007-06-14
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.
On the renormalization group transformation for scalar hierarchical models
Koch, H. (Texas Univ., Austin (USA). Dept. of Mathematics); Wittwer, P. (Geneva Univ. (Switzerland). Dept. de Physique Theorique)
1991-06-01
We give a new proof for the existence of a non-Gaussian hierarchical renormalization group fixed point, using what could be called a beta-function for this problem. We also discuss the asymptotic behavior of this fixed point, and the connection between the hierarchical models of Dyson and Gallavotti. (orig.).
LDA+DMFT implemented with the pseudopotential plane-wave approach
Trimarchi, G; Leonov, I; Binggeli, N [Abdus Salam International Centre for Theoretical Physics, Trieste 34014 (Italy); Korotin, Dm; Anisimov, V I [Institute of Metal Physics, Russian Academy of Sciences, Ural Division, 620219 Yekaterinburg GSP-170 (Russian Federation)], E-mail: binggeli@ictp.it
2008-04-02
We present a joint implementation of dynamical-mean-field theory (DMFT) with the pseudopotential plane-wave approach, via Wannier functions, for the determination of the electronic properties of strongly correlated materials. The scheme uses, as input for the DMFT calculations, a tight-binding Hamiltonian obtained from the plane-wave calculations by projection onto atomic-centered symmetry-constrained Wannier functions for the correlated orbitals. We apply this scheme to two prototype systems: a paramagnetic correlated metal, SrVO{sub 3}, and a paramagnetic correlated system, V{sub 2}O{sub 3}, which exhibits a metal-insulator transition. Comparisons with available linear-muffin-tin-orbital (LMTO) plus DMFT calculations demonstrate the suitability of the joint DMFT pseudopotential plane-wave approach to describe the electronic properties of strongly correlated materials. This opens the way to future developments using the pseudopotential plane-wave DMFT approach to address total-energy properties, such as structural properties.
Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Mihaila, L; Sorella, S P; Vercauteren, D
2014-01-01
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino, as explicitly shown through a three loop calculation.
Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization
Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna
2014-12-01
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.
Mélin, Régis; Caputo, Jean-Guy; Yang, Kang; Douçot, Benoît
2017-02-01
A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction (Sa,Sb,Sc) biased with voltages (V ,-V ,0 ) is considered, but the conclusions hold more generally for resonant semiconducting quantum wire setups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for V =0 ) evolve into nonequilibrium Floquet-Wannier-Stark-Andreev (FWS-Andreev) ladders of resonances (for V ≠0 ). These resonances acquire a finite width due to multiple Andreev reflection (MAR) processes. We also consider the effect of an extrinsic linewidth broadening on the quantum dot, introduced through a Dynes phenomenological parameter. The dc-quartet current manifests a crossover between the extrinsic relaxation dominated regime at low voltage to an intrinsic relaxation due to MAR processes at higher voltage. Finally, we study the coupling between the two FWS-Andreev ladders due to Landau-Zener-Stückelberg transitions, and its effect on the crossover in the relaxation mechanism. Three important low-energy scales are identified, and a perspective is to relate those low-energy scales to a recent noise cross-correlation experiment (Y. Cohen et al., arXiv:1606.08436).
Korytar, Richard; Lorente, Nicolas, E-mail: rkorytar@cin2.es [Centro de investigacion en nanociencia y nanotecnologIa (CSIC-ICN), Campus de la UAB, E-08193 Bellaterra (Spain)
2011-09-07
We have developed a multi-orbital approach to compute the electronic structure of a quantum impurity using the non-crossing approximation. The calculation starts with a mean-field evaluation of the system's electronic structure using a standard quantum chemistry code; here we use density functional theory (DFT). We transformed the one-electron structure into an impurity Hamiltonian by using maximally localized Wannier functions. Hence, we have developed a method to study the Kondo effect in systems based on an initial one-electron calculation. We have applied our methodology to a copper phthalocyanine molecule chemisorbed on Ag(100), and we have described its spectral function for three different cases where the molecule presents a single spin or two spins with ferro- and anti-ferromagnetic exchange couplings. We find that the use of broken-symmetry mean-field theories such as Kohn-Sham DFT cannot deal with the complexity of the spin of open-shell molecules on metal surfaces and extra modeling is needed. (paper)
Renormalization group study of excitonic and superconducting order in doped honeycomb bilayer
Murray, James; Vafek, Oskar
2014-03-01
We explore the competition between spin-charge order and unconventional superconductivity in the context of the AB stacked bilayer honeycomb lattice, realized experimentally as bilayer graphene, which features approximately parabolically touching electron bands. Using a weak-coupling renormalization group theory, we show that unconventional superconductivity arises generically for repulsively interacting fermions as excitonic order is suppressed by adding charge carriers to the system. We investigate the effects of finite temperature and further-neighbor hopping, the latter of which leads to so-called ``trigonal warping'' and destroys the perfect circular symmetry of the Fermi surfaces. We show that superconductivity survives for a finite range of trigonal warping, and that the nature of the superconducting phase may change as a function of further neighbor hopping. Depending on the range of interactions and the degree of trigonal warping, we find that the most likely superconducting instabilities are to f-wave, chiral d-wave, and pair density wave phases. It is shown that unconventional superconductivity is significantly enhanced by fluctuations in particle-hole channels, with the critical temperature reaching a maximum near the excitonic phase. Supported by the NSF CAREER award under Grant No. DMR-0955561, NSF Cooperative Agreement No. DMR-0654118, and the State of Florida, as well as by ICAM-I2CAM (NSF grant DMR-0844115) and by DoE, Office of Basic Energy Sciences (Award DE-FG02-08ER46544).
A non-perturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model
Degenhard, Andreas
1999-01-01
In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin-1/2 XXX Heisenberg model in the finite temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behaviour in the temperature depende...
Computing the effective action with the functional renormalization group
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)
2016-04-15
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.)
Numerical renormalization group method for quantum impurity systems
Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
2008-04-01
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.
Matrix product density operators: Renormalization fixed points and boundary theories
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [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)
2017-03-15
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).
Signal inference with unknown response: calibration uncertainty renormalized estimator
Dorn, Sebastian; Greiner, Maksim; Selig, Marco; Böhm, Vanessa
2014-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of CURE is starting with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify CURE by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov Chain Monte Carlo sampling. We conclude that the...
Rapidity renormalized TMD soft and beam functions at two loops
Luebbert, Thomas [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Oredsson, Joel [DESY, Hamburg (Germany). Theory Group; Lund Univ. (Sweden). Dept. of Astronomy and Theoretical Physics; Stahlhofen, Maximilian [DESY, Hamburg (Germany). Theory Group; Mainz Univ. (Germany). PRISMA Cluster of Excellence
2016-03-15
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p {sub perpendicular} {sub to} -differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Topologically twisted renormalization group flow and its holographic dual
Nakayama, Yu
2017-03-01
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.
Holographic entanglement entropy of N =2* renormalization group flow
Pang, Da-Wei
2015-10-01
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.
Ghost wavefunction renormalization in asymptotically safe quantum gravity
Groh, Kai; Saueressig, Frank, E-mail: kgroh@thep.physik.uni-mainz.d, E-mail: saueressig@thep.physik.uni-mainz.d [Institute of Physics, University of Mainz, Staudingerweg 7, D-55099 Mainz (Germany)
2010-09-10
Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wavefunction renormalization of the ghost fields. The latter induces non-trivial corrections to the {beta}-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point, in agreement with the asymptotic safety conjecture which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is {eta}*{sub c} = -1.8, supporting spacetime being effectively two dimensional at short distances.
On the renormalization of non-commutative field theories
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Dynamical renormalization group resummation of finite temperature infrared divergences
Boyanovsky, D; Holman, R; Simionato, M
1999-01-01
We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and applied it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form $e^{-\\alpha T t \\ln[t/t_0]}$ which prevents a quasiparticle interpretation of charged collective excitations at finite temperature. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that trascends the conceptual limitations of the quasiparticle picture and other type of resummation schemes. We derive a simple criterion for establishing the validity of the quasiparticle picture to lowest order.
Renormalization out of equilibrium in a superrenormalizable theory
Garny, Mathias
2016-01-01
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.
Renormalization group study of damping in nonequilibrium field theory
Zanella, J
2006-01-01
In this paper we shall study whether dissipation in a $\\lambda\\phi^{4}$ may be described, in the long wavelength, low frequency limit, with a simple Ohmic term $\\kappa\\dot{\\phi}$, as it is usually done, for example, in studies of defect formation in nonequilibrium phase transitions. We shall obtain an effective theory for the long wavelength modes through the coarse graining of shorter wavelengths. We shall implement this coarse graining by iterating a Wilsonian renormalization group transformation, where infinitesimal momentum shells are coarse-grained one at a time, on the influence action describing the dissipative dynamics of the long wavelength modes. To the best of our knowledge, this is the first application of the nonequilibrium renormalization group to the calculation of a damping coefficient in quantum field theory.
One Loop Mass Renormalization of Unstable Particles in Superstring Theory
Sen, Ashoke
2016-01-01
Most of the massive states in superstring theory are expected to undergo mass renormalization at one loop order. Typically these corrections should contain imaginary parts, indicating that the states are unstable against decay into lighter particles. However in such cases, direct computation of the renormalized mass using superstring perturbation theory yields divergent result. Previous approaches to this problem involve various analytic continuation techniques, or deforming the integral over the moduli space of the torus with two punctures into the complexified moduli space near the boundary. In this paper we use insights from string field theory to describe a different approach that gives manifestly finite result for the mass shift satisfying unitarity relations. The procedure is applicable to all states of (compactified) type II and heterotic string theories. We illustrate this by computing the one loop correction to the mass of the first massive state on the leading Regge trajectory in SO(32) heterotic st...
Real space renormalization group theory of disordered models of glasses.
Angelini, Maria Chiara; Biroli, Giulio
2017-03-28
We develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.
Fully renormalized stress tensor correlator in flat space
Fröb, Markus B
2013-01-01
We present a general procedure to renormalize the stress tensor two-point correlation function on a Minkowski background in position space. The method is shown in detail for the case of a free massive scalar field in the standard Minkowski vacuum state, and explicit expressions are given for the counterterms and finite parts, which are in full accordance with earlier results for the massless case. For the general case in position space, only regularized --- but not renormalized --- results have been obtained previously. After a Fourier transformation to momentum space, we also check agreement with a previous calculation there. We generalize our results to general Hadamard states. Furthermore, the proposed procedure can presumably be generalized to the important case of an inflationary spacetime background, where the transition to momentum space is in general not possible.
E-cigarette Marketing and Older Smokers: Road to Renormalization
Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas
2015-01-01
Objectives 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. Methods 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. Results 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. Conclusions 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. PMID:25741681
A Dynamical Role for Acetylcholine in Synaptic Renormalization
Fink, Christian G.; Murphy, Geoffrey G.; Zochowski, Michal; Booth, Victoria
2013-01-01
Although sleep is a fundamental behavior observed in virtually all animal species, its functions remain unclear. One leading proposal, known as the synaptic renormalization hypothesis, suggests that sleep is necessary to counteract a global strengthening of synapses that occurs during wakefulness. Evidence for sleep-dependent synaptic downscaling (or synaptic renormalization) has been observed experimentally, but the physiological mechanisms which generate this phenomenon are unknown. In this study, we propose that changes in neuronal membrane excitability induced by acetylcholine may provide a dynamical mechanism for both wake-dependent synaptic upscaling and sleep-dependent downscaling. We show in silico that cholinergically-induced changes in network firing patterns alter overall network synaptic potentiation when synaptic strengths evolve through spike-timing dependent plasticity mechanisms. Specifically, network synaptic potentiation increases dramatically with high cholinergic concentration and decreases dramatically with low levels of acetylcholine. We demonstrate that this phenomenon is robust across variation of many different network parameters. PMID:23516342
Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response.
Stauber, T; Parida, P; Trushin, M; Ulybyshev, M V; Boyda, D L; Schliemann, J
2017-06-30
We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.
Scaling relations and multicritical phenomena from functional renormalization.
Boettcher, Igor
2015-06-01
We investigate multicritical phenomena in O(N)+O(M) models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of functional renormalization.
Substrate-induced Band Gap Renormalization in Semiconducting Carbon Nanotubes
Lanzillo, Nicholas A.; Kharche, Neerav; Nayak, Saroj K.
2014-01-01
The quasiparticle band gaps of semiconducting carbon nanotubes (CNTs) supported on a weakly-interacting hexagonal boron nitride (h-BN) substrate are computed using density functional theory and the GW Approximation. We find that the direct band gaps of the (7,0), (8,0) and (10,0) carbon nanotubes are renormalized to smaller values in the presence of the dielectric h-BN substrate. The decrease in the band gap is the result of a polarization-induced screening effect, which alters the correlation energy of the frontier CNT orbitals and stabilizes valence band maximum and conduction band minimum. The value of the band gap renormalization is on the order of 0.25 to 0.5 eV in each case. Accounting for polarization-induced band gap changes is crucial in comparing computed values with experiment, since nanotubes are almost always grown on substrates. PMID:24402238
Renormalization group approach to causal bulk viscous cosmological models
Belinchon, J A [Grupo Inter-Universitario de Analisis Dimensional, Dept. Fisica ETS Arquitectura UPM, Av. Juan de Herrera 4, Madrid (Spain); Harko, T [Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong (China); Mak, M K [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (China)
2002-06-07
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor.
Charge renormalization in planar and spherical charged lipidic aqueous interfaces.
Bordi, Federico; Cametti, Cesare; Sennato, Simona; Paoli, Beatrice; Marianecci, Carlotta
2006-03-16
The charge renormalization in planar and spherical charged lipidic aqueous interfaces has been investigated by means of thermodynamic and electrokinetic measurements. We analyzed the behavior of mixed DOTAP/DOPE monolayers at the air-electrolyte solution interface and DOTAP/DOPE liposomes 100 nm in size dispersed in an aqueous phase of varying ionic strength. For the two systems, we have compared the "effective" surface charge derived from the measurements of surface potential and zeta-potential to the "bare" charge based on the stoichiometry of the lipid mixture investigated. The results confirm that a strong charge renormalization occurs, whose strength depends on the geometry of the mesoscopic system. The dependence of the "effective" charge on the "bare" charge is discussed in light of an analytical approximation based on the Poisson-Boltzmann equation recently proposed.
Topologically twisted renormalization group flow and its holographic dual
Nakayama, Yu
2016-01-01
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a non-trivial 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 non-trivial 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 AdS metric.
More on the renormalization group limit cycle in QCD
Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga
2006-02-26
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.
Keldysh functional renormalization group for electronic properties of graphene
Fräßdorf, Christian; Mosig, Johannes E. M.
2017-03-01
We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible nonzero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer et al., Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409.
Renormalization and asymptotic expansion of Dirac's polarized vacuum
Gravejat, Philippe; Séré, Eric
2010-01-01
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\\alphaph$, provided that the ultraviolet cut-off behaves as $\\Lambda\\sim e^{3\\pi(1-Z_3)/2\\alphaph}\\gg1$. The renormalization parameter $0
Dimensional Reduction, Hard Thermal Loops and the Renormalization Group
Stephens, C R; Hess, P O; Astorga, F; Weber, Axel; Hess, Peter O.; Astorga, Francisco
2004-01-01
We study the realization of dimensional reduction and the validity of the hard thermal loop expansion for lambda phi^4 theory at finite temperature, using an environmentally friendly finite-temperature renormalization group with a fiducial temperature as flow parameter. The one-loop renormalization group allows for a consistent description of the system at low and high temperatures, and in particular of the phase transition. The main results are that dimensional reduction applies, apart from a range of temperatures around the phase transition, at high temperatures (compared to the zero temperature mass) only for sufficiently small coupling constants, while the HTL expansion is valid below (and rather far from) the phase transition, and, again, at high temperatures only in the case of sufficiently small coupling constants. We emphasize that close to the critical temperature, physics is completely dominated by thermal fluctuations that are not resummed in the hard thermal loop approach and where universal quant...
Cyclic renormalization and automorphism groups of rooted trees
Bass, Hyman; Rockmore, Daniel; Tresser, Charles
1996-01-01
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.
Renormalization of 3d quantum gravity from matrix models
Ambjørn, Jan; Loll, R
2004-01-01
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
Renormalization Group Analysis of Weakly Rotating Turbulent Flows
王晓宏; 周全
2011-01-01
Dynamic renormalization group (RNG) analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence. For turbulent How subject to weak rotation, the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part. Then, with a low-order approximation, the coarsening procedure of RNG transformation is performed. After implementing the coarsening and rescaling procedures, the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k) ∝ k11/5 for weakly rotating turbulence. It is also shown that the Coriolis force will disturb the stability of the Kolmogorov -5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.%Dynamic renormalization group(RNG)analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence.For turbulent flow subject to weak rotation,the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part.Then,with a low-order approximation,the coarsening procedure of RNG transformation is performed.After implementing the coarsening and rescaling procedures,the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k)∝ k-11/5 for weakly rotating turbulence.It is also shown that the Coriolis force will disturb the stability of the Kolmogorov-5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.
Philosophical Implications of Kadanoff's Work on the Renormalization Group
Batterman, Robert W.
2017-05-01
This paper investigates the consequences for our understanding of physical theories as a result of the development of the renormalization group. Kadanoff's assessment of these consequences is discussed. What he called the "extended singularity theorem" (that phase transitons only can occur in infinite systems) poses serious difficulties for philosophical interpretation of theories. Several responses are discussed. The resolution demands a philosophical rethinking of the role of mathematics in physical theorizing.
The Numerical Renormalization Group Method for correlated electrons
Bulla, Ralf
2000-01-01
The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular th...
Lattice renormalization of the static quark derivative operator
Blossier, B; Morénas, V; Pène, O
2006-01-01
We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $\\tau_{1/2}(1)$ and $\\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.
Renormalization of the Spin-dependent WIMP scattering off nuclei
Divari, P C
2013-01-01
We study the amplitude for the spin-dependent WIMP scattering off nuclei by including the leading long-range two-body currents in the most important isovector contribution. We show that such effects are essentially independent of the target nucleus and, as a result, they can be treated as a mere renormalization of the effective nucleon cross section or, equivalently, of the corresponding effective coupling with values around 25%.
Renormalization and Induced Gauge Action on a Noncommutative Space
Grosse, Harald
2007-01-01
Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to $\\phi^3$ models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\\theta$-deformed space and derive noncommutative gauge actions.
The proton-proton scattering without Coulomb force renormalization
Glöckle W.
2010-04-01
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.
Scalar meson mass from renormalized One Boson Exchange Potential
Cordon, A Calle
2008-01-01
We determine the mass and strength of the scalar meson from NN scattering data by renormalizing the One Boson Exchange Potential. This procedure provides a great insensitivity to the unknown short distance interaction making the vector mesons marginally important and allowing for SU(3) couplings in the 1S0 channel. The scalar meson parameters are tightly constrained by low energy np. We discuss whether this scalar should be compared to the recent findings based on the Roy equations analysis of pipi scattering.
Renormalization group analysis of the gluon mass equation
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2014-04-01
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.
Spatial Brownian motion in renormalized Poisson potential: A critical case
Chen, Xia
2011-01-01
Let $B_s$ be a three dimensional Brownian motion and $\\omega(dx)$ be an independent Poisson field on $\\mathbb{R}^3$. It is proved that for any $t>0$, conditionally on $\\omega(\\cdot)$, \\label{*} \\mathbb{E}_0 \\exp\\{\\theta \\int_0^t \\bar{V}(B_s) ds\\} \\ 1/16, where $\\bar{V}(x)$ is the renormalized Poisson potential
A renormalization approach to the universality of scaling in phyllotaxis
Reick, Christian H.
2015-04-01
Phyllotaxis, i.e. the arrangement of plant organs like leaves, florets, scales, bracts etc. around a shoot, stem, or cone, is often highly regular. Across the plant kingdom phyllotaxis shows not only qualitatively, but also quantitatively identical features, like the occurrence of divergence angles close to noble irrationals. In a previous study (Reick, 2012) a mechanism has been identified that explains the selection of these particular divergence angles on the basis of self-similarity and scaling, numerically found in the bifurcation diagrams of simple dynamical models of phyllataxis. In the present paper, by constructing a renormalization theory, the universality of this scaling is proved for a whole class of models, prototypically represented by Thornley's model of phyllotaxis (Thornley, 1975). The renormalization is constructed from another self-similarity found numerically for the Fourier transform of the abstract potential governing the mutual inhibition of primordia. Surprisingly, the resulting renormalization transformation is already known from the treatment of the quasiperiodic transition to chaos but operates here on a different function space. It turns out that the fixed points of the renormalization transformation are characterized by divergences of the form Θ (κ) = 1 /τ (κ), where, written as continued fraction, τ (κ) = [ κ ; κ , κ , … ] , κ ∈N+. To show the universality of the scaling, it is demonstrated that the fixed points are unstable and that the associated scaling factors α (κ) = -(τ (κ)) 2 and β (κ) =τ (κ) are exactly those that were numerically found in (Reick, 2012) to rule the selfsimilarity of the bifurcation structure. Thereby, the present paper puts forward an explanation for the universal appearance of certain phyllotactic patterns that is independent of physiological detail of plant growth.
Background independent exact renormalization group for conformally reduced gravity
2015-01-01
Within the conformally reduced gravity model, where the metric is parametrised by a function f ( ϕ ) of the conformal factor ϕ , we keep dependence on both the background and fluctuation fields, to local potential approximation and O ∂ 2 $$ \\mathcal{O}\\left({\\partial}^2\\right) $$ respectively, making no other approximation. Explicit appearances of the background metric are then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) ...
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization
Kniehl, Bernd A
2009-01-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
Renormalization-group calculation of excitation properties for impurity models
Yoshida, M.; Whitaker, M. A.; Oliveira, L. N.
1990-05-01
The renormalization-group method developed by Wilson to calculate thermodynamical properties of dilute magnetic alloys is generalized to allow the calculation of dynamical properties of many-body impurity Hamiltonians. As a simple illustration, the impurity spectral density for the resonant-level model (i.e., the U=0 Anderson model) is computed. As a second illustration, for the same model, the longitudinal relaxation rate for a nuclear spin coupled to the impurity is calculated as a function of temperature.
A Constraint on Defect and Boundary Renormalization Group Flows
Jensen, Kristan
2015-01-01
A conformal field theory (CFT) in dimension $d\\geq 3$ coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" $b$ that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that $b$ must decrease or remain constant from ultraviolet to infrared. Our result applies also to a CFT in $d=3$ flat space with a planar boundary.
Massive renormalization scheme and perturbation theory at finite temperature
Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [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)
2015-02-04
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.
The Renormalization Effects in the Microstrip-SQUID Amplifier
Berman, G P; Tsifrinovich, V I
2011-01-01
The peculiarities of the microstrip-DC SQUID amplifier caused by the resonant structure of the input circuit are analyzed. It is shown that the mutual inductance, that couples the input circuit and the SQUID loop, depends on the frequency of electromagnetic field. The renormalization of the SQUID parameters due to the screening effect of the input circuit vanishes when the Josephson frequency is much greater than the signal frequency.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
One-dimensional contact process: duality and renormalization.
Hooyberghs, J; Vanderzande, C
2001-04-01
We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.
Renormalization-group transformations and correlations of seismicity.
Corral, Alvaro
2005-07-08
The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. A recently reported scaling law for the distribution of recurrence times implies that these distributions must be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. This approach puts the study of the temporal structure of seismicity in the context of critical phenomena.
Constraint on Defect and Boundary Renormalization Group Flows.
Jensen, Kristan; O'Bannon, Andy
2016-03-04
A conformal field theory (CFT) in dimension d≥3 coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" b that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that b must decrease or remain constant from the ultraviolet to the infrared. Our result applies also to a CFT in d=3 flat space with a planar boundary.
Renormalization group analysis for an asymmetric simple exclusion process.
Mukherji, Sutapa
2017-03-01
A perturbative renormalization group method is used to obtain steady-state density profiles of a totally asymmetric simple exclusion process with particle adsorption and evaporation. This method allows us to obtain a globally valid solution for the density profile without the asymptotic matching of bulk and boundary layer solutions. In addition, we show a nontrivial scaling of the boundary layer width with the system size close to specific phase boundaries.
Subtractive Renormalization Group Invariance: Pionless EFT at NLO
Timóteo, Varese S.; Szpigel, Sérgio; Durães, Francisco O.
2010-11-01
We show some results concerning the renormalization group (RG) invariance of the nucleon-nucleon (NN) interaction in pionless effective field theory at next-to-leading order (NLO), using a non-relativistic Callan-Symanzik equation (NRCS) for the driving term of the Lippmann-Schwinger (LS) equation with three recursive subtractions. The phase-shifts obtained for the RG evolved potential are same as those for the original potential, apart from relative differences of order 10-15.
Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model
Wang, Zhituo
2012-01-01
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
Renormalization-group flows and fixed points in Yukawa theories
Mølgaard, Esben; Shrock, R.
2014-01-01
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....... 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....
Power counting and Wilsonian renormalization in nuclear effective field theory
Valderrama, Manuel Pavón
2016-05-01
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.
Unifying renormalization group and the continuous wavelet transform
Altaisky, M. V.
2016-05-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e., those depending on both the position x and the resolution a . Such a theory, earlier described in [1,2], is finite by construction. The space of scale-dependent functions {ϕa(x )} is more relevant to a physical reality than the space of square-integrable functions L2(Rd); because of the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than a point. The effective action Γ(A ) of our theory turns out to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet—an "aperture function" of a measuring device used to produce the snapshot of a field ϕ at the point x with the resolution a . The standard renormalization group results for ϕ4 model are reproduced.
Fourier Monte Carlo renormalization-group approach to crystalline membranes.
Tröster, A
2015-02-01
The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.
One-loop renormalization of a gravity-scalar system
Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)
2017-05-15
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.)
Renormalized spacetime is two-dimensional at the Planck scale
Padmanabhan, T; Kothawala, Dawood
2015-01-01
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}...
Real-space renormalized dynamical mean field theory
Kubota, Dai; Sakai, Shiro; Imada, Masatoshi
2016-05-01
We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.
Song, Mi-Young; Yoon, Jung-Sik [Plasma Technology Research Center, National Fusion Research Institute, 814-2 Osikdo-Dong, Gunsan-City, Jeollabuk-Do 573-540 (Korea, Republic of); Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr [Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States); Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of)
2015-04-15
The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it is found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.
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: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2017-01-30
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.
Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
Skouroupathis, A.; Panagopoulos, H.
2007-11-01
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators ψ¯Γψ, where Γ denotes the scalar and pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Zm. As a prerequisite for the above, we also compute the quark field renormalization, Zψ, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in cSW, in terms of both the renormalized and bare coupling constants, in the renormalized Feynman gauge. We also confirm the one-loop renormalization functions, for generic gauge. Finally, we present our results in the MS¯ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in the Appendix.
Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
Skouroupathis, A
2007-01-01
We compute the two-loop renormalization functions, in the RI $^\\prime$ scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_{\\psi}$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. Finally, we present our results in the $\\bar{MS}$ scheme, for easier comparison with calculations in the continuum.
Dryga, Anatoly; Warshel, Arieh
2010-01-01
Simulations of long time process in condensed phases in general and in biomolecules in particular, presents a major challenge that cannot be overcome at present by brute force molecular dynamics (MD) approaches. This work takes the renormalization method, intruded by us sometime ago, and establishes its reliability and potential in extending the time scale of molecular simulations. The validation involves a truncated gramicidin system in the gas phase that is small enough to allow very long explicit simulation and sufficiently complex to present the physics of realistic ion channels. The renormalization approach is found to be reliable and arguably presents the first approach that allows one to exploit the otherwise problematic steered molecular dynamics (SMD) treatments in quantitative and meaningful studies. It is established that we can reproduce the long time behavior of large systems by using Langevin dynamics (LD) simulations of a renormalized implicit model. This is done without spending the enormous time needed to obtain such trajectories in the explicit system. The present study also provides a promising advance in accelerated evaluation of free energy barriers. This is done by adjusting the effective potential in the implicit model to reproduce the same passage time as that obtained in the explicit model, under the influence of an external force. Here having a reasonable effective friction provides a way to extract the potential of mean force (PMF) without investing the time needed for regular PMF calculations. The renormalization approach, which is illustrated here in realistic calculations, is expected to provide a major help in studies of complex landscapes and in exploring long time dynamics of biomolecules. PMID:20836533
The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
Hergert, H; Morris, T D; Schwenk, A; Tsukiyama, K
2015-01-01
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito 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 fun...
Gómez-Rocha, María
2016-01-01
The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling with the renormalization-group scale and summarize the basic elements needed in the formulation of the bound-state problem.
Duka, P; Zralek, M
2000-01-01
Quantization and renormalization of the left-right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev-Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on mass shell renormalization is performed and, as a test of consistency, the renormalization of the ZNiNj vertex is analyzed.
Tensor renormalization group approach to two-dimensional classical lattice models.
Levin, Michael; Nave, Cody P
2007-09-21
We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.
Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai J.; Rejzner, Katarzyna Anna
2013-01-01
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. For scalar fields the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and...
Geometry of Dynamic Large Networks: A Scaling and Renormalization Group Approach
2013-12-11
Geometry of Dynamic Large Networks - A Scaling and Renormalization Group Approach IRAJ SANIEE LUCENT TECHNOLOGIES INC 12/11/2013 Final Report...Z39.18 Final Performance Report Grant Title: Geometry of Dynamic Large Networks: A Scaling and Renormalization Group Approach Grant Award Number...test itself may be scaled to much larger graphs than those we examined via renormalization group methodology. Using well-understood mechanisms, we
One-loop renormalization of fermionic currents with the overlap-Dirac operator
Alexandrou, C; Panagopoulos, H; Vicari, E
2000-01-01
We compute the one-loop lattice renormalization of the two-quark operators$\\bar{\\psi} \\Gamma \\psi$, where $\\Gamma$ denotes the generic Dirac matrix, forthe lattice formulation of QCD using the overlap-Dirac operator. We also study the renormalization of quark bilinears which are more extendedand have better chiral properties. Finally, we present improved estimates of these renormalization constants,coming from cactus resummation and from mean field perturbation theory.
Jiang, Shixiao W.; Lu, Haihao; Zhou, Douglas; Cai, David
2016-08-01
Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β-Fermi-Pasta-Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems.
Connection between the renormalization groups of Stueckelberg-Petermann and Wilson
Duetsch, Michael [Courant Research Centre in Mathematics, Universitaet Goettingen (Germany); Brunetti, Romeo [Dipartimento di Matematica, Universita di Trento (Italy); Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2010-07-01
The Stueckelberg-Petermann renormalization group (RG) relies on the non-uniqueness of the S-matrix in causal perturbation theory (i.e. Epstein-Glaser renormalization); it is the family of all finite renormalizations. The RG in the sense of Wilson refers to the dependence of the theory on a cutoff. A new formalism for perturbative algebraic quantum field theory allows to clarify the relation between these different notions of RG. In particular we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method.
Setting the renormalization scale in QCD: The principle of maximum conformality
Brodsky, S. J.; Di Giustino, L.
2012-01-01
the renormalization scale is set properly, all nonconformal beta not equal 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...
Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-04-28
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.
On advanced fluid modelling of drift wave turbulence
Weiland, J; Zasenko, V
2007-01-01
The Dupree-Weinstock renormalization is used to prove that a reactive closure exists for drift wave turbulence in magnetized plasmas. The result is used to explain recent results in gyrokinetic simulations and is also related to the Mattor-Parker closure. The level of closure is found in terms of applied external sources.
Renormalized dynamics of the Dean-Kawasaki model
Bidhoodi, Neeta; Das, Shankar P.
2015-07-01
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.
Renormalization group flow of scalar models in gravity
Guarnieri, Filippo
2014-04-08
In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.
Renormalized dynamics of the Dean-Kawasaki model.
Bidhoodi, Neeta; Das, Shankar P
2015-07-01
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 D(0) to D(R) is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997)]. D(R) 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 D(R)=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.
Antonov N.V.
2016-01-01
Full Text Available We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t′/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa–Kardar model is irrelevant and to the “pure” Hwa–Kardar model (the advection is irrelevant. For the special case ξ = 2(4 − d/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.
Truncation Effects in Monte Carlo Renormalization Group Improved Lattice Actions
Takaishi, T; Forcrand, Ph. de
1998-01-01
We study truncation effects in the SU(3) gauge actions obtained by the Monte Carlo renormalization group method. By measuring the heavy quark potential we find that the truncation effects in the actions coarsen the lattice by 40-50 % from the original blocked lattice. On the other hand, we find that rotational symmetry of the heavy quark potentials is well recovered on such coarse lattices, which may indicate that rotational symmetry breaking terms are easily cancelled out by adding a short distance operator. We also discuss the possibility of reducing truncation effects.
Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
Constantinou, M; Panagopoulos, H; Spanoudes, G
2016-01-01
In this paper we present the perturbative evaluation of the difference between the renormalization functions of flavor singlet and nonsinglet bilinear quark operators on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, for a class of improved lattice actions, including Wilson, tree-level (TL) Symanzik and Iwasaki gluons, twisted mass and SLiNC Wilson fermions, as well as staggered fermions with twice stout-smeared links. In the staggered formalism, the stout smearing procedure is also applied to the definition of bilinear operators.