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.
Brueckner-Hartree-Fock calculations for finite nuclei with renormalized realistic forces
Hu, B. S.; Xu, F. R.; Wu, Q.; Ma, Y. Z.; Sun, Z. H.
2017-03-01
One can adopt two-step G -matrix approximations for the Brueckner-Hartree-Fock (BHF) calculations. The first G matrix is to soften the bare force, and the second one is to include the high-order correlations of the interaction in medium. The first G -matrix calculation for two-nucleon interaction should be done in the center-of-mass coordinate. As another alternative BHF approach, we have adopted the Vlow-k technique to soften the interaction and used the G matrix to include high-order correlations. The Vlow-k renormalization leads to high-momentum and low-momentum components of the interaction decoupled. With the Vlow-k potential, we have performed the BHF calculations for finite nuclei. The G -matrix elements with exact Pauli exclusions are calculated in the self-consistent BHF basis. To see effects from further possible correlations beyond BHF, we have simultaneously performed renormalized BHF (RBHF) calculations with the same potential. In RBHF, the mean field derived from realistic forces is modified by introducing the particle-occupation depletion resulting from many-body correlations. The ground-state energies and radii of the closed-shell nuclei, 4He, 16O, and 40Ca, have been investigated. The convergences of the BHF and RBHF calculations have been discussed and compared with other ab initio calculations with the same potential.
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.
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.
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.
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.
Applications of the Similarity Renormalization Group to the Nuclear Interaction
Jurgenson, E D
2009-01-01
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the inter-nucleon interaction. We examine decoupling quantitatively for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small. To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces. The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. ...
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.
Dynamical Symmetries Reflected in Realistic Interactions
Sviratcheva, K.D.; Draayer, J.P.; /Louisiana State U.; Vary, J.P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-06
Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei. Based on spectral distribution methods, a comparison of these interactions to a most general Sp(4) dynamically symmetric interaction, which previously we found to reproduce well that part of the interaction that is responsible for shaping pairing-governed isobaric analog 0{sup +} states, can determine the extent to which this significantly simpler model Hamiltonian can be used to obtain an approximate, yet very good description of low-lying nuclear structure. And furthermore, one can apply this model in situations that would otherwise be prohibitive because of the size of the model space. In addition, we introduce a Sp(4) symmetry breaking term by including the quadrupole-quadrupole interaction in the analysis and examining the capacity of this extended model interaction to imitate realistic interactions. This provides a further step towards gaining a better understanding of the underlying foundation of realistic interactions and their ability to reproduce striking features of nuclei such as strong pairing correlations or collective rotational motion.
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 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.
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.
Nanoplasmonic renormalization and enhancement of Coulomb interactions
Durach, M; Rusina, A; Stockman, M I [Department of Physics and Astronomy, Georgia State University, Atlanta, GA (United States); Klimov, V I [Chemistry Division, C-PCS, Los Alamos National Laboratory, Los Alamos, NM (United States)], E-mail: mstockman@gsu.edu
2008-10-15
In this paper, we propose a general and powerful theory of the plasmonic enhancement of the many-body phenomena resulting in a closed expression for the surface plasmon-dressed Coulomb interaction. We illustrate this theory by computing the dressed interaction explicitly for an important example of metal-dielectric nanoshells which exhibits a rich resonant behavior in magnitude and phase. This interaction is used to describe the nanoplasmonic-enhanced Foerster resonant energy transfer (FRET) between nanocrystal quantum dots near a nanoshell.
Nanoplasmonic renormalization and enhancement of Coulomb interactions
Durach, M.; Rusina, A.; Klimov, V. I.; Stockman, M. I.
2008-10-01
In this paper, we propose a general and powerful theory of the plasmonic enhancement of the many-body phenomena resulting in a closed expression for the surface plasmon-dressed Coulomb interaction. We illustrate this theory by computing the dressed interaction explicitly for an important example of metal-dielectric nanoshells which exhibits a rich resonant behavior in magnitude and phase. This interaction is used to describe the nanoplasmonic-enhanced Förster resonant energy transfer (FRET) between nanocrystal quantum dots near a nanoshell.
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.
Realistic model for radiation-matter interaction
Pakula, R A
2004-01-01
This paper presents a realistic model that describes radiation-matter interactions. This is achieved by a generalization of first quantization, where the Maxwell equations are interpreted as the electromagnetic component of the Schrodinger equation. This picture is complemented by the consideration of electrons and photons as real particles in three-dimensional space, following guiding conditions derived from the particle-wave-functions to which they are associated. The guiding condition for the electron is taken from Bohmian mechanics, while the photon velocity is defined as the ratio between the Poynting vector and the electromagnetic energy density. The case of many particles is considered, taking into account their statistical properties. The formalism is applied to a two level system, providing an intuitive description for spontaneous emission, Lamb shift, scattering, absorption, dispersion, resonance fluorescence and vacuum fields. This model describes quantum jumps by the entanglement between the photo...
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, CA 94117-1080 (United States)]. E-mail: camblong@usfca.edu; Epele, Luis N. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Fanchiotti, Huner [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Garcia Canal, Carlos A. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, TX 77204-5506 (United States)
2007-05-14
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
Three-neutron resonance trajectories for realistic interaction models
Lazauskas, R
2005-01-01
Three-neutron resonances are searched using realistic nucleon-nucleon interaction models. Resonance pole trajectories were explored by artificially binding three-neutron and then gradually removing additional interaction. The final pole positions for three-neutron states up to $|J|$=5/2 finish in the fourth energy quadrant with Re(E)$\\leqslant0$ before additional interaction is removed. This study shows that realistic nucleon-nucleon interaction models exclude possible existence of observable three-neutron resonances.
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.
High-performance functional Renormalization Group calculations for interacting fermions
Lichtenstein, J.; Sánchez de la Peña, D.; Rohe, D.; Di Napoli, E.; Honerkamp, C.; Maier, S. A.
2017-04-01
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the t ,t‧ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.
Pairing properties of realistic effective interactions
Gargano A.
2016-01-01
Full Text Available We investigate the pairing properties of an effective shell-model interaction defined within a model space outside 132Sn and derived by means of perturbation theory from the CD-Bonn free nucleon-nucleon potential. It turns out that the neutron pairing component of the effective interaction is significantly weaker than the proton one, which accounts for the large pairing gap difference observed in the two-valence identical particle nuclei 134Sn and 134Te. The role of the contribution arising from one particle-one hole excitations in determining the pairing force is discussed and its microscopic structure is also analyzed in terms of the multipole decomposition.
The functional renormalization group for interacting quantum systems with spin-orbit interaction
Grap, Stephan Michael [RWTH Aachen (Germany). Inst. fuer Theorie der Statistischen Physik
2013-07-15
We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer
Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
Ghosh, A; Talukdar, B; Ghosh, Angsula; Adhikari, Sadhan K.
1998-01-01
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.
Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
Ghosh, Angsula; Adhikari, Sadhan K.; Talukdar, B.
1998-10-01
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.
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.
Szpigel, S. [Centro de Ciencias e Humanidades, Universidade Presbiteriana Mackenzie, Sao Paulo, SP (Brazil); Timoteo, V.S. [Faculdade de Tecnologia, Universidade Estadual de Campinas, Limeira, SP (Brazil); Duraes, F. de O [Centro de Ciencias e Humanidades, Universidade Presbiteriana Mackenzie, Sao Paulo, SP (Brazil)
2010-02-15
In this work we study the Similarity Renormalization Group (SRG) evolution of effective nucleon-nucleon (NN) interactions derived using the Subtracted Kernel Method (SKM) approach. We present the results for the phaseshifts in the {sup 1}S{sub 0} channel calculated using a SRG potential evolved from an initial effective potential obtained by implementing the SKM scheme for the leading-order NN interaction in chiral effective field theory (ChEFT).
Renormalization of the Off-shell chiral two-pion exchange NN interactions
Entem, D R
2009-01-01
The renormalization, finiteness and off-shellness of short distance power like singular interactions is discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding on-shell amplitude without proliferation of new counterterms. We illustrate the result by complementary calculations both in coordinate as well as in momentum space in the simplest 1S0 channel for chiral np interactions including Two Pion Exchange.
Exposure render: an interactive photo-realistic volume rendering framework.
Thomas Kroes
Full Text Available The field of volume visualization has undergone rapid development during the past years, both due to advances in suitable computing hardware and due to the increasing availability of large volume datasets. Recent work has focused on increasing the visual realism in Direct Volume Rendering (DVR by integrating a number of visually plausible but often effect-specific rendering techniques, for instance modeling of light occlusion and depth of field. Besides yielding more attractive renderings, especially the more realistic lighting has a positive effect on perceptual tasks. Although these new rendering techniques yield impressive results, they exhibit limitations in terms of their exibility and their performance. Monte Carlo ray tracing (MCRT, coupled with physically based light transport, is the de-facto standard for synthesizing highly realistic images in the graphics domain, although usually not from volumetric data. Due to the stochastic sampling of MCRT algorithms, numerous effects can be achieved in a relatively straight-forward fashion. For this reason, we have developed a practical framework that applies MCRT techniques also to direct volume rendering (DVR. With this work, we demonstrate that a host of realistic effects, including physically based lighting, can be simulated in a generic and flexible fashion, leading to interactive DVR with improved realism. In the hope that this improved approach to DVR will see more use in practice, we have made available our framework under a permissive open source license.
Can realistic nuclear interactions tolerate a resonant tetraneutron ?
Lazauskas, R
2005-01-01
The possible existence of four-neutron resonances close to the physical energy region is explored. Faddeev-Yakubovsky equations have been solved in configuration space using realistic nucleon-nucleon interaction models. Complex Scaling and Analytical Continuation in the Coupling Constant methods were used to follow the resonance pole trajectories, which emerge out of artificially bound tetraneutron states. The final pole positions for four-neutron states lie in the third energy quadrant with negative real energy parts and should thus not be physically observable.
Erler, Bastian
2012-07-18
Realistic nucleon-nucleon interactions transformed via the Unitary Correlation Operator Method (UCOM) or the Similarity Renormalization Group (SRG) have proven to be a suitable starting point for the description of closed-shell nuclei via mean-field methods like Hartree-Fock (HF). This allows the treatment of a number of heavy nuclei with realistic nucleon-nucleon interactions, which would otherwise only be possible with phenomenological interactions. To include three-nucleon forces in an approximate way, the UCOM or SRG transformed interactions can be augmented by a three-body contact interaction, which is necessary to reproduce measured charge radii. However, many interesting nuclei, including those near the neutron drip line, are far away from closed shells. These nuclei are of great importance for modeling nucleosynthesis processes in the universe, but experiments can only be performed at a few research facilities. In this work, the Hartree Fock (HF) approach with realistic interactions is extended to light deformed nuclei. Pairing correlations are not taken into account. A crucial step in this process is to allow deformed ground states on the mean-field level, as only nuclei with at least one closed shell can be described with spherical HF ground states. To restore the rotational symmetry in the lab frame, exact angular-momentum projection (AMP) is implemented. Constrained HF calculations are used for an approximate variation after projection approach. The AMP-HF description of open-shell nuclei is on par with the pure HF description of closed-shell nuclei. Charge-radii and systematics of binding energies agree well with experiment. However, missing correlations, lead to an underestimated absolute value of the binding energy. Projection on higher angular momenta approximately reproduces the energy systematics of rotational bands. To describe collective excitations, the Random Phase Approximation (RPA) constitutes a well tested approach, which can also be
Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments
Duriez, Christian; Kheddar, Abderrahmane; Andriot, Claude
2008-01-01
A new computer haptics algorithm to be used in general interactive manipulations of deformable virtual objects is presented. In multimodal interactive simulations, haptic feedback computation often comes from contact forces. Subsequently, the fidelity of haptic rendering depends significantly on contact space modeling. Contact and friction laws between deformable models are often simplified in up to date methods. They do not allow a "realistic" rendering of the subtleties of contact space physical phenomena (such as slip and stick effects due to friction or mechanical coupling between contacts). In this paper, we use Signorini's contact law and Coulomb's friction law as a computer haptics basis. Real-time performance is made possible thanks to a linearization of the behavior in the contact space, formulated as the so-called Delassus operator, and iteratively solved by a Gauss-Seidel type algorithm. Dynamic deformation uses corotational global formulation to obtain the Delassus operator in which the mass and s...
Renormalization of the three-boson system with short-range interactions revisited
Epelbaum, E. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Gegelia, J. [Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia); Meissner, Ulf G. [Universitaet Bonn, Helmholtz Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Yao, De-Liang [Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany)
2017-05-15
We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The obtained leading-order equation is perturbatively renormalizable and non-perturbatively finite and does not require a three-body counter term in contrast to its non-relativistic approximation. (orig.)
Generalized seniority with realistic interactions in open-shell nuclei
Caprio, M A; Cai, K; Constantinou, Ch; Hellemans, V
2014-01-01
Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr iso...
Foreword: In situ gas surface interactions: approaching realistic conditions
Lundgren, Edvin; Over, Herbert
2008-03-01
This special issue is devoted to the application of in situ surface-sensitive techniques in the elucidation of catalysed reactions at (model) catalyst surfaces. Both reaction intermediates and the nature of the catalytically active phase are the targets of these investigations. In situ surface science techniques are also used to study the interaction of water with surfaces under realistic conditions. Since 80% of all technical chemicals are manufactured by utilizing (heterogeneous) catalysis, scientific understanding and technological development of catalysis are of central practical importance in modern society [1]. Heterogeneously catalysed reactions take place at the gas/solid interface. Therefore one of the major topics in surface chemistry and physics is closely related to heterogeneous catalysis, with the aim of developing novel catalysts and to improve catalysts' performances on the basis of atomic scale based knowledge. Despite the economical and environmental rewards—if such a goal is achieved—and despite 40 years of intensive research, practical catalysis is still safely in a black box: the reactivity and selectivity of a catalyst are commercially still optimized on a trial and error basis, applying the high throughput screening approach. The reason for this discrepancy between ambition and reality lies in the inherent complexity of the catalytic system, consisting of the working catalyst and the interaction of the catalyst with the reactant mixture. Practical (solid) catalysts consist of metal or oxide nanoparticles which are dispersed and stabilized on a support and which may be promoted by means of additives. These particles catalyse a reaction in pressures as high as 100 bar. Practical catalysis is in general considered to be far too complex for gaining atomic-scale understanding of the mechanism of the catalysed reaction of an industrial catalyst during its operation. Therefore it has been necessary to introduce idealization and simplification of
Li, Xiao; Tse, Wang-Kong
2017-02-01
We develop a theory for the optical conductivity of doped ABC-stacked multilayer graphene including the effects of electron-electron interactions. Applying the quantum kinetic formalism, we formulate a set of pseudospin Bloch equations that govern the dynamics of the nonequilibrium density matrix driven by an external ac electric field under the influence of Coulomb interactions. These equations reveal a dynamical mechanism that couples the Drude and interband responses arising from the chirality of pseudospin textures in multilayer graphene systems. We demonstrate that this results in an interaction-induced enhancement of the Drude weight and plasmon frequency strongly dependent on the pseudospin winding number. Using bilayer graphene as an example, we also study the influence of higher-energy bands and find that they contribute considerable renormalization effects not captured by a low-energy two-band description. We argue that this enhancement of Drude weight and plasmon frequency occurs generally in materials characterized by electronic chirality.
Branco, N S; de Sousa, J Ricardo; Ghosh, Angsula
2008-03-01
Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.
Pereira, E. [Departamento Fisica-ICEx, UFMG, CP 702, Belo Horizonte MG 30.161-970 (Brazil); Procacci, A. [Departamento Matematica-ICEx, UFMG, CP 702, Belo Horizonte MG 30.161-970 (Brazil)
1997-03-01
Searching for a general and technically simple multiscale formalism to treat interacting fermions, we develop a (Wilson{endash}Kadanoff) block renormalization group mechanism, which, due to the property of {open_quotes}orthogonality between scales,{close_quotes} establishes a trivial link between the correlation functions and the effective potential flow, leading to simple expressions for the generating and correlation functions. Everything is based on the existence of {open_quotes}special configurations{close_quotes} (lattice wavelets) for multiscale problems: using a simple linear change of variables relating the initial fields to these configurations, we establish the formalism. The algebraic formulas show a perfect parallel with those obtained for bosonic problems, considered in previous works. {copyright} 1997 Academic Press, Inc.
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.
Weidinger, Lukas; Bauer, Florian; von Delft, Jan
2017-01-01
We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance
Can realistic interaction be useful for nuclear mean-field approaches?
Nakada, H.; Sugiura, K. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Inakura, T. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Kyoto University, Yukawa Institute of Theoretical Physics, Sakyo, Kyoto (Japan); Niigata University, Department of Physics, Niigata (Japan); Margueron, J. [Universite de Lyon 1, CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2016-07-15
Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2N and 3N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches. (orig.)
Hering, Max; Reuther, Johannes
2017-02-01
We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated J1-J2 kagome-Heisenberg model using the pseudofermion functional renormalization group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of noncollinear magnetic orders of the J1-J2 Heisenberg model (q =0 , √{3 }×√{3 } , and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral herbertsmithite which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicate that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for herbertsmithite, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.
Amazon, Jonathan J.; Feigenson, Gerald W.
2015-01-01
When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant. PMID:25353504
Renormalization of the hydrogen sulfide properties due to the strong electron-phonon interaction
Kudryashov, N. A.; Kutukov, A. A.; Mazur, E. A.
2017-01-01
The normal state of a metal is described by generalized Eliashberg theory which takes into account the finite width of an electron band, strong electron-phonon coupling and electron-hole nonequivalence. Reconstructed parameters of the conduction band of the metallic hydrogen sulfide for both the real and imaginary parts of the mass renormalization of the electron Green’s function and the real and imaginary parts of the renormalization of the chemical potential have been found.
A state interaction spin-orbit coupling density matrix renormalization group method
Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic
2016-06-01
We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4]3-, determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.
A state interaction spin-orbit coupling density matrix renormalization group method.
Sayfutyarova, Elvira R; Chan, Garnet Kin-Lic
2016-06-21
We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4](3-), determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.
Coe, Jeremy P; Almeida, Nuno M S; Paterson, Martin J
2017-09-02
We investigate if a range of challenging spin systems can be described sufficiently well using Monte Carlo configuration interaction (MCCI) and the density matrix renormalization group (DMRG) in a way that heads toward a more "black box" approach. Experimental results and other computational methods are used for comparison. The gap between the lowest doublet and quartet state of methylidyne (CH) is first considered. We then look at a range of first-row transition metal monocarbonyls: MCO when M is titanium, vanadium, chromium, or manganese. For these MCO systems we also employ partially spin restricted open-shell coupled-cluster (RCCSD). We finally investigate the high-spin low-lying states of the iron dimer, its cation and its anion. The multireference character of these molecules is also considered. We find that these systems can be computationally challenging with close low-lying states and often multireference character. For this more straightforward application and for the basis sets considered, we generally find qualitative agreement between DMRG and MCCI. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Shapiro, Ilya L. [Universite de Geneve, Departement de Physique Theorique and Center for Astroparticle Physics, Geneva 4 (Switzerland); Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); Tomsk State Pedagogical University, Tomsk (Russian Federation); Tomsk State University, Tomsk (Russian Federation); Morais Teixeira, Poliane de [Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); SISSA, Trieste (Italy); Wipf, Andreas [Friedrich-Schiller-Universitaet, Theoretisch-Physikalisches-Institut, Jena (Germany)
2015-06-15
The running of the non-minimal parameter ξ of the interaction of the real scalar field and scalar curvature is explored within the non-perturbative setting of the functional renormalization group (RG). We establish the RG flow in curved space-time in the scalar field sector, in particular derive an equation for the non-minimal parameter. The RG trajectory is numerically explored for different sets of initial data. (orig.)
Liu, X M; Cheng, W W; Liu, J-M
2016-01-19
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.
Collective excitations in deformed sd-shell nuclei from realistic interactions
Erler, Bastian
2014-01-01
Background: Collective excitations of nuclei and their theoretical descriptions provide an insight into the structure of nuclei. Replacing traditional phenomenological interactions with unitarily transformed realistic nucleon-nucleon interactions increases the predictive power of the theoretical calculations for exotic or deformed nuclei. Purpose: Extend the application of realistic interactions to deformed nuclei and compare the performance of different interactions, including phenomenological interactions, for collective excitations in the sd-shell. Method: Ground-state energies and charge radii of 20-Ne, 28-Si and 32-S are calculated with the Hartree-Fock method. Transition strengths and transition densities are obtained in the Random Phase Approximation with explicit angular-momentum projection. Results: Strength distributions for monopole, dipole and quadrupole excitations are analyzed and compared to experimental data. Transition densities give insight into the structure of collective excitations in def...
Realistic tool-tissue interaction models for surgical simulation and planning
Misra, Sarthak
2009-01-01
Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in pre- and intra-operative surgical planning. Realistic modeling of medical interventions involving tool-tissue interactions has been considered to be a key requirement in the development
Photodisintegration of light nuclei for testing a correlated realistic interaction in the continuum
Bacca, S
2006-01-01
An exact calculation of the photodisintegration cross section of 3H, 3He and 4He is performed using as interaction the correlated Argonne V18 potential, constructed within the Unitary Correlation Operator Method (VUCOM). Calculations are carried out using the Lorentz Integral Transform method in conjunction with an hyperspherical harmonics basis expansion. A comparison with other realistic potentials and with available experimental data is discussed. The VUCOM potential leads to a very similar description of the cross section as the Argonne V18 interaction with the inclusion of the Urbana IX three-body force for photon energies 45< w < 120 MeV, while larger differences are found close to threshold.
Renormalization of fermion mixing
Schiopu, R.
2007-05-11
hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories. (orig.)
Kinza, Michael; Honerkamp, Carsten
2015-07-01
In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random-phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multiband systems and compare the resulting effective interactions to the cRPA. First, we consider a multiband model for monolayer graphene, where we integrate out the σ bands to get an effective theory for π bands. It turns out that terms beyond cRPA are strongly suppressed by the different x y -plane reflection symmetry of the bands. In our model the cfRG corrections to cRPA become visible when one disturbs this symmetry difference slightly, however, without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu 3 d -like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.
Dohet-Eraly, Jeremy [F.R.S.-FNRS (Belgium); Sparenberg, Jean-Marc; Baye, Daniel, E-mail: jdoheter@ulb.ac.be, E-mail: jmspar@ulb.ac.be, E-mail: dbaye@ulb.ac.be [Physique Nucleaire et Physique Quantique, CP229, Universite Libre de Bruxelles (ULB), B-1050 Brussels (Belgium)
2011-09-16
The elastic phase shifts for the {alpha} + {alpha} and {alpha} + {sup 3}He collisions are calculated in a cluster approach by the Generator Coordinate Method coupled with the Microscopic R-matrix Method. Two interactions are derived from the realistic Argonne potentials AV8' and AV18 with the Unitary Correlation Operator Method. With a specific adjustment of correlations on the {alpha} + {alpha} collision, the phase shifts for the {alpha} + {alpha} and {alpha} + {sup 3}He collisions agree rather well with experimental data.
Modeling short-term dynamics and variability for realistic interactive facial animation.
Stoiber, Nicolas; Breton, Gaspard; Seguier, Renaud
2010-01-01
Modern modeling and rendering techniques have produced nearly photorealistic face models, but truly expressive digital faces also require natural-looking movements. Virtual characters in today's applications often display unrealistic facial expressions. Indeed, facial animation with traditional schemes such as keyframing and motion capture demands expertise. Moreover, the traditional schemes aren't adapted to interactive applications that require the real-time generation of context-dependent movements. A new animation system produces realistic expressive facial motion at interactive speed. The system relies on a set of motion models controlling facial-expression dynamics. The models are fitted on captured motion data and therefore retain the dynamic signature of human facial expressions. They also contain a nondeterministic component that ensures the variety of the long-term visual behavior. This system can efficiently animate any synthetic face. The video illustrates interactive use of a system that generates facial-animation sequences.
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.
Demir, I.
2013-12-01
Recent developments in web technologies make it easy to manage and visualize large data sets with general public. Novel visualization techniques and dynamic user interfaces allow users to create realistic environments, and interact with data to gain insight from simulations and environmental observations. The floodplain simulation system is a web-based 3D interactive flood simulation environment to create real world flooding scenarios. The simulation systems provides a visually striking platform with realistic terrain information, and water simulation. Students can create and modify predefined scenarios, control environmental parameters, and evaluate flood mitigation techniques. The web-based simulation system provides an environment to children and adults learn about the flooding, flood damage, and effects of development and human activity in the floodplain. The system provides various scenarios customized to fit the age and education level of the users. This presentation provides an overview of the web-based flood simulation system, and demonstrates the capabilities of the system for various flooding and land use scenarios.
Ab Initio No-Core Shell Model Calculations Using Realistic Two- and Three-Body Interactions
Navratil, P; Ormand, W E; Forssen, C; Caurier, E
2004-11-30
There has been significant progress in the ab initio approaches to the structure of light nuclei. One such method is the ab initio no-core shell model (NCSM). Starting from realistic two- and three-nucleon interactions this method can predict low-lying levels in p-shell nuclei. In this contribution, we present a brief overview of the NCSM with examples of recent applications. We highlight our study of the parity inversion in {sup 11}Be, for which calculations were performed in basis spaces up to 9{Dirac_h}{Omega} (dimensions reaching 7 x 10{sup 8}). We also present our latest results for the p-shell nuclei using the Tucson-Melbourne TM three-nucleon interaction with several proposed parameter sets.
Photodisintegration of light nuclei for testing a correlated realistic interaction in the continuum
Bacca, Sonia
2007-04-01
An exact calculation of the photodisintegration cross section of H3, He3, and He4 is performed by using as interaction the correlated Argonne V18 potential, constructed within the unitary correlation operator method (VUCOM). Calculations are carried out by using the Lorentz integral transform method in conjunction with a hyperspherical harmonics basis expansion. A comparison with other realistic potentials and with available experimental data is discussed. The VUCOM potential leads to a description of the cross section that is very similar to that of the Argonne V18 interaction with the inclusion of the Urbana IX three-body force for photon energies 45⩽ω⩽120 MeV, whereas larger differences are found close to threshold.
Bashinsky, Sergei
2015-01-01
We study a finite basic structure that possibly underlies the observed elementary quantum fields with gauge and gravitational interactions. Realistic wave functions of locally interacting quantum fields emerge naturally as fitting functions for the generic distribution of many quantifiable properties of arbitrary static objects. We prove that in any quantum theory with the superposition principle, evolution of a current state of fields unavoidably continues along alternate routes with every conceivable Hamiltonian for the fields. This applies to the emergent quantum fields too. Yet the Hamiltonian is unambiguous for isolated emergent systems with sufficient local symmetry. The other emergent systems, without specific physical laws, cannot be inhabitable. The acceptable systems are eternally inflating universes with reheated regions. We see how eternal inflation perpetually creates new short-scale physical degrees of freedom and why they are initially in the ground state. In the emergent quantum worlds probabi...
Collective multipole excitations based on correlated realistic nucleon-nucleon interactions
Paar, N. [Zagreb Univ. (Croatia). Fac. of Science, Physics Dept.; Papakonstantinou, P.; Hergert, H.; Roth, R. [Technische Univ. Darmstadt (Germany). Inst. fuer Kernphysik
2006-05-24
We investigate collective multipole excitations for closed shell nuclei from {sup 16}O to {sup 208}Pb using correlated realistic nucleon-nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations a re treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phase-shift equivalent correlated interaction VUCOM adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using VUCOM we solve the Hartree-Fock problem and employ the single-particle states as starting point for the RPA. By construction, the UCOM-RPA is fully self-consistent, i.e. the same correlated nucleon-nucleon interact ion is used in calculations of the HF ground state and in the residual RPA interaction. Consequently, the spurious state associated with the center-of-mass motion is properly removed and the sum-rules are exhausted within {+-}3%. The UCOM-RPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closed-shell nuclei across the nuclear chart. For the isoscalar giant monopole resonance, the resonance energies are in agreement with experiment hinting at a reasonable compressibility. However, in the 1{sup -} and 2{sup +} channels the resonance energies are overestimated due to missing long-range correlations and three-body contributions. (orig.)
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.
Interaction between electromagnetic waves and energetic particles by a realistic density model
无
2010-01-01
Using a realistic density model,we present a first study on the interactions between electromagnetic waves and energetic particles in the inner magnetosphere.Numerical calculations show that as the latitude λ increases,the number density ne increases,and resonant frequency range moves to lower pitch angles.During L-mode/electron and L-mode/proton interactions,the pitch angle diffusion dominates over the momentum diffusion.This indicates that L-mode waves are primarily responsible for pitch angle scattering.For R-mode/electron interaction,the momentum diffusion is found to be comparable to the pitch angle diffusion,implying that R-mode waves can play an important role in both pitch angle scattering and stochastic acceleration of electrons.For R-mode/proton interaction,diffusion coefficients locate primarily below pitch angle 60° and increase as kinetic energy increases,suggesting that R-mode waves have potential for pitch angle scattering of highly energetic (~1 MeV) protons but cannot efficiently accelerate protons.
A realistic assessment of methods for extracting gene/protein interactions from free text
Shepherd Adrian J
2009-07-01
Full Text Available Abstract Background The automated extraction of gene and/or protein interactions from the literature is one of the most important targets of biomedical text mining research. In this paper we present a realistic evaluation of gene/protein interaction mining relevant to potential non-specialist users. Hence we have specifically avoided methods that are complex to install or require reimplementation, and we coupled our chosen extraction methods with a state-of-the-art biomedical named entity tagger. Results Our results show: that performance across different evaluation corpora is extremely variable; that the use of tagged (as opposed to gold standard gene and protein names has a significant impact on performance, with a drop in F-score of over 20 percentage points being commonplace; and that a simple keyword-based benchmark algorithm when coupled with a named entity tagger outperforms two of the tools most widely used to extract gene/protein interactions. Conclusion In terms of availability, ease of use and performance, the potential non-specialist user community interested in automatically extracting gene and/or protein interactions from free text is poorly served by current tools and systems. The public release of extraction tools that are easy to install and use, and that achieve state-of-art levels of performance should be treated as a high priority by the biomedical text mining community.
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins.
May, Ali; Pool, René; van Dijk, Erik; Bijlard, Jochem; Abeln, Sanne; Heringa, Jaap; Feenstra, K Anton
2014-02-01
To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full atomistic molecular simulation methods do have this potential, but are completely unfeasible for large-scale applications in terms of computational cost required. Here we investigate whether applying coarse-grained (CG) molecular dynamics simulations is a viable alternative for complexes of known structure. We calculate the free energy barrier with respect to the bound state based on molecular dynamics simulations using both a full atomistic and a CG force field for the TCR-pMHC complex and the MP1-p14 scaffolding complex. We find that the free energy barriers from the CG simulations are of similar accuracy as those from the full atomistic ones, while achieving a speedup of >500-fold. We also observe that extensive sampling is extremely important to obtain accurate free energy barriers, which is only within reach for the CG models. Finally, we show that the CG model preserves biological relevance of the interactions: (i) we observe a strong correlation between evolutionary likelihood of mutations and the impact on the free energy barrier with respect to the bound state; and (ii) we confirm the dominant role of the interface core in these interactions. Therefore, our results suggest that CG molecular simulations can realistically be used for the accurate prediction of protein-protein interaction strength. The python analysis framework and data files are available for download at http://www.ibi.vu.nl/downloads/bioinformatics-2013-btt675.tgz.
Renormalization Group Constraints on New Top Interactions from Electroweak Precision Data
De Blas, J. [INFN, Sezione di Roma (Italy); Chala, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Santiago, J. [Granada Univ. (Spain). Dept. de Fisica Teorica y del Cosmos; Granada Univ. (Spain). CAFPE
2015-07-15
Anomalous interactions involving the top quark contribute to some of the most difficult observables to directly access experimentally. They can give however a sizeable correction to very precisely measured observables at the loop level. Using a model-independent effective Lagrangian approach, we present the leading indirect constraints on dimension-six effective operators involving the top quark from electroweak precision data. They represent the most stringent constraints on these interactions, some of which may be directly testable in future colliders.
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.
Aqua, J-N; Cornu, F
2004-11-01
The aim of the paper is to study the renormalizations of the charge and screening length that appear in the large-distance behavior of the effective pairwise interaction w(alphaalpha') between two charges e(alpha) and e(alpha') in a dilute electrolyte solution, both along a dielectric wall and in the bulk. The electrolyte is described by the so-called primitive model in the framework of classical statistical mechanics and the electrostatic response of the wall is characterized by its dielectric constant. In a previous paper [Phys. Rev. E 68, 022133 (2003)] a graphic reorganization of resummed Mayer diagrammatics has been devised in order to exhibit the general structure of the 1/y3 leading tail of w(alphaalpha') (x,x',y) for two charges located at distances x and x' from the wall and separated by a distance y along the wall. When all species have the same closest approach distance b to the wall, the coefficient of the 1/y3 tail is the product Dalpha(x)Dalpha'(x') of two effective dipoles. Here we use the same graphic reorganization in order to systematically investigate the exponential large-distance behavior of w(alphaalpha') in the bulk. (We show that the reorganization also enables one to derive the basic screening rules in both cases.) Then, in a regime of high dilution and weak coupling, the exact analytical corrections to the leading tail of w(alphaalpha'), both in the bulk or along the wall, are calculated at first order in the coupling parameter epsilon and in the limit where b becomes negligible with respect to the Debye screening length. (Epsilon is proportional to the so-called plasma parameter.) The structure of corrections to the terms of order epsilon is exhibited, and the scaling regime for the validity of the Debye limit is specified. In the vicinity of the wall, we use the density profiles calculated previously [J. Stat. Phys. 105, 211 (2001)] up to order epsilon and a method devised [J. Stat. Phys. 105, 245 (2001)] for the determination of the
Nucleon-pair states of even-even Sn isotopes based on realistic effective interactions
Cheng, Y. Y.; Qi, C.; Zhao, Y. M.; Arima, A.
2016-08-01
In this paper we study yrast states of 128,126,124Sn and 104,106,108Sn by using the monopole-optimized realistic interactions in terms of both the shell model (SM) and the nucleon-pair approximation (NPA). For yrast states of 128,126Sn and 104,106Sn, we calculate the overlaps between the wave functions obtained in the full SM space and those obtained in the truncated NPA space, and find that most of these overlaps are very close to 1. Very interestingly, for most of these states with positive parity and even spin or with negative parity and odd spin, the SM wave function is found to be well represented by one nucleon-pair basis state, viz., a simple picture of "nucleon-pair states" (nucleon-pair configuration without mixings) emerges. In 128,126Sn, the positive-parity (or negative-parity) yrast states with spin J >10 (or J >7 ) are found to be well described by breaking one or two S pairs in the 101+ (or 71-) state, i.e., the yrast state of seniority-two, spin-maximum, and positive-parity (or negative-parity), into non-S pair(s). Similar regularity is also pointed out for 104,106Sn. The evolution of E 2 transition rates between low-lying states in 128,126,124Sn is discussed in terms of the seniority scheme.
Angular-momentum projection for Hartree-Fock and RPA with realistic interactions
Erler, Bastian; Roth, Robert [Institut fuer Kernphysik, TU Darmstadt (Germany)
2012-07-01
Hartree-Fock (HF) with a Hamiltonian constructed from similarity transformed realistic NN potentials plus 3N contact interactions provides a good starting point for the description of closed shell nuclei. In conjunction with Many-Body-Perturbation-Theory, experimental ground-state energies and radii are well reproduced. To describe collective excitations, the Random-Phase-Approximation (RPA) is the method of choice. Beyond closed shells, e.g. in the sd-shell region, ground-states might exhibit intrinsic deformation, resulting in HF states where angular-momentum ceases to be a good quantum number. Lab-frame observables, like ground-state energies or rotational bands can be recovered from the intrinsic states via angular-momentum projection. We study axially deformed even-even sd-shell nuclei, namely {sup 20}Ne, {sup 28}Si and {sup 32}S. Starting from a HF ground state obtained by exact angular-momentum projection, we use the RPA to study collective excitations. The transition strengths obtained from the RPA are projected to good angular momentum in an exact formalism, without resorting to popular approximations. We investigate the effect of deformed intrinsic states on giant resonances.
de Soria-Santacruz, M.; Shprits, Y. Y.; Drozdov, A.; Menietti, J. D.; Garrett, H. B.; Zhu, H.; Kellerman, A. C.; Horne, R. B.
2017-05-01
The role of plasma waves in shaping the intense Jovian radiation belts is not well understood. In this study we use a realistic wave model based on an extensive survey from the Plasma Wave Investigation on the Galileo spacecraft to calculate the effect of pitch angle and energy diffusion on Jovian energetic electrons due to upper and lower band chorus. Two Earth-based models, the Full Diffusion Code and the Versatile Electron Radiation Belt code, are adapted to the case of the Jovian magnetosphere and used to resolve the interaction between chorus and electrons at L = 10. We also present a study of the sensitivity to the latitudinal wave coverage and initial electron distribution. Our analysis shows that the contribution to the electron dynamics from upper band chorus is almost negligible compared to that from lower band chorus. For 100 keV electrons, we observe that diffusion leads to redistribution of particles toward lower pitch angles with some particle loss, which could indicate that radial diffusion or interchange instabilities are important. For energies above >500 keV, an initial electron distribution based on observations is only weakly affected by chorus waves. Ideally, we would require the initial electron phase space density before transport takes place to assess the importance of wave acceleration, but this is not available. It is clear from this study that the shape of the electron phase space density and the latitudinal extent of the waves are important for both electron acceleration and loss.
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.
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.
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.
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 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.
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.
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.
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins
A. May; R. Pool; E. van Dijk; J. Bijlard; S. Abeln; J. Heringa; K.A. Feenstra
2014-01-01
MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full at
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins
May, A.; Pool, R.; van Dijk, E.; Bijlard, J.; Abeln, S.; Heringa, J.; Feenstra, K.A.
2014-01-01
MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full
Smith, L N; Farooq, A R; Smith, M L; Ivanov, I E; Orlando, A
2017-06-01
Remote consultations that are realistic enough to be useful medically offer considerable clinical, logistical and cost benefits. Despite advances in virtual reality and vision hardware and software, these benefits are currently often unrealised. The proposed approach combines high spatial and temporal resolution 3D and 2D machine vision with virtual reality techniques, in order to develop new environments and instruments that will enable realistic remote consultations and the generation of new types of useful clinical data. New types of clinical data have been generated for skin analysis and respiration measurement; and the combination of 3D with 2D data was found to offer potential for the generation of realistic virtual consultations. An innovative combination of high resolution machine vision data and virtual reality online methods, promises to provide advanced functionality and significant medical benefits, particularly in regions where populations are dispersed or access to clinicians is limited. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\\Delta \\lceil C^{\\infty}_{0}({\\bf R} \\backslash\\{0\\})$. It is achieved in the small distance limit of equally spaced three neighboring Dirac's $\\delta$ potentials. The strength for each $\\delta$ is appropriately renormalized according to the distance and it diverges, in general, in the small distance limit. The validity of our method is ensured by numerical calculations. In general cases except for usual $\\delta$, the wave function discontinuity appears around the interaction and one can observe such a tendency even at a finite distance level.
Towards More Realistic Simulation of Air-Sea Interaction over Lakes on Titan
Rafkin, Scot; Soto, Alejandro
2016-06-01
The exchange of methane between the atmosphere and surface liquid reservoirs dominates the short time-scale methanological cycle. In this study, previous two-dimensional simulations of the exchange of methane vapor, sensible heat and momentum between the atmosphere and lakes are updated with the inclusion of radiative forcing and extended to three dimensions, including the introduction of realistic coastlines. Previous studies of Titan's air-sea exchange in two dimensions suggested that the exchange process was self-limiting. Evaporation from lakes produced a shallow but extremely stable marine layer that suppressed turbulent exchange. Furthermore, the circulation associated with the higher buoyancy of methane-rich atmosphere over the lake was offset by the oppositely directed thermal sea breeze circulation, which muted the mean wind. Two major weaknesses of this previous work were the lack of radiative forcing and the imposition of two dimensionality that limited the full range of dynamical solutions. Based on early theoretical studies, it was thought that magnitude of turbulent energy flux exchanges would be much larger than radiative fluxes, thereby justifying the neglect of radiation, but the two-dimensional simulations indicated that this was not a valid assumption. The dynamical limitations of two-dimensional simulations are well known. Vorticity stretching (i.e., circulation intensification through vertical motion) is not possible and it is also not possible to produce dynamically balanced gradient wind-type circulations. As well, the irregular shape of a realistic coastline cannot be expressed in two dimensions, and these realistic structures will generally induce complex convergence and divergence circulations in the atmosphere. The impact of radiative forcing and the addition of the third dimension on the air-sea exchange are presented.
Sviratcheva, K.D.; Draayer, J.P.; /Louisiana State U. /Iowa State U. /LLNL, Livermore /SLAC
2006-06-27
In the framework of the theory of spectral distributions we perform an overall comparison of three modern realistic interactions, CD-Bonn, CD-Bonn+3terms, and GXPF1 in a broad range of nuclei in the upper fp shell and study their ability to account for the development of isovector pairing correlations and collective rotational motion in many-particle nuclear systems. Our findings reveal a close similarity between CD-Bonn and CD-Bonn+3terms, while both interactions possess features different from the ones of GXPF1. The GXPF1 interaction is used to determine the strength parameter of a quadrupole term that augments an isovector-pairing model interaction with Sp(4) dynamical symmetry, which in turn is shown to yield a reasonable agreement with the experimental low-lying energy spectra of {sup 58}Ni and {sup 58}Cu.
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.
Mineev, V S
2003-01-01
In the paper the one-dimensional one-center scattering problem with the initial potential $\\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as necessary conditions in the singular point alongside with account of the analytical structure of fundamental solutions, it allows us to receive exact expressions for the wave functions (i.e. for the boundary conditions), scattering coefficients and the singular corrections to the potential, as well as the corresponding bound state spectrum. It turns out that the point $\\delta$-shaped correction to the potential should be present without fail at any choice of the allowable self-adjoint extension, moreover a form of these corrections corresponds to the form of renormalization terms obtained in quantum electrodynamics. Thus, the proposed method shows the unequivocal connection among the boundary conditions, scattering coefficients and $\\delta$-shaped additions to the potential. Ta...
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.)
Sznajd, J.
2016-12-01
The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.
Sznajd, J
2016-12-01
The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J) and interchain nearest-neighbor (J_{1}) and next-nearest-neighbor (J_{2}) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J_{2}=-J_{1}/2 for a rectangular lattice and J_{2}=-J_{1} for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.
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.
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.
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.
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...
Dongdong Ni
2015-05-01
Full Text Available The weak-decay (β+ and EC rates of neutron-deficient Kr, Sr, Zr, and Mo isotopes are investigated within the deformed quasiparticle random-phase approximation with realistic nucleon–nucleon interactions. The particle–particle and particle–hole channels of residual interactions are handled in large single-particle model spaces, based on the Brückner G-matrix with charge-dependent Bonn nucleon–nucleon forces. Contributions from allowed Gamow–Teller and Fermi transitions as well as first-forbidden transitions are calculated. The calculated half-lives show good agreement with the experimental data over a wide range of magnitude, from 10−2 to 107 s. Moreover, predictions of β-decay half-lives are made for some extremely proton-rich isotopes, which could be useful for future experiments.
Julio Ruiz
2015-10-01
Full Text Available The New developments in 3D data registration and post processing have enabled us to obtain models whose final design means a qualitative step in order to reach a much more realistic viewing of them for both cases: sculptures and architectural monuments. Uniting 3D scanning technologies, photogrammetry, texture mapping, 3D imaging software tools and interactive content, we found novel and higher levels of quality in the images. Thanks to the new software display - with these images made in Unity - a new field emerges which find applications in improved interactivity , cellular phones, tablets, augmented reality and related technologies, as well as in the development of future platforms such as holodisplays, auto stereoscopic 3D television computer vision, etc. In this way it provides an excellent tool for heritage but a valuable working tool for professionals too.
Simulated evolution of protein-protein interaction networks with realistic topology.
Peterson, G Jack; Pressé, Steve; Peterson, Kristin S; Dill, Ken A
2012-01-01
We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other proteins in the target protein's neighborhood. We find good agreement of the model on 10 different network properties compared to high-confidence experimental PPI networks in yeast, fruit flies, and humans. Key findings are: (1) PPI networks evolve modular structures, with no need to invoke particular selection pressures. (2) Proteins in cells have on average about 6 degrees of separation, similar to some social networks, such as human-communication and actor networks. (3) Unlike social networks, which have a shrinking diameter (degree of maximum separation) over time, PPI networks are predicted to grow in diameter. (4) The model indicates that evolutionarily old proteins should have higher connectivities and be more centrally embedded in their networks. This suggests a way in which present-day proteomics data could provide insights into biological evolution.
Lee, Mi Kyung; Huo, Pengfei; Coker, David F.
2016-05-01
This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.
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...
A correlated basis-function description of 16O with realistic interactions
Boscá, M. C.
1994-01-01
The correlated basis-function theory is applied at the lowest order to analyze the ground state and low-energy spectrum of the 16O nucleus. Results are quoted for both the Urbana and the Argonne υ 14 nucleon-nucleon interactions. The work includes state-dependent correlations and their radial components are determined by solving a set of Euler-Lagrange equations. The matrix elements are computed by using a cluster expansion and the sequential condition is imposed in order to insure convergence. The results clearly disagree with the experimental values.
Realistic Modeling of Interaction of Quiet-Sun Magnetic Fields with the Chromosphere
Kitiashvili, Irina; Kosovichev, Alexander G.; Mansour, Nagi N.; Wray, Alan A.
2017-08-01
High-resolution observations and 3D MHD simulations reveal intense interaction between the convection zone dynamics and the solar atmosphere on subarcsecond scales. To investigate processes of the dynamical coupling and energy exchange between the subsurface layers and the chromosphere we perform 3D radiative MHD modeling for a computational domain that includes the upper convection zone and the chromosphere, and investigate the structure and dynamics for different intensity of the photospheric magnetic flux. For comparison with observations, the simulation models have been used to calculate synthetic Stokes profiles of various spectral lines. The results show intense energy exchange through small-scale magnetized vortex tubes rooted below the photosphere, which provide extra heating of the chromosphere, initiate shock waves, and small-scale eruptions.
Brenner, David J.
2009-07-21
The 16th ASA Conference on Radiation and Health, held June 27-30, 2004 in Beaver Creek, CO, offered a unique forum for discussing research related to the effects of radiation exposures on human health in a multidisciplinary setting. The Conference furnishes investigators in health related disciplines the opportunity to learn about new quantitative approaches to their problems and furnishes statisticians the opportunity to learn about new applications for their discipline. The Conference was attended by about 60 scientists including statisticians, epidemiologists, biologists and physicists interested in radiation research. For the first time, ten recipients of Young Investigator Awards participated in the conference. The Conference began with a debate on the question: “Do radiation doses below 1 cGy increase cancer risks?” The keynote speaker was Dr. Martin Lavin, who gave a banquet presentation on the timely topic “How important is ATM?” The focus of the 2004 Conference on Radiation and Health was Radiation in Realistic Environments: Interactions Between Radiation and Other Risk Modifiers. The sessions of the conference included: Radiation, Smoking, and Lung Cancer Interactions of Radiation with Genetic Factors: ATM Radiation, Genetics, and Epigenetics Radiotherapeutic Interactions The Conference on Radiation and Health is held bi-annually, and participants are looking forward to the 17th conference to be held in 2006.
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.)
Quartet correlations in N = Z nuclei induced by realistic two-body interactions
Sambataro, M. [Istituto Nazionale di Fisica Nucleare - Sezione di Catania, Catania (Italy); Sandulescu, N. [National Institute of Physics and Nuclear Engineering, Bucharest-Magurele (Romania)
2017-03-15
Two variational quartet models previously employed in a treatment of pairing forces are extended to the case of a general two-body interaction. One model approximates the nuclear states as a condensate of identical quartets with angular momentum J = 0 and isospin T = 0 while the other let these quartets to be all different from each other. With these models we investigate the role of alpha-like quartet correlations both in the ground state and in the lowest J = 0, T = 0 excited states of even-even N = Z nuclei in the sd -shell. We show that the ground-state correlations of these nuclei can be described to a good extent in terms of a condensate of alpha-like quartets. This turns out to be especially the case for the nucleus {sup 32}S for which the overlap between this condensate and the shell model wave function is found close to one. In the same nucleus, a similar overlap is found also in the case of the first excited 0{sup +} state. No clear correspondence is observed instead between the second excited states of the quartet models and the shell model eigenstates in all the cases examined. (orig.)
A realistic model for Dark Matter interactions in the neutrino portal paradigm
González-Macías, Vannia; Wudka, José
2016-01-01
We discuss a simple extension of the Standard Model (SM) that provides an explicit realization of the dark-matter (DM) neutrino-portal paradigm. The dark sector is composed of a scalar $ \\Phi $ and a Dirac fermion $ \\Psi $, with the latter assumed to be lighter than the former. These particles interact with the SM through the exchange of a set of heavy Dirac fermion mediators that are neutral under all local SM symmetries, and also under the dark-sector symmetry that stabilizes the $ \\Psi $ against decay. We show that this model can accommodate all experimental and observational constraints provided the DM mass is below $\\sim 35\\, \\gev $ or is in a resonant region of the Higgs or $Z$ boson. We also show that if the dark scalar and dark fermion are almost degenerate in mass, heavier DM fermions are not excluded. We note that in this scenario DM annihilation in the cores of astrophysical objects and the galactic halo produces a monochromatic neutrino beam of energy $ \\mfe $, which provides a clear signature for...
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.
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
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...
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.
Marie L. Bassford
2016-09-01
Full Text Available Interactive experiences are rapidly becoming popular via the surge of ‘escape rooms’; part game and part theatre, the ‘escape’ experience is exploding globally, having gone from zero offered at the outset of 2010 to at least 2800 different experiences available worldwide today. CrashEd is an interactive learning experience that parallels many of the attractions of an escape room – it incorporates a staged, realistic ‘crime scene’ and invites participants to work together to gather forensic evidence and question a witness in order to solve a crime, all whilst competing against a ticking clock. An animation can enhance reality and engage with cognitive processes to help learning; in CrashEd, it is the last piece of the jigsaw that consolidates the students’ incremental acquisition of knowledge to tie together the pieces of evidence, identify a suspect and ultimately solve the crime. This article presents the background to CrashEd and an overview of how a timely placed animation at the end of an educational experience can enhance learning. The lessons learned, from delivering bespoke versions of the experience to different demographic groups, are discussed. The article will consider the successes and challenges raised by the collaborative project, future developments and potential wider implications of the development of CrashEd.
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.
Chen, Xiang; Zhuang, Yinghong
2017-07-01
The scaling critical behaviors of Gd12Co7 compound around TC were investigated based on the M-H curves in a magnetic field change of 0-2 T. The critical exponents β and γ determined by modified Arrott plot (MAP) and Kouvel-Fisher (KF) methods are [β=0.479(5) and γ=1.004(2)] and [β=0.473(2) and γ=0.983(3)], respectively. The exponents δ derived from Widom scaling relation (M T =TC = 163 K = DH 1/δ) and universal relation of the relative cooling power (RCP ∝H 1 +1/δ) are δ=3.032(8) and δ=2.903(1). The average values of critical exponent (β=0.476(3), γ=0.993(7), and δ=2.967(9)) are very close to mean-field model (β=0.5, γ=1, and δ=3), which indicates that the magnetic interactions in Gd12Co7 compound are long-range interactions. The average value of critical exponent n for MAP (0.649(1)), KF (0.638(3)), and | ΔSM | ∝Hn(0.714(8)) at TC is 0.667(4) and well in agreement with mean field long-range interaction model (n = 2 / 3). The plot M 1/βvs.(H / M) 1/γ constructed by above critical exponents fall into two distinct branches above and below TC and completely complies with the scaling hypothesis. At the same time, the normalized curve of magnetic entropy change shows that renormalized magnetic entropy change Δ S ‧ of Gd12Co7 is mainly determined by a=1.548(1) and b=1.549(3) in Lorentz function.
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
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.)
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.
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.
Realistic shell model; 132Sn region; 208Pb region
Covello, A; Gargano, A; Itaco, N
2008-01-01
We report on a study of exotic nuclei around doubly magic 132Sn in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the latter is renormalized by constructing a smooth low-momentum potential, V-low-k, that is used directly as input for the calculation of the effective interaction. In this paper, we focus attention on proton-neutron multiplets in the odd-odd nuclei 134Sb, 136Sb. We show that the behavior of these multiplets is quite similar to that of the analogous multiplets in the counterpart nuclei in the 208Pb region, 210Bi and 212Bi.
Is realistic neuronal modeling realistic?
Almog, Mara; Korngreen, Alon
2016-11-01
Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models. Copyright © 2016 the American Physiological Society.
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...
Brenna, Marco
2014-01-01
The self-consistent mean-field (SCMF) theory describes many properties of the ground state and excited states of the atomic nucleus, such as masses, radii, deformations and giant resonance energies. SCMF models are based on the independent particle picture where nucleons are assumed to move in a self-generated average potential. In the first part of this work, we apply a state-of-the-art SCMF approach, based on the Skyrme effective interaction, to two different excitations (viz. the pygmy dipole resonance and the isovector giant quadrupole resonance), investigating their relation with the nuclear matter symmetry energy, which corresponds to the energy cost for changing protons into neutrons and is a key parameter for the nuclear equation of state. However, SCMF models present well known limitations which require the inclusion of further dynamical correlations, e.g. the ones coming from the interweaving between single-particle and collective degrees of freedom (particle-vibration coupling - PVC). In the second...
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,...
Antenucci, F; Crisanti, A; Leuzzi, L
2014-07-01
The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.
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.
Efstratiadis, Andreas; Papalexiou, Simon-Michael
2010-05-01
We present a methodological framework for the estimation of flood risk in the Boeoticos Kephisos river basin, in Greece, draining an area of 1850 km2. This is a challenging task since the basin has many peculiarities. Due to the dominance of highly-permeable geologic formations, significant portion of runoff derives from karst springs, which rapidly contribute to the streamflow, in contrast to the unusually low contribution of direct (flood) runoff. In addition, due to the combined abstractions from surface and groundwater recourses and the existence of an artificial drainage network in the lower part of the basin (where slopes are noticeably low), the system is heavily modified. To evaluate the probability of extreme floods, especially in such complex basins, it is essential to provide both a statistically consistent description of forcing (precipitation) and a realistic simulation of the runoff mechanisms. Typically, flood modelling is addressed through event-based tools that use deterministic design storms and empirical formulas for the estimation of the "effective" rainfall and its transformation to runoff. Yet, there are several shortcomings in such approaches, especially when employed to large-scale systems. First, the widely-used methodologies for constructing design storms fail to properly represent the variability of rainfall, since they do not account for the temporal and spatial correlations of the historical records. For instance, it is assumed that the input storms to all sub-basins correspond to the same return period. On the other hand, "event-based" models do not allow for interpreting flood risk as joint probabilities of all hydrological variables that interrelate in runoff generation (rainfall, stream-aquifer interactions, soil moisture accounting). Finally, for the estimation of model parameters, the typical approach is to calibrate them against normally few historical flood events, which is at least questionable - the information embedded within
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.
Three Dimensional SRG Evolution of the NN Interactions Using Picard Iteration
Hadizadeh M. R.
2016-01-01
Full Text Available The Similarity Renormalization Group (SRG evolution of nucleon-nucleon (NN interactions is calculated directly as function of momentum vectors for realistic potentials. To overcome the stiffness of the SRG flow equations in differential form for far off diagonal matrix elements, the differential equation is transformed to an integral form without employing a partial wave decomposition.
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.
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.
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...
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.
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 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.
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.
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.
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...
Alvioli, M; Morita, H
2003-01-01
A linked cluster expansion for the calculation of ground state observables of complex nuclei with realistic interactions has been used to calculate the ground state energy, density and momentum distribution of 16O and 40Ca. Using the same cluster expansion and the wave function and correlation parameters obtained from the energy calculation, we have evaluated the semi inclusive reaction A(e,e'p)X taking final state interaction (FSI) into account by a Glauber type approach; the comparison between the distorted and undistorted momentum distributions provides an estimate of the transparency of the nuclear medium to the propagation of the hit proton. The effect of color transparency is also included by considering the Finite Formation Time (FFT) that the hit hadron needs to reach its asymptotic physical state.
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).
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 ...
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.
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.
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.
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...
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.
A Realistic Description of Nucleon-Nucleon and Hyperon-Nucleon Interactions in the SU_6 Quark Model
Fujiwara, Y; Kohno, M; Nakamoto, C; Suzuki, Y
2001-01-01
We upgrade a SU_6 quark-model description for the nucleon-nucleon and hyperon-nucleon interactions by improving the effective meson-exchange potentials acting between quarks. For the scalar- and vector-meson exchanges, the momentum-dependent higher-order term is incorporated to reduce the attractive effect of the central interaction at higher energies. The single-particle potentials of the nucleon and Lambda, predicted by the G-matrix calculation, now have proper repulsive behavior in the momentum region q_1=5 - 20 fm^-1. A moderate contribution of the spin-orbit interaction from the scalar-meson exchange is also included. As to the vector mesons, a dominant contribution is the quadratic spin-orbit force generated from the rho-meson exchange. The nucleon-nucleon phase shifts at the non-relativistic energies up to T_lab=350 MeV are greatly improved especially for the 3E states. The low-energy observables of the nucleon-nucleon and the hyperon-nucleon interactions are also reexamined. The isospin symmetry break...
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.
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...
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.)
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)
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.
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 proper
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
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.
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.
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.
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).
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.
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
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.
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.
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.
Lebens-Higgins, Z.; Scanlon, D. O.; Paik, H.; Sallis, S.; Nie, Y.; Uchida, M.; Quackenbush, N. F.; Wahila, M. J.; Sterbinsky, G. E.; Arena, Dario A.; Woicik, J. C.; Schlom, D. G.; Piper, L. F. J.
2016-01-01
We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO _{3} , using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La - BaSnO _{3} is driven purely by electrostatic interactions.
Lebens-Higgins, Z; Scanlon, D O; Paik, H; Sallis, S; Nie, Y; Uchida, M; Quackenbush, N F; Wahila, M J; Sterbinsky, G E; Arena, Dario A; Woicik, J C; Schlom, D G; Piper, L F J
2016-01-15
We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO_{3}, using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La-BaSnO_{3} is driven purely by electrostatic interactions.
Renormalization group and scaling within the microcanonical fermionic average approach
Azcoiti, V; Di Carlo, G; Galante, A; Grillo, A F; Azcoiti, V; Laliena, V; Di Carlo, G; Galante, A; Grillo, A F
1994-01-01
The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the \\beta, m plane for the study of chiral condensate in QED) without the need of computing the fermionic determinant at each point. We exploit this possibility for extracting both the renormalization group trajectories ("constant physics lines") and the scaling function, and we test it in the Schwinger Model. We discuss the applicability of this method to realistic theories.
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.
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.
David-Uraz, A.; Owocki, S. P.; Wade, G. A.; Sundqvist, J. O.; Kee, N. D.
2017-09-01
OB stars exhibit various types of spectral variability historically associated with wind structures, including the apparently ubiquitous discrete absorption components (DACs). These features have been proposed to be caused either by magnetic fields or non-radial pulsations. In this second paper of this series, we revisit the canonical phenomenological hydrodynamical modelling used to explain the formation of DACs by taking into account modern observations and more realistic theoretical predictions. Using constraints on putative bright spots located on the surface of the O giant ξ Persei derived from high precision space-based broad-band optical photometry obtained with the Microvariability and Oscillations of Stars (MOST) space telescope, we generate 2D hydrodynamical simulations of corotating interaction regions in its wind. We then compute synthetic ultraviolet (UV) resonance line profiles using Sobolev Exact Integration and compare them with historical timeseries obtained by the International Ultraviolet Explorer (IUE) to evaluate if the observed behaviour of ξ Persei's DACs is reproduced. Testing three different models of spot size and strength, we find that the classical pattern of variability can be successfully reproduced for two of them: the model with the smallest spots yields absorption features that are incompatible with observations. Furthermore, we test the effect of the radial dependence of ionization levels on line driving, but cannot conclusively assess the importance of this factor. In conclusion, this study self-consistently links optical photometry and UV spectroscopy, paving the way to a better understanding of cyclical wind variability in massive stars in the context of the bright spot paradigm.
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...
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.
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.
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.
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.
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 of an Abelian Tensor Group Field Theory: Solution at Leading Order
Lahoche, Vincent; Rivasseau, Vincent
2015-01-01
We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
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.
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.
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...
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...
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.
Noncommutative QFT and renormalization
Grosse, H.; Wulkenhaar, R.
2006-03-01
It was a great pleasure for me (Harald Grosse) to be invited to talk at the meeting celebrating the 70th birthday of Prof. Julius Wess. I remember various interactions with Julius during the last years: At the time of my studies at Vienna with Walter Thirring, Julius left already Vienna, I learned from his work on effective chiral Lagrangians. Next we met at various conferences and places like CERN (were I worked with Andre Martin, an old friend of Julius), and we all learned from Julius' and Bruno's creation of supersymmetry, next we realized our common interests in noncommutative quantum field theory and did have an intensive exchange. Julius influenced our perturbative approach to gauge field theories were we used the Seiberg-Witten map after his advice. And finally I lively remember the sad days when during my invitation to Vienna Julius did have the serious heart attack. So we are very happy, that you recovered so well, and we wish you all the best for the forthcoming years. Many happy recurrences.
Noncommutative QFT and renormalization
Grosse, H. [Institut fuer Theoretische Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Wien (Austria); Wulkenhaar, R. [Mathematisches Institut der Westfaelischen Wilhelms-Universitaet, Einsteinstrasse 62, 48149 Muenster (Germany)
2006-03-01
It was a great pleasure for me (Harald Grosse) to be invited to talk at the meeting celebrating the 70th birthday of Prof. Julius Wess. I remember various interactions with Julius during the last years: At the time of my studies at Vienna with Walter Thirring, Julius left already Vienna, I learned from his work on effective chiral Lagrangians. Next we met at various conferences and places like CERN (were I worked with Andre Martin, an old friend of Julius), and we all learned from Julius' and Bruno's creation of supersymmetry, next we realized our common interests in noncommutative quantum field theory and did have an intensive exchange. Julius influenced our perturbative approach to gauge field theories were we used the Seiberg-Witten map after his advice. And finally I lively remember the sad days when during my invitation to Vienna Julius did have the serious heart attack. So we are very happy, that you recovered so well, and we wish you all the best for the forthcoming years. Many happy recurrences. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
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.
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
Hewson, A. C.
2016-11-01
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
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.
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.
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.
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.
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.
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-07-01
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
Kim, Sung Soo [Department of Applied Mathematics, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Jung, Young-Dae [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590 (United States)
2013-12-15
The renormalization plasma screening effects on the electron-ion collision are investigated in dense partially ionized hydrogen plasmas. The Hamilton-Jacobi and eikonal methods with the effective interaction potential are employed to obtain the eikonal scattering phase shift and eikonal cross section for the electron-ion collision. It is found that the influence of renormalization screening strongly suppresses the eikonal scattering phase shift as well as the eikonal cross section, especially, for small impact parameter regions. In addition, the renormalization screening effect reduces the total eikonal cross section in all energy domains. The variation of the renormalization effects on the electron-ion collision in dense partially ionized hydrogen plasmas is also discussed.
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.
Fukushima, Noboru, E-mail: noboru.fukushima@gmail.com [Motomachi 13-23, Sanjo, Niigata 955-0072 (Japan)
2011-02-18
Renormalization of non-magnetic and magnetic impurities due to electron double-occupancy prohibition is derived analytically by an improved Gutzwiller approximation. Non-magnetic impurities are effectively weakened by the same renormalization factor as that for the hopping amplitude, whereas magnetic impurities are strengthened by the square root of the spin-exchange renormalization factor, in contrast to results by the conventional Gutzwiller approximation. We demonstrate it by showing that transition matrix elements of number operators between assumed excited states and between an assumed ground state and excited states are renormalized differently than diagonal matrix elements. Deviation from such simple renormalization with a factor is also discussed. In addition, as a related calculation, we correct an error in treatment of the renormalization of charge interaction in the literature. Namely, terms from the second order of the transition matrix elements are strongly suppressed. Since all these results do not depend on the signs of impurity potential or the charge interaction parameter, they are valid both in attractive and repulsive cases.
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.
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 (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.
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.
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.
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.
Dimensional reduction of Markov state models from renormalization group theory
Orioli, S.; Faccioli, P.
2016-09-01
Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.
Dimensional reduction of Markov state models from renormalization group theory.
Orioli, S; Faccioli, P
2016-09-28
Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
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).
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.
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.
Michel Ghins
1998-06-01
Full Text Available Although Kuhn is much more an antirealist than a realist, the earlier and later articulations of realist and antirealist ingredients in his views merit close scrutiny. What are the constituents of the real invariant World posited by Kuhn and its relation to the mutable paradigm-related worlds? Various proposed solutions to this problem (dubbed the "new-world problem" by Ian Hacking are examined and shown to be unsatisfactory. In The Structure of Scientific Revolutions, the stable World can reasonably be taken to be made up of ordinary perceived objects, whereas in Kuhn's later works the transparadigmatic World is identified with something akin to the Kantian world-in-itself. It is argued that both proposals are beset with insuperable difficulties which render Kuhn's earlier and later versions of antirealism implausible.
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...
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 .
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.
Regularity properties and pathologies of position-space renormalization-group transformations
van Enter, Aernout C. D.; Fernández, Roberto; Sokal, Alan D.
1991-05-01
We consider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the other hand, we prove in several cases that near a first-order phase transition the renormalized measure is not a Gibbs measure for any reasonable interaction. It follows that the conventional RG description of first-order transitions is not universally valid.
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.
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
Protecting the conformal symmetry via bulk renormalization on Anti deSitter space
Duetsch, Michael
2010-01-01
The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.
Dynamical gap generation in graphene with frequency dependent renormalization effects
Carrington, M E; von Smekal, L; Thoma, M H
2016-01-01
We study the frequency dependencies in the renormalization of the fermion Greens function for the $\\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.
Angular structure of lacunarity, and the renormalization group
Ball; Caldarelli; Flammini
2000-12-11
We formulate the angular structure of lacunarity in fractals, in terms of a symmetry reduction of the three point correlation function. This provides a rich probe of universality, and first measurements yield new evidence in support of the equivalence between self-avoiding walks (SAW's) and percolation perimeters in two dimensions. We argue that the lacunarity reveals much of the renormalization group in real space. This is supported by exact calculations for random walks and measured data for percolation clusters and SAW's. Relationships follow between exponents governing inward and outward propagating perturbations, and we also find a very general test for the contribution of long-range interactions.
2005-01-01
We calculate the Coulomb interaction induced density, temperature and magnetization dependent many-body band-gap renormalization in a typical diluted magnetic semiconductor GaMnAs in the optimally-doped metallic regime as a function of carrier density and temperature. We find a large (about 0.1 eV) band gap renormalization which is enhanced by the ferromagnetic transition. We also calculate the impurity scattering effect on the gap narrowing. We suggest that the temperature, magnetization, an...
Renormalization and small-world model of fractal quantum repeater networks
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. PMID:23386977
Renormalization and small-world model of fractal quantum repeater networks.
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
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.
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...
Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
de Rham, Claudia; Heisenberg, Lavinia; Pirtskhalava, David
2012-01-01
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum co...
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.
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...
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
Carrier plasmon induced nonlinear band gap renormalization in two-dimensional semiconductors.
Liang, Yufeng; Yang, Li
2015-02-13
In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. However, the physical origin of this generic effect remains obscure. We develop a new plasmon-pole theory that efficiently and accurately captures this coupling. Using monolayer MoS(2) and MoSe(2) as prototype two-dimensional (2D) semiconductors, we reveal a striking band gap renormalization above 400 meV and an unusual nonlinear evolution of their band gaps with doping. This prediction significantly differs from the linear behavior that is observed in one-dimensional structures. Notably, our predicted band gap renormalization for MoSe(2) is in excellent agreement with recent experimental results. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques.
Functional renormalization group approach to the singlet-triplet transition in quantum dots.
Magnusson, E B; Hasselmann, N; Shelykh, I A
2012-09-12
We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in the presence of Hund's coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch et al (2006 Phys. Rev. B 73 235337), which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.
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.
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.
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.
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.
Optically induced effective mass renormalization: the case of graphite image potential states
Montagnese, M.; Pagliara, S.; Galimberti, G.; Dal Conte, S.; Ferrini, G.; van Loosdrecht, P. H. M.; Parmigiani, F.
2016-10-01
Many-body interactions with the underlying bulk electrons determine the properties of confined electronic states at the surface of a metal. Using momentum resolved nonlinear photoelectron spectroscopy we show that one can tailor these many-body interactions in graphite, leading to a strong renormalization of the dispersion and linewidth of the image potential state. These observations are interpreted in terms of a basic self-energy model, and may be considered as exemplary for optically induced many-body interactions.
Optically induced effective mass renormalization: the case of graphite image potential states.
Montagnese, M; Pagliara, S; Galimberti, G; Dal Conte, S; Ferrini, G; van Loosdrecht, P H M; Parmigiani, F
2016-10-14
Many-body interactions with the underlying bulk electrons determine the properties of confined electronic states at the surface of a metal. Using momentum resolved nonlinear photoelectron spectroscopy we show that one can tailor these many-body interactions in graphite, leading to a strong renormalization of the dispersion and linewidth of the image potential state. These observations are interpreted in terms of a basic self-energy model, and may be considered as exemplary for optically induced many-body interactions.
Dissipative two-electron transfer: A numerical renormalization group study
Tornow, Sabine; Bulla, Ralf; Anders, Frithjof B.; Nitzan, Abraham
2008-07-01
We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
Mass renormalization and binding energies in quantum field theory
Lv, Q. Z.; Stefanovich, E.; Su, Q.; Grobe, R.
2017-10-01
We compare the predictions of two methods of determining the amount of binding energy between two distinguishable fermions that interact with each other through force-intermediating bosons. Both measures try to quantify this binding energy by the downward shift of the fully interacting two-fermion ground state energy relative to the sum of the corresponding two single-particle ground state energies. The first method computes this energy difference directly from the standard quantum field theoretical Hamiltonian. The second method uses the mass renormalized form of this Hamiltonian. In order to have a concrete example for this comparison, we employ a simple Yukawa-like model system in one spatial dimension. We find that both approaches lead to identical predictions in the second and fourth order perturbation of the coupling constant, and they remain remarkably close even in the strong coupling domain where perturbation theory diverges. This illustrates that there are field theoretical systems for which rather accurate binding energies can be obtained even without the mass renormalization procedure.
Real-space renormalization group approach to the Anderson model
Campbell, Eamonn
Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.
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.
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.
Laursen, Lasse Farnung
Pigs and pig meat are major sources of income for Denmark. As one of the country's primary exports, it is no wonder that Denmark strives to maintain its competitive edge in the meat market. As part of an on-going effort to lower costs and maintain high standards, X-ray computed tomography (CT...... technology in the product prototyping process. In broad terms, the focus can be divided into two areas of focus: visualization and interaction. Visualizing volume data, obtained via CT-scanning, is a common area of research within other areas of research, e.g. for medical applications. The availability...... when concerned with product development. Product earnings projection, product specifications, and interactive training are just a few of the applicable areas. In this thesis we present an interaction method intended for the commercial development of meat product prototypes. The interaction method...
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.)
Strong parameter renormalization from optimum lattice model orbitals
Brosco, Valentina; Ying, Zu-Jian; Lorenzana, José
2017-01-01
Which is the best single-particle basis to express a Hubbard-like lattice model? A rigorous variational answer to this question leads to equations the solution of which depends in a self-consistent manner on the lattice ground state. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the noninteracting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model Hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density-matrix functional theory, thus establishing an unsuspected correspondence between continuum and lattice approaches.
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 the graphene dispersion velocity determined from scanning tunneling spectroscopy.
Chae, Jungseok; Jung, Suyong; Young, Andrea F; Dean, Cory R; Wang, Lei; Gao, Yuanda; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L; Kim, Phillip; Zhitenev, Nikolai B; Stroscio, Joseph A
2012-09-14
In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200 meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.
Algorithm for Realistic Modeling of Graphitic Systems
A.V. Khomenko
2011-01-01
Full Text Available An algorithm for molecular dynamics simulations of graphitic systems using realistic semiempirical interaction potentials of carbon atoms taking into account both short-range and long-range contributions is proposed. Results of the use of the algorithm for a graphite sample are presented. The scalability of the algorithm depending on the system size and the number of processor cores involved in the calculations is analyzed.
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
Groh, Kai
2012-10-15
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement
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.
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.
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...
Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene
Araujo, Paulo T.; Mafra, Daniela L.; Sato, Kentaro; Saito, Riichiro; Kong, Jing; Dresselhaus, Mildred S.
2012-01-01
In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS2, WSe2, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications. PMID:23264879
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.
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.
High-precision thermodynamic and critical properties from tensor renormalization-group flows.
Hinczewski, Michael; Berker, A Nihat
2008-01-01
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.
High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows
Hinczewski, Michael; Berker, A. Nihat
2008-03-01
The recently developed tensor renormalization-group (TRG) method [1] provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related [2] to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows. [1] M. Levin and C.P. Nave, Phys. Rev. Lett. 99, 120601 (2007). [2] M. Hinczewski and A.N. Berker, arXiv:0709.2803v1 [cond-mat.stat-mech], Phys. Rev. E, in press.
RAMESES publication standards: realist syntheses
Wong Geoff
2013-01-01
Full Text Available Abstract Background There is growing interest in realist synthesis as an alternative systematic review method. This approach offers the potential to expand the knowledge base in policy-relevant areas - for example, by explaining the success, failure or mixed fortunes of complex interventions. No previous publication standards exist for reporting realist syntheses. This standard was developed as part of the RAMESES (Realist And MEta-narrative Evidence Syntheses: Evolving Standards project. The project's aim is to produce preliminary publication standards for realist systematic reviews. Methods We (a collated and summarized existing literature on the principles of good practice in realist syntheses; (b considered the extent to which these principles had been followed by published syntheses, thereby identifying how rigor may be lost and how existing methods could be improved; (c used a three-round online Delphi method with an interdisciplinary panel of national and international experts in evidence synthesis, realist research, policy and/or publishing to produce and iteratively refine a draft set of methodological steps and publication standards; (d provided real-time support to ongoing realist syntheses and the open-access RAMESES online discussion list so as to capture problems and questions as they arose; and (e synthesized expert input, evidence syntheses and real-time problem analysis into a definitive set of standards. Results We identified 35 published realist syntheses, provided real-time support to 9 on-going syntheses and captured questions raised in the RAMESES discussion list. Through analysis and discussion within the project team, we summarized the published literature and common questions and challenges into briefing materials for the Delphi panel, comprising 37 members. Within three rounds this panel had reached consensus on 19 key publication standards, with an overall response rate of 91%. Conclusion This project used multiple
Volume Renormalization and the Higgs
Dai, De-Chang
2014-01-01
Traditionally, Quantum Field Theory (QFT) treats particle excitations as point-like objects, which is the source of ubiquitous divergences. We demonstrate that a minimal modification of QFT with finite volume particles may cure QFT of divergences and illuminate the physics behind the mathematical construct of our theories. The method allows for a non-perturbative treatment of the free field and self-interacting theories (though extensions to all interacting field theories might be possible). In particular, non-perturbatively defined mass is finite. When applied to the standard model Higgs mechanism, the method implies that a finite range of parameters allows for creation of a well defined Higgs particle, whose Compton wavelength is larger than its physical size, in the broken symmetry phase (as small oscillations around the vacuum). This has profound consequences for Higgs production at the LHC. The parameter range in which the Higgs excitation with the mass of 125 GeV behaves as a proper particle is very res...
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.
Gauge theory renormalizations from the open bosonic string
Di Vecchia, P; Magnea, L; Marotta, R; Di Vecchia, P; Lerda, A; Magnea, L; Marotta, R
1995-01-01
We present a unified point of view on the different methods available in the literature to extract gauge theory renormalization constants from the low-energy limit of string theory. The Bern-Kosower method, based on an off-shell continuation of string theory amplitudes, and the construction of low-energy string theory effective actions for gauge particles, can both be understood in terms of strings interacting with background gauge fields, and thus reproduce, in the low-energy limit, the field theory results of the background field method. We present in particular a consistent off-shell continuation of the one-loop gluon amplitudes in the open bosonic string that reproduces exactly the results of the background field method in the Feynman gauge.
The Polarizable Embedding Density Matrix Renormalization Group Method
Hedegård, Erik D
2016-01-01
The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected 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 ...
Symmetry-Preserving Loop Regularization and Renormalization of QFTs
Wu, Yue-Liang
A new symmetry-preserving loop regularization method proposed in Ref. 1 is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the Lagrangian formalism or the spacetime dimension of original theory. The appearance of characteristic energy scale Mc and sliding energy scale μs offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.
The density matrix renormalization group for ab initio quantum chemistry
Wouters, Sebastian
2014-01-01
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational co...
Resummation and renormalization in effective theories of particle physics
Jakovac, Antal
2015-01-01
Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...
Anomalous contagion and renormalization in networks with nodal mobility
Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.
2016-07-01
A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.
Momentum-subtraction renormalization techniques in curved space-time
Foda, O.
1987-10-01
Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.
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
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...
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.
You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke
We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.
Pengqin Shi
2016-09-01
Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.
Shi, Pengqin; Hu, Menghan; Ying, Yaofeng; Jin, Jinshuang
2016-09-01
Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.
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.
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.
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.)
Should scientific realists be platonists?
Busch, Jacob; Morrison, Joe
2015-01-01
Realists about are arrived at by any inferen- tial route which eschews causes (§3), and nor is there any direct pressure for Scientific Real- ists to change their inferential methods (§4). We suggest that in order to maintain inferential parity with Scientific Realism, proponents of EIA need to give......Enhanced Indispensability Arguments (EIA) claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the Best Explana- tion (IBE). Our central question concerns this purported parity of reasoning: do people who defend the EIA make...... an appropriate use of the resources of Scientific Realism (in particular, IBE) to achieve platonism? (§2) We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we should be Scientific...
Realistic Visualization of Virtual Views
Livatino, Salvatore
2005-01-01
Computer Graphics allows us today to visualize in real-time innumerable and amazing scenarios with no limits on viewpoint and viewing direction. However, to design accurate object models and to simulate all the physical phenomena occurring in analogous real situations often represents a job...... that can be impractical and sometime impossible. In addition, the artificial nature of data often makes visualized virtual scenarios not realistic enough. Not realistic in the sense that a synthetic scene is easy to discriminate visually from a natural scene. A new field of research has consequently...... developed and received much attention in recent years: Realistic Virtual View Synthesis. The main goal is a high fidelity representation of virtual scenarios while easing modeling and physical phenomena simulation. In particular, realism is achieved by the transfer to the novel view of all the physical...
Alternative similarity renormalization group generators in nuclear structure calculations
Dicaire, Nuiok M; Navratil, Petr
2014-01-01
The similarity renormalization group (SRG) has been successfully applied to soften interactions for ab initio nuclear calculations. In almost all practical applications in nuclear physics, an SRG generator with the kinetic energy operator is used. With this choice, a fast convergence of many-body calculations can be achieved, but at the same time substantial three-body interactions are induced even if one starts from a purely two-nucleon (NN) Hamiltonian. Three-nucleon (3N) interactions can be handled by modern many-body methods. However, it has been observed that when including initial chiral 3N forces in the Hamiltonian, the SRG transformations induce a non-negligible four-nucleon interaction that cannot be currently included in the calculations for technical reasons. Consequently, it is essential to investigate alternative SRG generators that might suppress the induction of many-body forces while at the same time might preserve the good convergence. In this work we test two alternative generators with oper...
Magnetic moments induce strong phonon renormalization in FeSi.
Krannich, S; Sidis, Y; Lamago, D; Heid, R; Mignot, J-M; Löhneysen, H v; Ivanov, A; Steffens, P; Keller, T; Wang, L; Goering, E; Weber, F
2015-11-27
The interactions of electronic, spin and lattice degrees of freedom in solids result in complex phase diagrams, new emergent phenomena and technical applications. While electron-phonon coupling is well understood, and interactions between spin and electronic excitations are intensely investigated, only little is known about the dynamic interactions between spin and lattice excitations. Noncentrosymmetric FeSi is known to undergo with increasing temperature a crossover from insulating to metallic behaviour with concomitant magnetic fluctuations, and exhibits strongly temperature-dependent phonon energies. Here we show by detailed inelastic neutron-scattering measurements and ab initio calculations that the phonon renormalization in FeSi is linked to its unconventional magnetic properties. Electronic states mediating conventional electron-phonon coupling are only activated in the presence of strong magnetic fluctuations. Furthermore, phonons entailing strongly varying Fe-Fe distances are damped via dynamic coupling to the temperature-induced magnetic moments, highlighting FeSi as a material with direct spin-phonon coupling and multiple interaction paths.
Renormalization (and power counting) of effective field theories for the nuclear force
Timoteo, Varese S. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Fac. de Tecnologia; Szpigel, Sergio; Duraes, Francisco O. [Universidade Presbiteriana Mackenzie, Sao Paulo, SP (Brazil). Centro de Ciencias e Humanidades
2011-07-01
The most common scheme used to regularize the Lippman-Schwinger (LS) equation is to introduce a sharp or smooth regularizing function that suppresses the contributions from the potential matrix elements for momenta larger than a given cutoff scale, which separates high-energy/short-distance scales and low-energy/long-distance scales, thus eliminating the ultraviolet divergences in the momentum integrals. Then, one needs determine the strengths of the contact interactions, the so called low-energy constants (LEC), by fitting a set of low-energy scattering data. Once the LECs are fixed for a given cutoff, the LS equation can be solved to evaluate other observables. Such a procedure, motivated by Wilsons renormalization group, relies on the fundamental premise of EFT that physics at low-energy/long-distance scales is insensitive with respect to the details of the dynamics at high-energy/short-distance scales, i.e. the relevant high-energy/short- distance effects for describing the low-energy observables can be captured in the cutoff-dependent LECs. The NN interaction can be considered properly renormalized when the calculated observables are independent of the cutoff scale within the range of validity of the ChEFT or involves a small residual cutoff dependence due to the truncation of the chiral expansion. In the language of Wilsons renormalization group, this means that the LECs must run with the cutoff scale in such a way that the scattering amplitude becomes renormalization group invariant (RGI). Here we consider pionless EFT up to NNLO and chiral EFT up to NNLO and use a subtractive renormalization scheme to describe the NN scattering channels with. We fix the strength of the contact interactions at a reference scale, chosen to be the one the provides the best fit, and then evolve the driving terms with a non-relativistic Callan-Symanzik equation to slide the renormalization scale. By computing phase shift relative differences, we show that the method is RGI. We
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.
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.
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.
Real-space renormalization group for the transverse-field Ising model in two and three dimensions.
Miyazaki, Ryoji; Nishimori, Hidetoshi; Ortiz, Gerardo
2011-05-01
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.
VANENTER, ACD; FERNANDEZ, R; SOKAL, AD
1991-01-01
We reconsider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description
Quantum coding theory with realistic physical constraints
Yoshida, Beni
2010-01-01
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.
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...
Time management: a realistic approach.
Jackson, Valerie P
2009-06-01
Realistic time management and organization plans can improve productivity and the quality of life. However, these skills can be difficult to develop and maintain. The key elements of time management are goals, organization, delegation, and relaxation. The author addresses each of these components and provides suggestions for successful time management.
Simple and Realistic Data Generation
Pedersen, Kenneth Houkjær; Torp, Kristian; Wind, Rico
2006-01-01
This paper presents a generic, DBMS independent, and highly extensible relational data generation tool. The tool can efficiently generate realistic test data for OLTP, OLAP, and data streaming applications. The tool uses a graph model to direct the data generation. This model makes it very simple...
Assessment and realistic mathematics education
Heuvel-Panhuizen, M.H.A.M. van den
1996-01-01
This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals, ideas a
Probabilistic Bisimulation for Realistic Schedulers
Eisentraut, Christian; Godskesen, Jens Christian; Hermanns, Holger
2015-01-01
. This holds in the classical context of arbitrary schedulers, but it has been argued that this class of schedulers is unrealistically powerful. This paper studies a strictly coarser notion of bisimilarity, which still enjoys these properties in the context of realistic subclasses of schedulers: Trace...
Assessment and realistic mathematics education
Heuvel-Panhuizen, M.H.A.M. van den
1996-01-01
This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals,
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Friederich, Simon
2010-12-08
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
True-to-Life? Realistic Fiction.
Jordan, Anne Devereaux
1995-01-01
Suggests that modern realistic fiction for young readers is intensely moralistic and directive at the spoken and unspoken behest of the adults who write, select, and buy that literature. Discusses moral tales, early realistic fiction, modern realistic fiction, and choosing realistic fiction. (RS)
True-to-Life? Realistic Fiction.
Jordan, Anne Devereaux
1995-01-01
Suggests that modern realistic fiction for young readers is intensely moralistic and directive at the spoken and unspoken behest of the adults who write, select, and buy that literature. Discusses moral tales, early realistic fiction, modern realistic fiction, and choosing realistic fiction. (RS)
Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
Lahoche, Vincent; Oriti, Daniele
2017-01-01
We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d = 4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.
Thermodynamics of the two-dimensional XY model from functional renormalization
Jakubczyk, Pawel
2016-01-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.
Three-body problem with short-range forces: Renormalized equations and regulator-independent results
Afnan, I. R.; Phillips, Daniel R.
2004-03-01
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron (nd) scattering at low energies. We demonstrate that in attractive channels the renormalization-group evolution of the 1+2 scattering amplitude may be complicated by the presence of eigenvalues greater than unity in the kernel. We also show that these eigenvalues can be removed from the kernel by one subtraction, resulting in an equation which is renormalization-group invariant. A unique solution for 1+2 scattering phase shifts is then obtained. We give an explicit demonstration of our procedure for both the case of three spinless bosons and the case of the doublet channel in nd scattering. After the contribution of the two-body effective range is included in the effective field theory, it gives a good description of the nd doublet phase shifts below deuteron breakup threshold.
Thermodynamics of the two-dimensional XY model from functional renormalization.
Jakubczyk, P; Eberlein, A
2016-06-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ^{4}-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.
Seiler, Christian; Evers, Ferdinand
2016-10-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.
Lee, Hyun-Jung [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Vojta, Matthias [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, D-76128 Karlsruhe (Germany)
2005-11-02
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
Lee, Hyun-Jung; Bulla, Ralf; Vojta, Matthias
2005-11-01
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
Menezes, Natália; Alves, Van Sérgio; Smith, Cristiane Morais
2016-12-01
The experimental observation of the renormalization of the Fermi velocity v F as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field B, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in B, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.
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...
Realist Criminology and its Discontents
Simon Winlow
2016-09-01
Full Text Available Critical criminology must move beyond twentieth-century empiricist and idealist paradigms because the concepts and research programmes influenced by these paradigms are falling into obsolescence. Roger Matthews’ recent work firmly advocates this position and helps to set the ball rolling. Here we argue that Matthews’ attempt to use critical realist thought to move Left Realism towards an advanced position can help to put criminology on a sound new footing. However, before this becomes possible numerous philosophical and theoretical issues must be ironed out. Most importantly, critical criminology must avoid political pragmatism and adopt a more critical stance towards consumer culture’s spectacle. A searching analysis of these issues suggests that, ultimately, criminology is weighed down with obsolete thinking to such an extent that to remain intellectually relevant it must move beyond both Left Realism and Critical Realism to construct a new ultra-realist position.
Assessment and realistic mathematics education
Heuvel-Panhuizen, M.H.A.M. van den
1996-01-01
This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals, ideas about teaching and learning mathematics, require new forms of assessment. Within RME this means a preference for observation and individual interviews. However, written tests have not been abandoned...
PyR@TE. Renormalization group equations for general gauge theories
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
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.
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.
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.
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
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
Monte Carlo renormalization: the triangular Ising model as a test case.
Guo, Wenan; Blöte, Henk W J; Ren, Zhiming
2005-04-01
We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.
Real-space renormalization group method for quantum 1/2 spins on the pyrochlore lattice.
Garcia-Adeva, Angel J
2014-04-02
A simple phenomenological real-space renormalization group method for quantum Heisenberg spins with nearest and next nearest neighbour interactions on a pyrochlore lattice is presented. Assuming a scaling law for the order parameter of two clusters of different sizes, a set of coupled equations that gives the fixed points of the renormalization group transformation and, thus, the critical temperatures and ordered phases of the system is found. The particular case of spins 1/2 is studied in detail. Furthermore, to simplify the mathematical details, from all the possible phases arising from the renormalization group transformation, only those phases in which the magnetic lattice is commensurate with a subdivision of the crystal lattice into four interlocked face-centred cubic sublattices are considered. These correspond to a quantum spin liquid, ferromagnetic order, or non-collinear order in which the total magnetic moment of a tetrahedral unit is zero. The corresponding phase diagram is constructed and the differences with respect to the classical model are analysed. It is found that this method reproduces fairly well the phase diagram of the pyrochlore lattice under the aforementioned constraints.
Savelyev, Alexey; Papoian, Garegin A.
2009-01-01
Coarse-graining of atomistic force fields allows us to investigate complex biological problems, occurring at long timescales and large length scales. In this work, we have developed an accurate coarse-grained model for double-stranded DNA chain, derived systematically from atomistic simulations. Our approach is based on matching correlators obtained from atomistic and coarse-grained simulations, for observables that explicitly enter the coarse-grained Hamiltonian. We show that this requirement leads to equivalency of the corresponding partition functions, resulting in a one-step renormalization. Compared to prior works exploiting similar ideas, the main novelty of this work is the introduction of a highly compact set of Hamiltonian basis functions, based on molecular interaction potentials. We demonstrate that such compactification allows us to reproduce many-body effects, generated by one-step renormalization, at low computational cost. In addition, compact Hamiltonians greatly increase the likelihood of finding unique solutions for the coarse-grained force-field parameter values. By successfully applying our molecular renormalization group coarse-graining technique to double-stranded DNA, we solved, for the first time, a long-standing problem in coarse-graining polymer systems, namely, how to accurately capture the correlations among various polymeric degrees of freedom. Excellent agreement is found among atomistic and coarse-grained distribution functions for various structural observables, including those not included in the Hamiltonian. We also suggest higher-order generalization of this method, which may allow capturing more subtle correlations in biopolymer dynamics. PMID:19450476
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.
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...
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...
Renormalization-group studies of three model systems far from equilibrium
Georgiev, Ivan Tsvetanov
illustrates the successful applicability of position-space renormalization-group and information theoretic approaches to driven lattice gases in one and two dimensions. These methods provide new insights into the critical properties and ordering in these systems, and set the stage for further development of these approaches and their application to additional, more realistic models.
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.
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.
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.
Driven similarity renormalization group: Third-order multireference perturbation theory.
Li, Chenyang; Evangelista, Francesco A
2017-03-28
A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N(6)) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST=ET-ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol(-1), a value that is within 0.1 kcal mol(-1) from multireference coupled cluster results.
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.
Realistic Real-Time Outdoor Rendering in Augmented Reality
Kolivand, Hoshang; Sunar, Mohd Shahrizal
2014-01-01
Realistic rendering techniques of outdoor Augmented Reality (AR) has been an attractive topic since the last two decades considering the sizeable amount of publications in computer graphics. Realistic virtual objects in outdoor rendering AR systems require sophisticated effects such as: shadows, daylight and interactions between sky colours and virtual as well as real objects. A few realistic rendering techniques have been designed to overcome this obstacle, most of which are related to non real-time rendering. However, the problem still remains, especially in outdoor rendering. This paper proposed a much newer, unique technique to achieve realistic real-time outdoor rendering, while taking into account the interaction between sky colours and objects in AR systems with respect to shadows in any specific location, date and time. This approach involves three main phases, which cover different outdoor AR rendering requirements. Firstly, sky colour was generated with respect to the position of the sun. Second step involves the shadow generation algorithm, Z-Partitioning: Gaussian and Fog Shadow Maps (Z-GaF Shadow Maps). Lastly, a technique to integrate sky colours and shadows through its effects on virtual objects in the AR system, is introduced. The experimental results reveal that the proposed technique has significantly improved the realism of real-time outdoor AR rendering, thus solving the problem of realistic AR systems. PMID:25268480
Realistic real-time outdoor rendering in augmented reality.
Kolivand, Hoshang; Sunar, Mohd Shahrizal
2014-01-01
Realistic rendering techniques of outdoor Augmented Reality (AR) has been an attractive topic since the last two decades considering the sizeable amount of publications in computer graphics. Realistic virtual objects in outdoor rendering AR systems require sophisticated effects such as: shadows, daylight and interactions between sky colours and virtual as well as real objects. A few realistic rendering techniques have been designed to overcome this obstacle, most of which are related to non real-time rendering. However, the problem still remains, especially in outdoor rendering. This paper proposed a much newer, unique technique to achieve realistic real-time outdoor rendering, while taking into account the interaction between sky colours and objects in AR systems with respect to shadows in any specific location, date and time. This approach involves three main phases, which cover different outdoor AR rendering requirements. Firstly, sky colour was generated with respect to the position of the sun. Second step involves the shadow generation algorithm, Z-Partitioning: Gaussian and Fog Shadow Maps (Z-GaF Shadow Maps). Lastly, a technique to integrate sky colours and shadows through its effects on virtual objects in the AR system, is introduced. The experimental results reveal that the proposed technique has significantly improved the realism of real-time outdoor AR rendering, thus solving the problem of realistic AR systems.
Realistic real-time outdoor rendering in augmented reality.
Hoshang Kolivand
Full Text Available Realistic rendering techniques of outdoor Augmented Reality (AR has been an attractive topic since the last two decades considering the sizeable amount of publications in computer graphics. Realistic virtual objects in outdoor rendering AR systems require sophisticated effects such as: shadows, daylight and interactions between sky colours and virtual as well as real objects. A few realistic rendering techniques have been designed to overcome this obstacle, most of which are related to non real-time rendering. However, the problem still remains, especially in outdoor rendering. This paper proposed a much newer, unique technique to achieve realistic real-time outdoor rendering, while taking into account the interaction between sky colours and objects in AR systems with respect to shadows in any specific location, date and time. This approach involves three main phases, which cover different outdoor AR rendering requirements. Firstly, sky colour was generated with respect to the position of the sun. Second step involves the shadow generation algorithm, Z-Partitioning: Gaussian and Fog Shadow Maps (Z-GaF Shadow Maps. Lastly, a technique to integrate sky colours and shadows through its effects on virtual objects in the AR system, is introduced. The experimental results reveal that the proposed technique has significantly improved the realism of real-time outdoor AR rendering, thus solving the problem of realistic AR systems.
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.)
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...
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...
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.
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...
Simulating realistic enough patient records.
Cunningham, James; Ainsworth, John
2015-01-01
Information systems for storing, managing and manipulating electronic medical records must place an emphasis on maintaining the privacy and security of those records. Though the design, development and testing of such systems also requires the use of data, the developers of these systems, rarely also their final end users, are unlikely to have ethical or governance approval to use real data. Alternative test data is commonly either randomly produced or taken from carefully anonymised subsets of records. In both cases there are potential shortcomings that can impact on the quality of the product being developed. We have addressed these shortcomings with a tool and methodology for efficiently simulating large amounts of realistic enough electronic patient records which can underpin the development of data-centric electronic healthcare systems.
Realist RCTs of complex interventions - an oxymoron.
Marchal, Bruno; Westhorp, Gill; Wong, Geoff; Van Belle, Sara; Greenhalgh, Trisha; Kegels, Guy; Pawson, Ray
2013-10-01
Bonell et al. discuss the challenges of carrying out randomised controlled trials (RCTs) to evaluate complex interventions in public health, and consider the role of realist evaluation in enhancing this design (Bonell, Fletcher, Morton, Lorenc, & Moore, 2012). They argue for a "synergistic, rather than oppositional relationship between realist and randomised evaluation" and that "it is possible to benefit from the insights provided by realist evaluation without relinquishing the RCT as the best means of examining intervention causality." We present counter-arguments to their analysis of realist evaluation and their recommendations for realist RCTs. Bonell et al. are right to question whether and how (quasi-)experimental designs can be improved to better evaluate complex public health interventions. However, the paper does not explain how a research design that is fundamentally built upon a positivist ontological and epistemological position can be meaningfully adapted to allow it to be used from within a realist paradigm. The recommendations for "realist RCTs" do not sufficiently take into account important elements of complexity that pose major challenges for the RCT design. They also ignore key tenets of the realist evaluation approach. We propose that the adjective 'realist' should continue to be used only for studies based on a realist philosophy and whose analytic approach follows the established principles of realist analysis. It seems more correct to call the approach proposed by Bonell and colleagues 'theory informed RCT', which indeed can help in enhancing RCTs. Copyright © 2013 Elsevier Ltd. All rights reserved.
Anharmonic stabilization and band gap renormalization in the perovskite CsSnI_{3}
Patrick, Christopher; Jacobsen, Karsten Wedel; Thygesen, Kristian Sommer
2015-01-01
to rotational instabilities of the SnI6 octahedra. Here, employing self-consistent phonon theory, we show that these soft modes are stabilized at experimental conditions through anharmonic phonon-phonon interactions between the Cs ions and their iodine cages. We further calculate the renormalization...... of the electronic energies due to vibrations and find an unusual opening of the band gap, estimated as 0.24 and 0.11 eV at 500 and 300 K, which we attribute to the stretching of Sn-I bonds. Our work demonstrates the important role of temperature in accurately describing these materials....
Dynamical gap generation in graphene with frequency-dependent renormalization effects
Carrington, M. E.; Fischer, C. S.; von Smekal, L.; Thoma, M. H.
2016-09-01
We study the frequency dependencies in the renormalization of the fermion Green's function for the π -band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region, we self-consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency-dependent Lindhard screening and retardation effects.
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.
Hu, Weifeng
2015-01-01
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. 9, 4462 (2013)). We introduce a DMRG wavefunction 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.
Morris, Titus; Bogner, Scott
2016-09-01
The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully to the ground state of closed shell finite nuclei. Recent work has extended its ability to target excited states of these closed shell systems via equation of motion methods, and also complete spectra of the whole SD shell via effective shell model interactions. A recent alternative method for solving of the IM-SRG equations, based on the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.
Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule
Kato, Mitsuhiro; So, Hiroto
2016-01-01
N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.
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.
Diep, H T; Kaufman, Miron
2009-09-01
We extend the model of a 2d solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.
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...
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 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].
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.
Tensor renormalization group methods for spin and gauge models
Zou, Haiyuan
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
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...
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
Kouri, Donald J; Vijay, Amrendra
2003-04-01
The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the frequency. By contrast, it is well known that the Born-Neumann series for the Volterra integral equations in quantum scattering are absolutely convergent, independent of the strength of the coupling characterizing the interaction. The transformation of the Lippmann-Schwinger equation from a Fredholm to a Volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering. In this paper, we employ the renormalization technique to obtain a Volterra equation framework for the inverse acoustic scattering series, proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values. The present results are for acoustic scattering in one dimension, but the method is general. The approach is illustrated by applications to two simple one-dimensional models for acoustic scattering.
Unified theory of electron-phonon renormalization and phonon-assisted optical absorption.
Patrick, Christopher E; Giustino, Feliciano
2014-09-10
We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the Herzberg-Teller effect and to phonon-assisted optical absorption in indirect band gap materials. In addition, our theory predicts sub-gap phonon-assisted optical absorption in direct gap materials, as well as an exponential edge which we tentatively assign to the Urbach tail. We also consider a semiclassical approach to the calculation of optical absorption spectra which simultaneously captures energy-level renormalization and phonon-assisted transitions and is especially suited to first-principles electronic structure calculations. We demonstrate this approach by calculating the phonon-assisted optical absorption spectrum of bulk silicon.
He, Lewei; Wang, Wen-Ge
2014-02-01
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.
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.
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.