Improved Monte Carlo Renormalization Group Method
DOE R&D Accomplishments Database
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.
Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model
NASA Technical Reports Server (NTRS)
Heller, Urs M.
1988-01-01
An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Liu, Yuzhi
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).
The analytic renormalization group
NASA Astrophysics Data System (ADS)
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.
Renormalization group functional equations
Curtright, Thomas L.; Zachos, Cosmas K.
2011-03-15
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from step-scaling {sigma} functions and lead to exact functional relations for the local flow {beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {sigma} are sometimes not true fixed points under continuous changes in scale and zeroes of {beta} do not necessarily signal fixed points of the flow but instead may only indicate turning points of the trajectories.
Renormalization Group Tutorial
NASA Technical Reports Server (NTRS)
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.
Gutzwiller renormalization group
NASA Astrophysics Data System (ADS)
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.
Cluster functional renormalization group
NASA Astrophysics Data System (ADS)
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.
Bonca, J.; Gubernatis, J. E.; Guerrero, M.; Jeckelmann, Eric; White, Steven R.
2000-02-01
Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a 12x3 Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For U/t{>=}6 we find a ground-state with charge inhomogeneities consistent with stripes. (c) 2000 The American Physical Society.
Gutzwiller renormalization group
Lanatà, Nicola; Yao, Yong -Xin; Deng, Xiaoyu; Wang, Cai -Zhuang; Ho, Kai -Ming; Kotliar, Gabriel
2016-01-06
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. Furthermore, we perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG mightmore » 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.« less
Renormalization group in internal space
Polonyi, J.; Sailer, K.
2005-01-15
Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.
Renormalization group in quantum mechanics
Polony, J.
1996-12-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.
Efficient implementation of the time renormalization group
NASA Astrophysics Data System (ADS)
Vollmer, Adrian; Amendola, Luca; Catena, Riccardo
2016-02-01
The time renormalization group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to precompute only 13 antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under control, we find that the computation time for nonlinear corrections to the matter power spectrum decreases by a factor of 50. This opens up the possibility to use TRG for mass production as in Markov chain Monte Carlo methods. A fortran code demonstrating this new algorithm is publicly available.
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2015-06-01
The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar super Yang-Mills theory.
Higher spin versus renormalization group equations
NASA Astrophysics Data System (ADS)
Sachs, Ivo
2014-10-01
We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on AdS4 for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.
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.
Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective
NASA Technical Reports Server (NTRS)
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.
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. PMID:26651641
Information geometry and the renormalization group
NASA Astrophysics Data System (ADS)
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.
Large-cell Monte Carlo renormalization of irreversible growth processes
NASA Technical Reports Server (NTRS)
Nakanishi, H.; Family, F.
1985-01-01
Monte Carlo sampling is applied to a recently formulated direct-cell renormalization method for irreversible, disorderly growth processes. Large-cell Monte Carlo renormalization is carried out for various nonequilibrium problems based on the formulation dealing with relative probabilities. Specifically, the method is demonstrated by application to the 'true' self-avoiding walk and the Eden model of growing animals for d = 2, 3, and 4 and to the invasion percolation problem for d = 2 and 3. The results are asymptotically in agreement with expectations; however, unexpected complications arise, suggesting the possibility of crossovers, and in any case, demonstrating the danger of using small cells alone, because of the very slow convergence as the cell size b is extrapolated to infinity. The difficulty of applying the present method to the diffusion-limited-aggregation model, is commented on.
Renormalization group equations for the CKM matrix
Kielanowski, P.; Juarez W, S. R.; Montes de Oca Y, J. H.
2008-12-01
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) 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 {phi}{sub 2} of the unitarity triangle. For the special case of the standard model and its extensions with v{sub 1}{approx_equal}v{sub 2} we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters {rho} and {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 might have a simple, special form at asymptotic energies.
Spectral renormalization group theory on nonspatial networks
NASA Astrophysics Data System (ADS)
Tuncer, Asli; Erzan, Ayse
We recently proposed a ``spectral renormalization group'' scheme, for non-spatial networks with no metric defined on them. We implemented the spectral renormalization group on two deterministic non-spatial networks without translational invariance, namely the Cayley tree and diamond lattice . The thermodynamic critical exponents for the Gaussian model are only functions of the spectral dimension, d ~. The Gaussian fixed point is stable with respect to a Ψ4 perturbation up to second order on these lattices with d ~ = 2 , the lower critical dimension for the Ising universality class. This is expected for the Cayley tree, but for the diamond lattice it is an indication that the perturbation expansion up to second order breaks down at d ~ = 2 , as it does for the Wilson scheme on the square lattice. On generalized diamond lattices, with 2 < d ~ < 4 , we find non-Gaussian fixed points with non-trivial exponents. For d ~ > 4 , the critical behavior is once again mean field.
Renormalization Group in the Standard Model
Kielanowski, P.; Juarez W, S. R.
2007-11-27
We discuss two applications of the renormalization group method in the Standard Model. In the first one we present some theorems about the running of the Cabibbo-Kobayashi-Maskawa matrix and show that the evolution depends on one function of energy only. In the second one we discuss the properties of the running of the Higgs potential and derive the limits for the Higgs mass.
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. PMID:21646269
Tensor renormalization group analysis of CP (N -1 ) model
NASA Astrophysics Data System (ADS)
Kawauchi, Hikaru; Takeda, Shinji
2016-06-01
We apply the higher-order tensor renormalization group to the lattice CP (N -1 ) model in two dimensions. A tensor network representation of the CP (N -1 ) model in the presence of the θ term is derived. We confirm that the numerical results of the CP(1) model without the θ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region β ≫1 and that obtained by the Monte Carlo simulation in a wider range of β . The numerical computation including the θ term is left for future challenges.
The renormalization group via statistical inference
NASA Astrophysics Data System (ADS)
Bény, Cédric; Osborne, Tobias J.
2015-08-01
In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalization group (RG) arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and reveals the role played by information in renormalization. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a Gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalization techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.
Attempered renormalization-group scheme for the SU(2)-Higgs model
Callaway, D.J.E.; Furlong, R.C.; Petronzio, R.
1987-06-15
The fact that most renormalization-group blocking schemes include each site link in many block links can generate spurious interactions in the block system. This shortcoming can lead to inconsistent flow diagrams in truncated calculations. A general method for avoiding this problem is formulated and applied to a Monte Carlo renormalization-group study of the SU(2)-Higgs model in four dimensions with scale factor ..sqrt..2 . .AE
Extreme-value distributions and renormalization group.
Calvo, Iván; Cuchí, Juan C; Esteve, J G; Falceto, Fernando
2012-10-01
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approached using the language of renormalization-group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections. PMID:23214531
Tensor networks and the numerical renormalization group
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas
2012-12-01
The full-density-matrix numerical renormalization group has evolved as a systematic and transparent setting for the calculation of thermodynamical quantities at arbitrary temperatures within the numerical renormalization group (NRG) framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets introduced by Anders and Schiller [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. In addition, specific attention is given to the possible feedback from low-energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-golden-rule calculations (fgrNRG) as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.
Functional renormalization group approach to noncollinear magnets
NASA Astrophysics Data System (ADS)
Delamotte, B.; Dudka, M.; Mouhanna, D.; Yabunaka, S.
2016-02-01
A functional renormalization group approach to d -dimensional, N -component, noncollinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between d =2.8 and d =4 for various values of N focusing on the critical value Nc(d ) that, for a given dimension d , separates a first-order region for N
Neutrino anarchy and renormalization group evolution
NASA Astrophysics Data System (ADS)
Brdar, Vedran; König, Matthias; Kopp, Joachim
2016-05-01
The observed pattern of neutrino mixing angles is in good agreement with the hypothesis of neutrino anarchy, which posits that nature has chosen the entries of the leptonic mixing matrix at random. In this paper we investigate how stable this conclusion is under renormalization group (RG) effects. Working in the simplest type-I seesaw model and two variants of the inverse seesaw model we study how the statistical distributions of the neutrino mixing parameters evolve between the grand unification scale and the electroweak scale. Especially in the inverse seesaw case we find significant distortions: Mixing angles tend to be smaller after RG running, and the Dirac C P phase tends to be closer to zero. The p -value describing the compatibility between the observed mixing angles and the anarchy hypothesis increases by 10%-20%. This illustrates that RG effects are highly relevant for quantitative studies of the anarchy scenario.
Manifestly diffeomorphism invariant classical Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Morris, Tim R.; Preston, Anthony W. H.
2016-06-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
Holographic trace anomaly and local renormalization group
NASA Astrophysics Data System (ADS)
Rajagopal, Srivatsan; Stergiou, Andreas; Zhu, Yechao
2015-11-01
The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.
Renormalization group analysis in nonrelativistic QCD for colored scalars
Hoang, Andre H.; Ruiz-Femenia, Pedro
2006-01-01
The velocity nonrelativistic QCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.
Tensor renormalization group approach to classical dimer models
NASA Astrophysics Data System (ADS)
Roychowdhury, Krishanu; Huang, Ching-Yu
2015-05-01
We analyze classical dimer models on a square and a triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "tensor renormalization group" (TRG) technique. The partition function for the dimer problem can be calculated exactly by the Pfaffian method, which is used here as a platform for comparing the numerical results. The TRG approach turns out to be a powerful tool for describing gapped systems with exponentially decaying correlations very efficiently due to its fast convergence. This is the case for the dimer model on the triangular lattice. However, the convergence becomes very slow and unstable in the case of the square lattice where the model has algebraically decaying correlations. We highlight these aspects with numerical simulations and critically appraise the robustness of the TRG approach by contrasting the results for small and large system sizes against the exact calculations. Furthermore, we benchmark our TRG results with the classical Monte Carlo method.
Nonperturbative Renormalization Group Approach to Polymerized Membranes
NASA Astrophysics Data System (ADS)
Essafi, Karim; Kownacki, Jean-Philippe; Mouhanna, Dominique
2014-03-01
Membranes or membrane-like materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Roughly speaking, membranes can be divided into two group: fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference between fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid membranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. non-self-avoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, graphene behaves just as a polymerized membrane in its flat phase.
Duality and holographic renormalization group flows
NASA Astrophysics Data System (ADS)
Halmagyi, Nicholas
This thesis contains a detailed study of holographic renormalization group flows in An quiver gauge theories. The flows considered are two fold. Firstly I consider flows generated by mass terms for the adjoint chiral superfields, these flows have conformal fixed point in the ultraviolet as well as the infrared. Two well known flows in this class are the Pilch-Warner flow and the Klebanov-Witten flow, which as deformations of the UV theory lie in the untwisted sector and twisted sector respectively. There is also known to be flows which mix the twisted and untwisted sectors. We study this whole family of flows using field theory methods combined with their M-theory construction. In particular I elaborate on the duality group which acts on this whole family of flows and a subgroup of the full duality group is identified directly in the field theory as Seiberg duality. The structure of the long sought after IIB supergravity solution to the Klebanov-Witten flow is provided, the entire flow is a metric on the singular conifold which we provide up to the solution of one non-linear p.d.e. Further, the IIB string is solved in the Penrose limit of the Pilch-Warner solution. Secondly, we consider flows which are confining in the infrared the same duality group which acts on this RG-flows mentioned above, also acts of this family of flows. A certain universal behaviour is discovered on this large family of flows and is attributed to certain properties of the affine Weyl group.
Applying Renormalization Group Techniques to Nuclear Reactions
NASA Astrophysics Data System (ADS)
Eldredge, Zachary; Bogner, Scott; Nunes, Filomena
2013-10-01
Nuclear reactions are commonly used to explore the physics of unstable nuclei. Therefore, it is important that accurate, computationally favorable methods exist to describe them. Reaction models often make use of effective nucleon-nucleus potentials (optical potentials) which fit low-energy scattering data and include an imaginary component to account for the removal of flux from the elastic channel. When describing reactions in momentum space, the coupling between low- and high-momentum states can pose a technical challenge. We would like potentials which allow us to compute low-momentum interactions without including highly virtual momentum states. A solution to this problem is to apply renormalization group (RG) techniques to produce a new effective potential in which high and low momentum degrees of freedom are decoupled, so that we need only consider momenta below some cutoff. This poster will present results relating to an implementation of RG techniques on optical potentials, including complex potentials and spin-orbit effects. We show that our evolved optical potentials reproduce bound states and scattering phase shifts without the inclusion of any momenta above a selected cutoff, and compare new potentials to old ones to examine the effect of transformation.
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. PMID:27537835
Quark lepton complementarity and renormalization group effects
Schmidt, Michael A.; Smirnov, Alexei Yu.
2006-12-01
We consider a scenario for the quark-lepton complementarity relations between mixing angles in which the bimaximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle {theta}{sub 12} is {approx}1{sigma} (1.5 degree sign -2 degree sign ) above the best fit point coinciding practically with the tribimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to {theta}{sub 12} as well as to {theta}{sub 13} in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in a large part of the parameter space corrections {delta}{theta}{sub 12} are small or negligible. In the MSSM version of the scenario, the correction {delta}{theta}{sub 12} is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of {nu}{sub 1} and {nu}{sub 2} when leading contributions to {theta}{sub 12} running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of {nu}{sub 1} and {nu}{sub 2}: {phi}>{pi}/2.
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
Brodsky, Stanley J.; Wu, Xing-Gang
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.
DLA with two species: Renormalization-group method renormalization-group method
NASA Astrophysics Data System (ADS)
Chang, Fuxuan; Li, Houqiang; Liu, De; Lin, Libin
1998-12-01
In this paper, we have studied the structure of DLA with two species by using the kinetic real-space renormalization group method introduced by Wang. Following the RG rules and growth processor, We have gained the configuration of 2×2 cell, calculated the fractal dimensions, multifractal spectra, and free energy when different value of p are applied. And we studied the problem of phase transition with different value of p. Our results demonstrate that the change of p doesn't affect the fractal dimension, but can affect the multifractal spectrum and the phase transition.
Renormalization group improved Higgs inflation with a running kinetic term
NASA Astrophysics Data System (ADS)
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.
An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
NASA Astrophysics Data System (ADS)
Chandre, C.; Jauslin, H. R.; Benfatto, G.
1999-01-01
We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.
XY-sliding phases - mirage of the Renormalization Group
NASA Astrophysics Data System (ADS)
Vayl, Steven; Kuklov, Anatoly; Oganesyan, Vadim
The so called sliding XY phases in layered systems are predicted to occur if the one loop renormalization group (RG) flow renders the interlayer Josephson coupling irrelevant, while each layer still features broken U(1) symmetry. In other words, such a layered system remains essentially two-dimensional despite the presence of inter-layer Josephson coupling. We have analyzed numerically a layered system consisting of groups of asymmetric layers where the RG analysis predicts sliding phases to occur. Monte Carlo simulations of such a system have been conducted in the dual representation by Worm Algorithm in terms of the closed loops of J-currents for layer sizes varying from 4 ×4 to 640 ×640 and the number of layers - from 2 to 40. The resulting flow of the inter-layer XY-stiffness has been found to be inconsistent with the RG prediction and fully consistent with the behavior of the 3D standard XY model where the bare inter-layer Josephson coupling is much smaller than the intra-layer stiffness. This result emphasizes the importance of the compactness of the U(1) variable for 2D to 3D transformation. This work was supported by the NSF Grant PHY1314469.
Nearest neighbor interaction in the Path Integral Renormalization Group method
NASA Astrophysics Data System (ADS)
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.
Renormalization group invariant of lepton Yukawa couplings
NASA Astrophysics Data System (ADS)
Tsuyuki, Takanao
2015-04-01
By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them, Iq, is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant Il for Dirac and Majorana neutrino cases and find that Il can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality Iq=Il can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.
The ab-initio density matrix renormalization group in practice
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic; Nakatani, Naoki
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.
Emergent geometry from field theory: Wilson's renormalization group revisited
NASA Astrophysics Data System (ADS)
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.
Renormalization group and the superconducting susceptibility of a Fermi liquid
Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.
2010-11-15
A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.
Nonlinear Reynolds stress models and the renormalization group
NASA Technical Reports Server (NTRS)
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.
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
Stephan I. Tzenov
2002-05-09
Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.
Renormalization Group Flows, Cycles, and c-Theorem Folklore
NASA Astrophysics Data System (ADS)
Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.
2012-03-01
Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.
SU(3) renormalization group study on parallel computer AP1000
NASA Astrophysics Data System (ADS)
Akemi, K.; de Forcrand, Ph.; Fujisaki, M.; Hashimoto, T.; Hege, H. C.; Hioki, S.; Makino, J.; Miyamura, O.; Nakamura, A.; Okada, M.; Stamatescu, I. O.; Tago, Y.; Takaishi, T.; QCD TARO (QCD on Thousand cell ARay processorOmnipurpose) Collaboration
We report results of a Monte Crlo renormalization group study with b = 2 blocking on a 34 4 lattice in progress. Δβ at β = 6.8 is consistent with previously obtained values at a large β and is smaller than the two-loop asymptotic value.
Nikolov, Nikolay M.
2010-06-17
The deviation from commutativity of the renormalization and the action of all linear partial differential operators is the main source of the anomalies in quantum field theory, including the renormalization group action. This deviation is characterized by certain 'renormalization cocycles' that are related to cohomologies of the so called (ordered) configuration spaces. Cohomological differential equations that determine the renormalization cocycles up to the renormalization freedom are obtained. The solution of these equations requires introducing transcendental extensions related to higher-dimensional polylogarithms.
Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review
NASA Astrophysics Data System (ADS)
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 Γ(H\\to b\\bar{b}) 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
Unifying renormalization group and the continuous wavelet transform
NASA Astrophysics Data System (ADS)
Altaisky, M. V.
2016-05-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e., those depending on both the position x and the resolution a . Such a theory, earlier described in [1,2], is finite by construction. The space of scale-dependent functions {ϕa(x )} is more relevant to a physical reality than the space of square-integrable functions L2(Rd); because of the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than a point. The effective action Γ(A ) of our theory turns out to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet—an "aperture function" of a measuring device used to produce the snapshot of a field ϕ at the point x with the resolution a . The standard renormalization group results for ϕ4 model are reproduced.
On a renormalization group scheme for causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.
2016-03-01
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme—in concert with finite size scaling analysis—is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in a previous paper (Cooperman, arXiv:gr-qc/1410.0026). As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.
Renormalization-group study of the four-body problem
Schmidt, Richard; Moroz, Sergej
2010-05-15
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
Computing the effective action with the functional renormalization group
NASA Astrophysics Data System (ADS)
Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław; Tonero, Alberto
2016-04-01
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action Γ _k. The ordinary effective action Γ _0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
More on the renormalization group limit cycle in QCD
Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga
2006-02-26
We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.
Consistent closure of renormalization group flow equations in quantum gravity
NASA Astrophysics Data System (ADS)
Codello, Alessandro; D'Odorico, Giulio; Pagani, Carlo
2014-04-01
We construct a consistent closure for the beta functions of the cosmological and Newton's constants by evaluating the influence that the anomalous dimensions of the fluctuating metric and ghost fields have on their renormalization group flow. In this generalized framework we confirm the presence of a UV attractive non-Gaussian fixed point, which we find characterized by real critical exponents. Our closure method is general and can be applied systematically to more general truncations of the gravitational effective average action.
Lattice and continuum wavelets and the block renormalization group
O'Carroll, M. )
1993-05-01
The authors obtain a resolution of the identity operator, for functions on a lattice [var epsilon]Z[sup d], which is derived from the block renormalization group. The authors use eigenfunctions of the terms of the decomposition to form a basis for l[sub 2]([var epsilon]Z[sup d]) and show how the basis is generated from lattice wavelets. The lattice spacing [var epsilon] is taken to zero and continuum wavelets are obtained. 12 refs.
Subtractive Renormalization Group Invariance: Pionless EFT at NLO
Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.
2010-11-12
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{sup -15}.
Holographic entanglement entropy of N =2* renormalization group flow
NASA Astrophysics Data System (ADS)
Pang, Da-Wei
2015-10-01
The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.
Infrared Renormalization-Group Flow for Heavy-Quark Masses
Hoang, Andre H.; Jain, Ambar; Stewart, Iain W.; Scimemi, Ignazio
2008-10-10
A short-distance heavy-quark mass depends on two parameters: the renormalization scale {mu} and a scale R controlling the absorption of infrared fluctuations. The radius for perturbative corrections that build up the mass beyond its pointlike definition in the pole scheme is {approx}1/R. Treating R as a variable gives a renormalization-group equation. R evolution improves the stability of conversion between short-distance mass schemes, allowing us to avoid large logs and the renormalon. R evolution can also be used to study IR renormalons without using bubble chains, yielding a convergent sum rule for the coefficient of the O({lambda}{sub QCD}) renormalon ambiguity of the pole mass.
Strong Disorder Renormalization Group for the Many Body Localization Transition
NASA Astrophysics Data System (ADS)
Refael, Gil; Oganesyan, Vadim; Iyer, Shankar
2012-02-01
The strong disorder renormalization group, originally devised by Ma and Dasgupta to study the random Heisenberg antiferromagnet, has subsequently been used to investigate the low energy physics and quantum phase transitions of a variety of strongly disordered systems. However, recent work by Basko, Aleiner, and Altshuler has focused attention on the many body localization transition, a dynamical quantum phase transition that involves the localization of highly excited eigenstates of a many body system in Fock space. Numerical results from an exact diagonalization study by Pal and Huse suggest that the many body localization transition may exhibit so-called infinite-randomness, a property that implies that a strong disorder renormalization group may be well-suited to study this transition. With the many body localization transition in mind, we therefore outline a strong disorder renormalization procedure that targets the least-localized eigenstate of a model. We then apply this procedure to study disordered quantum Ising and XXZ models. The latter model is similar to the one investigated by Pal and Huse and is expected to contain a dynamical transition between localized and ergodic phases; our principal aim is to use the strong disorder RG to characterize this transition.
Renormalization group analysis of the gluon mass equation
NASA Astrophysics Data System (ADS)
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2014-04-01
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.
NASA Astrophysics Data System (ADS)
Adzhemyan, L. Ts.; Hnatič, M.; Kompaniets, M.; Lučivjanský, T.; Mižišin, L.
2016-02-01
The renormalization group theory is used to the study of the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ɛ-expansion where ɛ is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.
Renormalization Group Analysis of the Stability of Turbulent Flows in Porous Media
NASA Astrophysics Data System (ADS)
Avramenko, A. A.; Dmitrenko, N. P.; Tyrinov, A. I.
2016-06-01
The concept of renormalization groups for modeling the parameters of flow in porous media is considered. An algorithm for the renormalization of the equations from the k-ɛ model of turbulence is given. An expression is obtained for the coefficient of renormalized viscosity. Based on the model developed, conditions of the turbulent flow instability in a porous medium have been analyzed.
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
NASA Technical Reports Server (NTRS)
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.
Information-geometric approach to the renormalization group
NASA Astrophysics Data System (ADS)
Bény, Cédric; Osborne, Tobias J.
2015-08-01
We propose a general formulation of the renormalization group (RG) as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are nonincreasing along the flow. Among those, we study the speed of the flow and its generalization to infinite lattices.
NASA Astrophysics Data System (ADS)
Kubica, Aleksander; Yoshida, Beni
2014-03-01
We invent a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponents ν near criticality of quantum Ising and clock models in higher dimensions. The method, based on a recent proposal by Miyazaki et al., Phys. Rev. E 83, 051103 (2011), is remarkably simple (often analytical), grouping only a few spins into a block spin so that renormalized Hamiltonian has a closed form. A previous difficulty of spatial anisotropy and unwanted terms arising in higher-dimensional RG schemes is avoided by incorporating rotational invariance and internal Zq symmetries of the Hamiltonian. By applying this scheme to (2+1)-dim Ising model on a triangular lattice, we obtained ν = 0 . 6300 which is within statistical error of the current best Monte-Carlo result and ϕ4 theory estimation with seven-loop corrections. We also apply the scheme to higher-dimensional clock (Potts) models for which ordinary Monte-Carlo methods are not efficient due to suppression of quantum fluctuation in first-order phase transition.
Renormalization group methods for the Reynolds stress transport equations
NASA Technical Reports Server (NTRS)
Rubinstein, R.
1992-01-01
The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.
Elliptical galaxies kinematics within general relativity with renormalization group effects
Rodrigues, Davi C.
2012-09-01
The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G{sub 0}∼<10{sup −7} across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type)
Determining the structure of supersymmetry breaking with renormalization group invariants
Carena, Marcela; Draper, Patrick; Shah, Nausheen R.; Wagner, Carlos E. M.
2010-10-01
If collider experiments demonstrate that the minimal supersymmetric standard model (MSSM) is a good description of nature at the weak scale, the experimental priority will be the precise determination of superpartner masses. These masses are governed by the weak scale values of the soft supersymmetry-breaking (SUSY-breaking) parameters, which are in turn highly dependent on the SUSY-breaking scheme present at high scales. It is therefore of great interest to find patterns in the soft parameters that can distinguish different high-scale SUSY-breaking structures, identify the scale at which the breaking is communicated to the visible sector, and determine the soft breaking parameters at that scale. In this work, we demonstrate that 1-loop renormalization group invariant quantities present in the MSSM may be used to answer each of these questions. We apply our method first to generic flavor-blind models of SUSY breaking, and then we examine in detail the subset of these models described by general gauge mediation and the constrained MSSM with nonuniversal Higgs masses. As renormalization group invariance generally does not hold beyond leading-log order, we investigate the magnitude and direction of the 2-loop corrections. We find that with superpartners at the TeV scale, these 2-loop effects are either negligible, or they are of the order of optimistic experimental uncertainties and have definite signs, which allows them to be easily accounted for in the overall uncertainty.
Numerical renormalization group study of a dissipative quantum dot
NASA Astrophysics Data System (ADS)
Glossop, M. T.; Ingersent, K.
2007-03-01
We study the quantum phase transition (QPT) induced by dissipation in a quantum dot device at the degeneracy point. We employ a Bose-Fermi numerical renormalization group approach [1] to study the simplest case of a spinless resonant-level model that couples the charge density on the dot to a dissipative bosonic bath with density of states B(φ)ŝ. In anticipation of future experiments [2] and to assess further the validity of theoretical techniques in this rapidly developing area, we take the conduction-electron leads to have a pseudogap density of states: ρ(φ) |φ|^r, as considered in a very recent perturbative renormalization group study [3]. We establish the conditions on r and s such that a QPT arises with increasing dissipation strength --- from a delocalized phase, where resonant tunneling leads to large charge fluctuations on the dot, to a localized phase where such fluctuations are frozen. We present results for the single-particle spectrum and the response of the system to a local electric field, extracting critical exponents that depend in general on r and s and obey hyperscaling relations. We make full comparison with results of [3] where appropriate. Supported by NSF Grant DMR-0312939. [1] M. T. Glossop and K. Ingersent, PRL 95, 067202 (2005); PRB (2006). [2] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, PRL 97, 096603 (2006). [3] C.-H. Chung, M. Kir'can, L. Fritz, and M. Vojta (2006).
Holographic renormalization group and cosmology in theories with quasilocalized gravity
NASA Astrophysics Data System (ADS)
Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-01
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-15
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling.
Park, M; O'Malley, D; Cushman, J H
2014-04-01
Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time. PMID:24827190
Two-loop perturbative quark mass renormalization from large {beta} Monte Carlo
Keisuke Jimmy Juge
2001-02-14
We present the calculation of heavy Wilson quark mass renormalization constants from large beta Monte Carlo simulations. Simulations were performed at various beta larger than 9, each on several spatial lattice sizes to allow for an infinite volume extrapolation. We use twisted boundary conditions to suppress tunneling and work in Coulomb gauge with appropriate adjustments for the temporal links. The one-loop coefficient obtained from this method is in agreement with the analytical result and a preliminary result for the second order coefficient is reported.
Superfluid phase transition with activated velocity fluctuations: Renormalization group approach
NASA Astrophysics Data System (ADS)
Dančo, Michal; Hnatič, Michal; Komarova, Marina V.; Lučivjanský, Tomáš; Nalimov, Mikhail Yu.
2016-01-01
A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ɛ ,δ ) -expansion scheme is employed, where ɛ is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4 /3 .
The large-N{sub c} renormalization group
Dorey, N.; Mattis, M.P.
1995-05-01
In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N{sub c}, limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N{sub c}, selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N{sub c}. We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius {Lambda}{sup {minus}1} ({Lambda} being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r {le} {Lambda}{sup {minus}1}. The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-{Delta} hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N{sub c}, renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as {Lambda} {yields} {infinity}.
Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.
Dančo, Michal; Hnatič, Michal; Komarova, Marina V; Lučivjanský, Tomáš; Nalimov, Mikhail Yu
2016-01-01
A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ε,δ)-expansion scheme is employed, where ε is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4/3. PMID:26871026
Dynamical renormalization group approach to relaxation in quantum field theory
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; de Vega, H. J.
2003-10-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.
Stability of renormalization group trajectories and the fermion flavor problem
NASA Astrophysics Data System (ADS)
Goldfain, Ervin
2007-04-01
An outstanding puzzle of the current standard model for particle physics (SM) is that both leptons and quarks arise in replicated patterns. Our work suggests that the number of fermion flavors occurring in the SM may be directly derived from the dynamics of renormalization group equations. The starting point is the system describing the coupling flow in the gauge sector [ dgidt.= βi(gi)=bi(N,nf)gi^3 +O(gi^5 ) ] where i=(1,2,3) labels the gauge group of dimension N, nf is the number of fermion flavors and t the sliding scale. With the help of the Routh-Hurwitz criterion, we find that the SM solution nf=6 follows from demanding stability of the linearized flow about its fixed points.
Recent progress in ab initio density matrix renormalization group methodology
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Dorando, Jonathan J.; Kin-Lic Chan, Garnet
2008-03-01
We present some recent developments in the ab initio density matrix renormalization group (DMRG) method for quantum chemical problems, in particular our local, quadratic scaling algorithm [1] for low dimensional systems. This method is particularly suited for the description of strong nondynamic correlation, and allows us to compute numerically exact (FCI) correlated energies for large active spaces, up to one order of magnitude larger then can be done by conventional CASCI techniques. Other features of this method are its inherent multireference nature, compactness, variational results, size-consistency and size-extensivity. In addition we will review the problems (predominantly organic electronic materials) on which we applied the ab initio DMRG: 1) metal-insulator transition in hydrogen chains [1] 2) all-trans polyacetylene [1] 3) acenes [2] 4) polydiacetylenes [3]. References [1] Hachmann, Cardoen, Chan, JCP 125 (2006), 144101. [2] Hachmann, Dorando, Avil'es, Chan, JCP 127 (2007), 134309. [3] unpublished.
A renormalization group analysis of two-dimensional magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Liang, Wenli Z.; Diamond, P. H.
1993-01-01
The renormalization group (RNG) method is used to study the physics of two-dimensional (2D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean-square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2D MHD system. A similar conclusion is reached for 2D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual-direction transfer.
CALL FOR PAPERS: Special issue on Renormalization Group 2005
NASA Astrophysics Data System (ADS)
Honkonen, Juha; Kazakov, Dmitri; Diehl, Hans Werner
2005-10-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of the Renormalization Group as featured in the international workshop Renormalization Group 2005, Helsinki, Finland 30 August-3 September 2005 (http://theory.physics.helsinki.fi/~rg2005/). Participants at that meeting as well as other researchers working in the field are invited to submit a research paper to this issue. The Editorial Board has invited Juha Honkonen, Dmitri Kazakov and Hans Werner Diehl to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: The subject of the paper should relate to the subject of the workshop. Contributions will be refereed and processed according to the usual procedure of the journal. Conference papers may be based on already published work but should eithercontain significant additional new results and/or insights orgive a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems Papers submitted by non-participants should be original and contain substantial new results. The guidelines for the preparation of contributions are as follows: The DEADLINE for submission of contributions is 1 December 2005. This deadline will allow the special issue to appear in June 2006. There is a nominal page limit of 16 printed pages per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. Contributions to the special issue should, if possible, be submitted electronically by web upload at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue—Renormalization Group 2005'. Submissions should ideally be in standard LaTeX form. Please see the web site for further
Renormalization group analysis of the Reynolds stress transport equation
NASA Technical Reports Server (NTRS)
Rubinstein, R.; Barton, J. M.
1992-01-01
The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.
Renormalization group analysis of anisotropic diffusion in turbulent shear flows
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Barton, J. Michael
1991-01-01
The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.
Higher spin Fronsdal equations from the exact renormalization group
NASA Astrophysics Data System (ADS)
Jin, Kewang; Leigh, Robert G.; Parrikar, Onkar
2015-06-01
We show that truncating the exact renormalization group equations of free U( N) vector models in the single-trace sector to the linearized level reproduces the Fronsdal equations on AdS d+1 for all higher spin fields, with the correct boundary conditions. More precisely, we establish canonical equivalence between the linearized RG equations and the familiar local, second order differential equations on AdS d+1, namely the higher spin Fronsdal equations. This result is natural because the second-order bulk equations of motion on AdS simply report the value of the quadratic Casimir of the corresponding conformal modules in the CFT. We thus see that the bulk Hamiltonian dynamics given by the boundary exact RG is in a different but equivalent canonical frame than that which is most natural from the bulk point of view.
The numerical renormalization group and multi-orbital impurity models
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas; Stadler, K. M.; von Delft, J.; Yin, Z. P.; Kotliar, G.; Mitchell, Andrew
The numerical renormalization group (NRG) is a highly versatile and accurate method for the simulation of (effective) fermionic impurity models. Despite that the cost of NRG is exponential in the number of orbitals, by now, symmetric three-band calculations have become available on a routine level. Here we present a recent detailed study on the spin-orbital separation in a three-band Hund metal with relevance for iron-pnictides via the dynamical mean field theory (DMFT). In cases, finally, where the orbital symmetry is broken, we demonstrate that interleaved NRG still offers an accurate alternative approach within the NRG with dramatically improved numerical efficiency at comparable accuracy relative to conventional NRG.
More on the infrared renormalization group limit cycle in QCD
E. Epelbaum; H.-W. Hammer; Ulf-G. Meissner; A. Nogga
2006-10-01
We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.
Magnus expansion and in-medium similarity renormalization group
NASA Astrophysics Data System (ADS)
Morris, T. D.; Parzuchowski, N. M.; Bogner, S. K.
2015-09-01
We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-Hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and 16O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.
Natural orbitals renormalization group approach to the two-impurity Kondo critical point
NASA Astrophysics Data System (ADS)
He, Rong-Qiang; Dai, Jianhui; Lu, Zhong-Yi
2015-04-01
The problem of two magnetic impurities in a normal metal exposes the two opposite tendencies in the formation of a singlet ground state, driven respectively by the single-ion Kondo effect with conduction electrons to screen impurity spins or the Ruderman-Kittel-Kasuya-Yosida interaction between the two impurities to directly form impurity spin singlet. However, whether the competition between these two tendencies can lead to a quantum critical point has been debated over more than two decades. Here, we study this problem by applying the newly proposed natural orbitals renormalization group method to a lattice version of the two-impurity Kondo model with a direct exchange K between the two impurity spins. The method allows for unbiased access to the ground state wave functions and low-lying excitations for sufficiently large system sizes. We demonstrate the existence of a quantum critical point, characterized by the power-law divergence of impurity staggered susceptibility with critical exponent γ =0.60 (1 ) , on the antiferromagnetic side of K when the interimpurity distance R is even lattice spacing, while a crossover behavior is recovered when R is odd lattice spacing. These results have ultimately resolved the long-standing discrepancy between the numerical renormalization group and quantum Monte Carlo studies, confirming a link of this two-impurity Kondo critical point to a hidden particle-hole symmetry predicted by the local Fermi liquid theory.
Renormalization group improved Yennie-Frautschi-Suura theory for Z/sup 0/ physics
Ward, B.F.L.
1987-06-01
Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z/sup 0/ physics at the SLC and LEP.
Renormalization-group methods for the spectra of disordered chains
NASA Astrophysics Data System (ADS)
Robbins, Mark O.; Koiller, Belita
1983-06-01
A family of real-space renormalization techniques for calculating the Green's functions of disordered chains is developed and explored. The techniques are based on a recently proposed renormalization method which is rederived here and shown to be equivalent to a virtual-crystal approximation on a renormalized Hamiltonian. The derivation suggests how other conventional alloy methods can be coupled to the renormalization concept. Various examples are discussed. Short-range order in the occupation of alloy sites and very general disorder in the Hamiltonian-diagonal, off-diagonal, and environmental-are readily incorporated. The techniques are exact in the limits of high and low concentration and of complete short-range order and for the Lloyd model. All states are found to be localized, in agreement with exact treatments. Results for the alloy density of states are presented for various cases and compared to numerical simulations on long chains (105 atoms).
Phase transitions in two dimensions and multiloop renormalization group expansions
NASA Astrophysics Data System (ADS)
Sokolov, A. I.
2013-07-01
We discuss using the field theory renormalization group (RG) to study the critical behavior of twodimensional (2D) models. We write the RG functions of the 2D λϕ 4 Euclidean n-vector theory up to five-loop terms, give numerical estimates obtained from these series by Padé-Borel-Leroy resummation, and compare them with their exact counterparts known for n = 1, 0,-1. From the RG series, we then derive pseudo-ɛ-expansions for the Wilson fixed point location g*, critical exponents, and the universal ratio R 6 = g 6 / g 2 , where g 6 is the effective sextic coupling constant. We show that the obtained expansions are "friendler" than the original RG series: the higher-order coefficients of the pseudo-ɛ-expansions for g*, R6, and γ -1 turn out to be considerably smaller than their RG analogues. This allows resumming the pseudo-ɛ-expansions using simple Padé approximants without the Borel-Leroy transformation. Moreover, we find that the numerical estimates obtained using the pseudo-ɛ-expansions for g* and γ -1 are closer to the known exact values than those obtained from the five-loop RG series using the Padé-Borel-Leroy resummation.
Renormalization group studies of many-body localization
NASA Astrophysics Data System (ADS)
Altman, Ehud
2015-03-01
Quantum correlations do not usually persist for long in systems at finite energy density and disappear once the system thermalizes. But many-body localization offers an alternative paradigm, whereby quantum matter can evade the usual fate of thermal equilibrium and retain retrievable quantum correlations even at high energies. I will survey a dynamical renormalization group (RG) approach used to characterize the novel dynamics and entanglement structures, which develop in the localized phase in lieu of classical thermalization. Then I will present a theory of the transition between the ergodic and the many-body localized phase based on a novel RG framework. Here eigenstate entanglement entropy emerges as a natural scaling variable; the RG describes a change from area-law to volume law entanglement through an intriguing critical point, where the distribution of entanglement entropy becomes maximally broad. The ergodic phase established near the critical point is a Griffiths phase, which exhibits sub-diffusive energy transport and sub-ballistic entanglement propagation. The anomalous diffusion exponent vanishes continuously at the critical point. Before closing I will discuss recent progress in confronting the emerging theoretical understanding of many-body localization with experimental tests. This research is supported in part by the ERC synergy grant UQUAM.
Bimetric renormalization group flows in quantum Einstein gravity
Manrique, Elisa; Reuter, Martin; Saueressig, Frank
2011-02-15
Research Highlights: > Gravitational Effective Action in the bimetric truncation. > First study of the full gravitational flow with a bimetric structure. > The non-trivial gravitational RG fixed point persists under bimetric truncations. > Second non-trivial fixed point emerges, which may control the IR behavior of the theory. - Abstract: The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of 'background independence' is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory's IR behavior.
Renormalization group evolution of the universal theories EFT
NASA Astrophysics Data System (ADS)
Wells, James D.; Zhang, Zhengkang
2016-06-01
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.
Functional renormalization group - a new approach to frustrated quantum magnetism
NASA Astrophysics Data System (ADS)
Reuther, Johannes
The experimental and theoretical investigation of quantum spin systems has become one of the central disciplines of contemporary condensed matter physics. From an experimental viewpoint, the field has been significantly fueled by the recent synthesis of novel strongly correlated materials with exotic magnetic or quantum paramagnetic ground states. From a theoretical perspective, however, the numerical treatment of realistic models for quantum magnetism in two and three spatial dimensions still constitutes a serious challenge. This particularly applies to frustrated systems, which complicate the employment of established methods. This talk intends to propagate the pseudofermion functional renormalization group (PFFRG) as a novel approach to determine large size ground state correlations of a wide class of spin Hamiltonians. Using a diagrammatic pseudofermion representation for quantum spin models, the PFFRG performs systematic summations in all two-particle fermionic interaction channels, capturing the correct balance between classical magnetic ordering and quantum fluctuations. Numerical results for various frustrated spin models on different 2D and 3D lattices are reviewed, and benchmarked against other methods if available.
Constraints on supersymmetric soft phases from renormalization group relations
Garisto, R.; Wells, J.D.
1997-02-01
By using relations derived from renormalization group equations (RGEs), we find that strong indirect constraints can be placed on the top squark mixing phase in A{sub t} from the electric dipole moment of the neutron (d{sub n}). Since m{sub t} is large, any GUT-scale phase in A{sub t} feeds into other weak scale phases through RGEs, which in turn contribute to d{sub n}. Thus CP-violating effects due to a weak-scale A{sub t} are strongly constrained. We find that {vert_bar}ImA{sub t}{sup EW}{vert_bar} must be smaller than or of order {vert_bar}ImB{sup EW}{vert_bar}, making the electric dipole moment of the top quark unobservably small in most models. Quantitative estimates of the contributions to d{sub n} from A{sub u}, A{sub d}, and B show that substantial fine-tuning is still required to satisfy the experimental bound on d{sub n}. While the low energy phases of the A{close_quote}s are not as strongly constrained as the phase of B{sup EW}, we note that the phase of a universal A{sup GUT} induces large contributions in the phase of B{sup EW} through RGEs, and is thus still strongly constrained in most models with squark masses below a TeV. {copyright} {ital 1997} {ital The American Physical Society}
Exploration of similarity renormalization group generators in 1-dimensional potentials
NASA Astrophysics Data System (ADS)
Heinz, Matthias
2015-10-01
The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. It includes a matrix called the generator that defines how the transformation will change the Hamiltonian. The commonly used SRG generators evolve the Hamiltonian into a band-diagonal shape. Evolving potentials using SRG induces many-body forces. If these forces are truncated at the N-body level, this systematically introduces errors from omitted (N+1)-body forces when modeling many-body systems. While established generators are fairly successful, alternative generators may converge faster, be faster to calculate, or lead to smaller many-body forces. In particular, recent findings suggest that a block diagonal generator may induce smaller many-body forces. We use 1-dimensional systems of two, three, and four bosons as a theoretical laboratory for studying how these alternative generators perform, and to observe how they induce many-body forces.
Interleaved numerical renormalization group as an efficient multiband impurity solver
NASA Astrophysics Data System (ADS)
Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.
2016-06-01
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.
Improved renormalization group theory for critical asymmetry of fluids
NASA Astrophysics Data System (ADS)
Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun
2013-09-01
We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.
Renormalization group theory for Kondo breakdown in Kondo lattice systems
NASA Astrophysics Data System (ADS)
Ballmann, K.; Nejati, A.; Kroha, J.
2015-03-01
We present a renormalization group (RG) theory for the breakdown of Kondo screening in the Kondo lattice model (KLM) without pre-assumptions about the competition between Kondo effect and magnetic ordering or Fermi surface criticality. We show that the vertex between a single, local Kondo spin and the extended conduction electrons obtains RKKY- induced, non-local contributions in the in-and out-going coordinates of scattering electrons due to scattering at surrounding Kondo sites, but it remains local in the Kondo spin position. This enables the existence of a local Kondo screening scale TK(y) in the KLM, controlled by the effective RKKY coupling parameter y. TK(y) is determined by the RG flow of the local spin exchange coupling in the presence of the self-consistent spin response on surrounding Kondo sites. We show that TK(y) exhibits universal behavior and is suppressed by the antiferromagnetic RKKY coupling. Beyond a maximal RKKY parameter value ymax Kondo screening ceases to exist even without magnetic ordering. The theory opens up the possibility of describing quantum critical scenarios involving spin wave instabilities or local Kondo breakdown on the same footing.
Functional renormalization group analysis of tensorial group field theories on Rd
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele
2016-07-01
Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.
Renormalization Group Theory Technique and Subgrid Scale Closure for Fluid and Plasma Turbulence.
NASA Astrophysics Data System (ADS)
Zhou, Ye.
Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the epsilon - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite epsilon , but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
Tensor renormalization group methods for spin and gauge models
NASA Astrophysics Data System (ADS)
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.
On higher order geometric and renormalization group flows
NASA Astrophysics Data System (ADS)
Prabhu, Kartik; Das, Sanjit; Kar, Sayan
2011-10-01
Renormalization group (RG) flows of the bosonic nonlinear σ-model are governed, perturbatively, at different orders of α', by perturbatively evaluated β-functions. In regions where {α'}/{Rc2}≪1 ( {1}/{Rc2} represents the curvature scale), the flow equations at various orders in α' can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S2, H2, unwarped S2×H2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.
Renormalization group constructions of topological quantum liquids and beyond
NASA Astrophysics Data System (ADS)
Swingle, Brian; McGreevy, John
2016-01-01
We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective. We report four main results. First, we argue for the "weak area law": any gapped phase with a unique ground state on every closed manifold obeys the area law. Second, we introduce an RG based classification scheme and give a detailed argument that all phases within the classification scheme obey the area law. Third, we define a special subclass of gapped phases, topological quantum liquids, which captures all examples of current physical relevance, and we rigorously show that topological quantum liquids obey an area law. Fourth, we show that all topological quantum liquids have MERA representations which achieve unit overlap with the ground state in the thermodynamic limit and which have a bond dimension scaling with system size L as ec logd(1+δ )(L ) for all δ >0 . For example, we show that chiral phases in d =2 dimensions have an approximate MERA with bond dimension ec log2(1+δ )(L ). We discuss extensively a number of subsidiary ideas and results necessary to make the main arguments, including field theory constructions. While our argument for the general area law rests on physically motivated assumptions (which we make explicit) and is therefore not rigorous, we may conclude that "conventional" gapped phases obey the area law and that any gapped phase which violates the area law must be a dragon.
A Renormalization-Group Approach of the Up-Scaling Problem of Flow in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
noetinger, B.
2001-12-01
Powerful methods coming from statistical physics are becoming increasingly popular to get a faithful theoretical description of flow and transport in heterogeneous aquifers that are described by mean of geostatistics. However,in current practice people still use Monte Carlo simulations that are well suited to account for complex boundaries and flow patterns. Here, we present an approach intending to up-scale directly the geostatistical description rather than realization by realization as usual. It is based upon a renormalization group analysis close in spirit with previous works and P King and Jaekel and Vereecken. Using a so called "weak approximation"(Neuman and Orr) , we obtain differential equations driving the permeability variogram parameters as a function of the wave-vector cut-off smoothing the permeability maps. At the end of the process, in the isotropic case, the Landau Lifshitz Matheron conjecture is recovered. This conjecture appears thus as being a consequence of both renormalization approach and the weak approximation. The approach is currently being generalized to anisotropic media. These results can be used to perform cheaper Monte Carlo simulations at a coarser scale. P. King, The Use of Field Theoretic Methods for the Study of Flow in Heterogeneous Porous Medium", J. Phys. A.: Math. Gen. 20, pp3935-3947,1987 U. Jaekel and H. Vereecken, Renormalization Group Analysis of Macrodispersion in a Directed Random Flow, Water Resources Research,33,10,pp 2287-2299, 1997 Neuman, S.P. and Orr, S. "Prediction of Steady State Flow in Nonuniform Geologic Media by Conditional Moments: Exact non local Formalism, Effective Conductivities and Weak Approximation", Water Resources Research 29 (2)341-364 (1993) Noetinger, B. Computing the Effective Permeability of log-normal permeability fields using renormalization methods. C.R . Acad. Des Sciences,Sciences de la Terre et des Planètes, 331 353-357 (2000)
Renormalization group and phase transitions in spin, gauge, and QCD like theories
NASA Astrophysics Data System (ADS)
Liu, Yuzhi
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare
Renormalization-group theory for Alfvén-wave turbulence
NASA Astrophysics Data System (ADS)
Zhou, Ye; Vahala, George
1988-06-01
є-Expansion renormalization-group theory is applied to a model Alfvén-wave turbulence equation. In particular, the effect of small ‘unresolvable’ subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function v. The Lorenzian wavenumber spectrum of Chen & Mahajan can be recovered for finite є, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher-order nonlinearities introduced by the renormalization-group procedure.
NASA Astrophysics Data System (ADS)
Yang, Chun; Feiguin, Adrian E.
2016-02-01
We study the spectral function of the two-dimensional Hubbard model using cluster perturbation theory, and a density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at and away from half-filling using 2 ×L ladders, with L up to 80 sites, yielding results with unprecedented resolution in excellent agreement with quantum Monte Carlo. The main features of the spectrum can be described with a mean-field dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom.
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
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. PMID:23005533
NASA Astrophysics Data System (ADS)
Benedetti, Dario; Lahoche, Vincent
2016-05-01
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of a just renormalizable model over U{(1)}\\otimes 6, with quartic interactions. The method allows us to obtain a closed but non-autonomous system of differential equations which describe the renormalization group flow of the couplings beyond perturbation theory. The explicit dependence of the beta functions on the running scale is due to the existence of an external scale in the model, the radius of {S}1≃ U(1). We study the occurrence of fixed points and their critical properties in two different approximate regimes, corresponding to the deep UV and deep IR. Besides confirming the asymptotic freedom of the model, we find also a non-trivial fixed point, with one relevant direction. Our results are qualitatively similar to those found previously for a rank-3 model without closure constraint, and it is thus tempting to speculate that the presence of a Wilson-Fisher-like fixed point is a general feature of asymptotically free tensorial group field theories.
Noncompact lattice QED with two charges: Phase diagram and renormalization group flow
Ali Khan, A.
1996-06-01
The phase diagram of noncompact lattice QED in four dimensions with staggered fermions of charges 1 and {minus}1/2 is investigated. The renormalized charges are determined and found to be in agreement with perturbation theory. This is an indication that there is no continuum limit with nonvanishing renormalized gauge coupling, and that the theory has a validity bound for every finite value of the renormalized coupling. The renormalization group flow of the charges is investigated and an estimate for the validity bound as a function of the cutoff is obtained. Generalizing this estimate to all fermions in the standard model, it is found that a cutoff at the Planck scale implies that {alpha}{sub {ital R}} has to be less than 1/80. Because of spontaneous chiral symmetry breaking, strongly bound fermion-antifermion composite states are generated. Their spectrum is discussed. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel
2013-08-01
We determine the strong coupling constant αs from the τ hadronic width using a renormalization group summed (RGS) expansion of the QCD Adler function. The main theoretical uncertainty in the extraction of αs is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard CIPT expansion. The value of the strong coupling in /lineMS scheme obtained with the RGS expansion is α s(M_τ 2) = 0.338 ± 0.010. The convergence properties of the new expansion can be improved by Borel transformation and analytic continuation in the Borel plane. This is discussed elsewhere in these issues.
a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.
NASA Astrophysics Data System (ADS)
Cowan, Mark Timothy
The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.
Renormalization group flow of entanglement entropy on spheres
NASA Astrophysics Data System (ADS)
Ben-Ami, Omer; Carmi, Dean; Smolkin, Michael
2015-08-01
We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2 ,3 ,4. Inthreedimensionswefindthatwhiletherenormalizedentanglemententropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.
Block-diagonal similarity renormalization group and effective nucleon-nucleon interactions
NASA Astrophysics Data System (ADS)
Szpigel, S.; Timóteo, V. S.; Ruiz Arriola, E.
2016-04-01
We apply the block-diagonal similarity renormalization group to a simple toy-model for the nucleon-nucleon (NN) interaction in the 1 S 0 channel, aiming to analyze the complementarity between the explicit and the implicit renormalization approaches in nuclear physics. By explicit renormalization we mean the methods based on the wilsonian renormalization group in which high-energy modes above a given cutoff scale are integrated out while their effects are replaced by scale dependent effective interactions consistently generated in the process. We call implicit renormalization the usual procedure of cutoff effective theories in which the high-energy modes above the cutoff scale are simply removed and their effects are included through parametrized cutoff dependent counterterms whose strengths are fixed by fitting low-energy data. We compare the effective interactions obtained in both schemes and find a wide range of cutoff scales where they overlap. We further analyze the role played by the one-pion exchange (OPE) considering a δ-shell plus OPE representation for the NN interaction.
NASA Astrophysics Data System (ADS)
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms. PMID:27394094
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George
1993-01-01
The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.
Hamza, A.M.; Sudan, R.N.
1995-03-01
The equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the ExB or gradient-drift instability were derived by Sudan and Keskinen for addressing the electrostatic turbulence in the E and F regions of the Earth`s ionosphere. The authors have developed a subgrid model suitable for the numerical simulation of these equations which is closely related to renormalized diffusion caused by small-scale fluctuation spectrum. {open_quotes}Dynamical Renormalization Group{close_quotes} (RNG) methods are employed to obtain the renormalized diffusion. This procedure computes the long-wavelength, long-time behavior of density correlations generated by the evolution equation for the plasma stirred by a Gaussian random force characterized by a correlation function {proportional_to} k{sup m} where k is the wavenumber of the forcing function. The effect of small scales on the large-scale dynamics in the limit k{yields}0 and infinite Reynolds number can be expressed in the form of renormalized coefficients; in this case, renormalized diffusion. If one assumes the power spectra to be given by the Kolmogorov argument of cascading of energy through k space then one can derive a subgrid model based on the results of RNG. 27 refs.
Renormalization group theory of anomalous transport in systems with Hamiltonian chaos.
Zaslavsky, G. M.
1994-03-01
We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the "normal" Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited. PMID:12780083
Renormalization group theory of anomalous transport in systems with Hamiltonian chaos
NASA Astrophysics Data System (ADS)
Zaslavsky, G. M.
1994-03-01
We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the ``normal'' Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited.
Kolmogorov-Arnold-Moser-Renormalization-Group Analysis of Stability in Hamiltonian Flows
NASA Astrophysics Data System (ADS)
Govin, M.; Chandre, C.; Jauslin, H. R.
1997-11-01
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
Momentum subtraction scheme renormalization group functions in the maximal Abelian gauge
NASA Astrophysics Data System (ADS)
Bell, J. M.; Gracey, J. A.
2013-10-01
The one-loop 3-point vertex functions of QCD in the maximal Abelian gauge are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum subtraction schemes, which are defined by the trivalent vertices, as well as in the MS¯ scheme. From these the two-loop renormalization group functions in the momentum schemes are derived using the one-loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge, which corresponds to the maximal Abelian gauge in a specific limit. The relation between the Λ parameters in different schemes is also provided.
Nonperturbative renormalization group approach for a scalar theory in higher-derivative gravity
Bonanno, A.; Zappala, D.
1997-05-01
A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of nonperturbative flow equations governing the evolution of the new interaction terms generated in both local potential and wave function renormalization is derived. It is shown for a specific model that these new terms play an important role in determining the scaling behavior of the system above the mass of the inflaton field. {copyright} {ital 1997} {ital The American Physical Society}
The One and Two Loops Renormalization Group Equations in the Standard Model
Juarez W, S. Rebeca; Solis R, H. Gabriel; Kielanowski, P.
2006-01-06
In the context of the Standard Model (SM), we compare the analytical and the numerical solutions of the Renormalization Group Equations (RGE) for the relevant couplings to one and two loops. This information will be an important ingredient for the precise evaluation of boundary values on the physical Higgs Mass.
Intuitive understanding of T → 0 behavior of 2d spin glasses via renormalization group analysis
NASA Astrophysics Data System (ADS)
Hartmann, A. K.
2012-07-01
Commentary on 'The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: entropy, universality, chaos and cascades in the renormalization group flow', by Thomas Jörg and Florent Krzakala, 2012 J. Stat. Mech. L01001.
Global solutions to two nonlinear perturbed equations by renormalization group method
NASA Astrophysics Data System (ADS)
Kai, Yue
2016-02-01
In this paper, according to the theory of envelope, the renormalization group (RG) method is applied to obtain the global approximate solutions to perturbed Burger's equation and perturbed KdV equation. The results show that the RG method is simple and powerful for finding global approximate solutions to nonlinear perturbed partial differential equations arising in mathematical physics.
Hedegård, Erik Donovan Knecht, Stefan; Reiher, Markus; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Kholodenko, A. L.; Freed, Karl F.
1983-06-01
The chain conformation space renormalization group method is transformed into a representation where the t'Hooft-Veltman method of dimensional regularization can directly be applied to problems involving polymer excluded volume. This t'Hooft-Veltman-type representation enables a comparison to be made with other direct renormalization methods for polymer excluded volume. In contrast to the latter, the current method and the chain conformation one from which it is derived are not restricted to the asymptotic limit of very long chains and do not require the cumbersome use of insertions to calculate the relevant exponents. Furthermore, the theory emerges directly in polymer language from the traditional excluded volume perturbation expansion which provides the correct weight factors for the diagrams. Special attention is paid to the general diagrammatic structure of the theory and to the renormalization prescription in order that this prescription follows from considerations on measurable quantities. The theory is illustrated by calculation of the mean square end-to-end distance and second virial coefficient to second order including the full crossover dependence on the renormalized strength of the excluded volume interaction and on the chain length. A subsequent paper provides the generalization of the theory to the treatment of excluded volume effects in polyelectrolytes.
NASA Astrophysics Data System (ADS)
Giuliano, Domenico; Nava, Andrea
2015-09-01
Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within the bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Karrasch, C.; Moore, J. E.
2015-09-01
We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over 104 samples for lattices as large as 105 sites. We identify regimes in which non-Ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In the presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.
Flow equation of functional renormalization group for three-body scattering problems
NASA Astrophysics Data System (ADS)
Tanizaki, Yuya
2013-11-01
Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish an exact flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.
Renormalization group flow of quartic perturbations in graphene: Strong coupling and large- N limits
NASA Astrophysics Data System (ADS)
Drut, Joaquín E.; Son, Dam Thanh
2008-02-01
We explore the renormalization group flow of quartic perturbations in the low-enegy theory of graphene, in the strong Coulomb coupling and large- N limits, where N is the number of fermion flavors. We compute the anomalous dimensions of the quartic couplings u up to leading order in 1/N and find both relevant and irrelevant directions in the space of quartic couplings. We discuss possible phase diagrams and relevance for the physics of graphene.
RGIsearch: A C++ program for the determination of renormalization group invariants
NASA Astrophysics Data System (ADS)
Verheyen, Rob
2016-05-01
RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the β-functions of quantum field theories, RGIsearch searches for several types of invariants that require different methods. Additionally, it supports the computation of invariants up to two-loop level. A manual for the program is given, including the settings and set-up of the program, as well as a test case.
The Magnus expansion and the in-medium similarity renormalization group
Morris, T. D.; Bogner, S. K.
2014-10-15
We present a variant of the in-medium similarity renormalization group(IMSRG) based on the Magnus expansion. In this new variant, the unitary transformation of the IMSRG is constructed explicitly, which allows for the transformation of observables quickly and easily. Additionally, the stiffness of equations encountered by the traditional solution of the IMSRG can be alleviated greatly. We present results and comparisons for the 3d electron gas.
Renormalization group analysis of thermal transport in the disordered Fermi liquid
NASA Astrophysics Data System (ADS)
Schwiete, G.; Finkel'stein, A. M.
2014-10-01
We present a detailed study of thermal transport in the disordered Fermi liquid with short-range interactions. At temperatures smaller than the impurity scattering rate, i.e., in the diffusive regime, thermal conductivity acquires nonanalytic quantum corrections. When these quantum corrections become large at low temperatures, the calculation of thermal conductivity demands a theoretical approach that treats disorder and interactions on an equal footing. In this paper, we develop such an approach by merging Luttinger's idea of using gravitational potentials for the analysis of thermal phenomena with a renormalization group calculation based on the Keldysh nonlinear sigma model. The gravitational potentials are introduced in the action as auxiliary sources that couple to the heat density. These sources are a convenient tool for generating expressions for the heat density and its correlation function from the partition function. Already in the absence of the gravitational potentials, the nonlinear sigma model contains several temperature-dependent renormalization group charges. When the gravitational potentials are introduced into the model, they acquire an independent renormalization group flow. We show that this flow preserves the phenomenological form of the correlation function, reflecting its relation to the specific heat and the constraints imposed by energy conservation. The main result of our analysis is that the Wiedemann-Franz law holds down to the lowest temperatures even in the presence of disorder and interactions and despite the quantum corrections that arise for both the electric and thermal conductivities.
Renormalization group analysis of ultracold Fermi gases with two-body attractive interaction
NASA Astrophysics Data System (ADS)
Guo, Xiaoyong; Chi, Zimeng; Zheng, Qiang; Wang, Zaijun
2016-01-01
We propose a new functional renormalization group (RG) strategy to investigate the many-body physics of interacting ultracold Fermi gases. By mapping the Ginzburg-Landau (GL) action of Fermi gases onto a complex φ4-model, we can obtain the closed flow equation in the one-loop approximation. An analysis of the emerging RG flow gives the ground state behavior. The Hamiltonian of a Fermi gas with a two-body attractive interaction is used as a demonstration to clarify our treatment. The fixed point structure reveals not only the condensation phase transition, but also the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. The effect of the imaginary time renormalization is also discussed. It is shown that for the dynamical field configuration our RG procedure can reproduce the well known theoretical results of BCS-BEC crossover, while under a static approximation the phase transition takes place at a higher critical temperature.
Gauge invariant composite operators of QED in the exact renormalization group formalism
NASA Astrophysics Data System (ADS)
Sonoda, H.
2014-01-01
Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ‘gauge fixing parameter independence,’ we show that any gauge independent composite operators can be made ‘gauge fixing parameter independent’ by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A Zee.
NASA Astrophysics Data System (ADS)
Bauer, Carsten; Rückriegel, Andreas; Sharma, Anand; Kopietz, Peter
2015-09-01
Using a nonperturbative functional renormalization group approach, we calculate the renormalized quasiparticle velocity v (k ) and the static dielectric function ɛ (k ) of suspended graphene as functions of an external momentum k . Our numerical result for v (k ) can be fitted by v (k ) /vF=A +B ln(Λ0/k ) , where vF is the bare Fermi velocity, Λ0 is an ultraviolet cutoff, and A =1.37 , B =0.51 for the physically relevant value (e2/vF=2.2 ) of the coupling constant. In contrast to calculations based on the static random-phase approximation, we find that ɛ (k ) approaches unity for k →0 . Our result for v (k ) agrees very well with a recent measurement by Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].
NASA Astrophysics Data System (ADS)
Kemper, A.; Schadschneider, A.; Zittartz, J.
2001-05-01
We apply the transfer-matrix density-matrix renormalization group (TMRG) to a stochastic model, the Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase transition in the directed percolation universality class. Estimates for the stochastic time evolution, phase boundaries and critical exponents can be obtained with high precision. This is possible using only modest numerical effort since the thermodynamic limit can be taken analytically in our approach. We also point out further advantages of the TMRG over other numerical approaches, such as classical DMRG or Monte Carlo simulations.
Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Huber, Markus Q.; Braun, Jens
2012-06-01
We present the Mathematica application DoFun which allows to derive Dyson-Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross-Neveu model. Program summaryProgram title:DoFun Catalogue identifier: AELN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELN_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.: 35 506 No. of bytes in distributed program, including test data, etc.: 571 837 Distribution format: tar.gz Programming language: Mathematica 7 and higher Computer: PCs and workstations Operating system: All on which Mathematica is available (Windows, Unix, MacOS) Classification: 11.1, 11.4, 11.5, 11.6 Nature of problem: Derivation of functional renormalization group equations and Dyson-Schwinger equations from the action of a given theory. Solution method: Implementation of an algorithm to derive functional renormalization group and Dyson-Schwinger equations. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. The output is compatible with the syntax of many other programs and is therefore suitable for further (algebraic) computations. Running time: Seconds to minutes
Application of the renormalization group to the decay of the false vacuum
NASA Astrophysics Data System (ADS)
Al-Kuwari, Hemyan A.; Taha, M. O.
1992-04-01
A renormalization group equation for the effective action of a massive scalar field theory is derived. It significantly restricts the dependence of the probability of the decay of the false vacuum on the physical parameters. It is also remarkably useful for the implementation of a certain approximation of finite-temperature effects. Within this approximation one finds mt ~ 165 GeV if SU(2) × U(1) is broken by barrier penetration and the transition occurs when the probability is maxiumum On leave of absence from Department of Physics, Faculty of Science, King Saud University, Riyadh, Saudi Arabia.
The Renormalization Group Running of the Higgs Quartic Coupling: Unification vs. Phenomenology
Montes de Oca Y, J. H.; Juarez W, S. R.; Kielanowski, P.
2007-02-09
Within the framework of the standard model (SM) of elementary particles, we obtained numerical solutions for the running Higgs mass, considering the renormalization group equations at the one and two loop approximation. Through the triviality condition (TC) and stability condition (SC) on the Higgs quartic coupling {lambda}H the bounds on the Higgs running mass have been fixed. The numerical results are presented for two special cases. One considering an unification of the three gauge couplings at the energy EU 1013 GeV and the other using the current experimental data for the gauge couplings.
NASA Astrophysics Data System (ADS)
Huitu, Katri; Pandita, P. N.; Tiitola, Paavo
2015-10-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.
NASA Astrophysics Data System (ADS)
Morris, Titus; Bogner, Scott
2015-10-01
The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully not only to several closed shell finite nuclei, but has recently been used to produce effective shell model interactions that are competitive with phenomenological interactions in the SD shell. A recent alternative method for solving of the IM-SRG equations, called 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.
Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation
Enberg, Rikard
2006-12-01
I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.
Real space renormalization group and totalitarian paradox of majority rule voting
NASA Astrophysics Data System (ADS)
Galam, Serge
2000-09-01
The effect of majority rule voting in hierarchical structures is studied using the basic concepts from real space renormalization group. It shows in particular that a huge majority can be self-eliminated while climbing up the hierarchy levels. This majority democratic self-elimination articulates around the existence of fixed points in the voting flow. An unstable fixed point determines the critical threshold to full and total power. It can be varied from 50% up to 77% of initial support. Our model could shed new light on the last century eastern European communist collapse.
Finite-scale singularity in the renormalization group flow of a reaction-diffusion system.
Gredat, Damien; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan
2014-01-01
We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a different (conjugated) universality class. PMID:24580152
Spectral renormalization group for the Gaussian model and ψ4 theory on nonspatial networks
NASA Astrophysics Data System (ADS)
Tuncer, Aslı; Erzan, Ayşe
2015-08-01
We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, d ˜. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At d ˜=2 , the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a ψ4 perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2
Functional renormalization group study of an 8-band model for the iron arsenides
NASA Astrophysics Data System (ADS)
Honerkamp, Carsten; Lichtenstein, Julian; Maier, Stefan A.; Platt, Christian; Thomale, Ronny; Andersen, Ole Krogh; Boeri, Lilia
2014-03-01
We investigate the superconducting pairing instabilities of eight-band models for 1111 iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.
Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group
NASA Astrophysics Data System (ADS)
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
We study the disordered XYZ spin chain using the recently developed Spectrum Bifurcation Renormalization Group (SBRG) numerical method. With large disorder, the phase diagram of the eigenstates consists of three many body localized (MBL) spin glass phases separated by marginal MBL critical phases. We examine the critical phases of this model by probing the entanglement entropy and Edwards-Anderson spin glass order parameter. We also show how long-range mutual information can be used to distinguish these phases (Jian, Kim, Qi 2015).
NASA Astrophysics Data System (ADS)
Kaushal, Nitin; Liu, Guangkun; Bishop, Chris; Liang, Shuhua; Li, Shaozhi; Johnston, Steve; Dagotto, Elbio
Using the Density Matrix Renormalization Group technique, we extensively study a three-orbital Hubbard model in one dimension without pair hopping and spin-flip Hund interactions. The phase diagram varying the electronic density n and Hubbard U is constructed and compared against previous results obtained using the full interaction Hamiltonian. Our results suggest that spin-flip and pair hopping terms are not crucially important to address the orbital-selective Mott phase. This analysis paves the way to study multiorbital Hubbard models using techniques such as the Constrained-Path Quantum Monte Carlo (CPQMC) and Determinant Quantum Monte Carlo (DQMC) methods since they perform better, reducing for instance the severity of the ``sign problem'', in the absence of pair hopping and spin flip terms in the interaction.
NASA Astrophysics Data System (ADS)
O'Malley, Daniel; Cushman, John H.
2012-03-01
Anomalous diffusion processes are often classified by their mean square displacement. If the mean square displacement grows linearly in time, the process is considered classical. If it grows like t β with β<1 or β>1, the process is considered subdiffusive or superdiffusive, respectively. Processes with infinite mean square displacement are considered superdiffusive. We begin by examining the ways in which power-law mean square displacements can arise; namely via non-zero drift, nonstationary increments, and correlated increments. Subsequently, we describe examples which illustrate that the above classification scheme does not work well when nonstationary increments are present. Finally, we introduce an alternative classification scheme based on renormalization groups. This scheme classifies processes with stationary increments such as Brownian motion and fractional Brownian motion in the same groups as the mean square displacement scheme, but does a better job of classifying processes with nonstationary increments and/or processes with infinite second moments such as α-stable Lévy motion. A numerical approach to analyzing data based on the renormalization group classification is also presented.
NASA Astrophysics Data System (ADS)
Pfeuty, Pierre M.; Wheeler, John C.
1983-04-01
Equilibrium polymerization is very different in one dimension than in higher dimensionality. The transition that occurs in the limit of vanishing initiation equilibrium constant (which is a critical point in higher dimensionality) becomes a first-order transition at non-vanishing temperature in one dimension. A simple model of equilibrium polymerization that has been discussed recently for higher dimensionality is solved exactly by the transfer-matrix method in one dimension. The equivalent n-->0 vector model of magnetism is also solved exactly for all fields and temperatures by transfer-matrix methods and is analyzed by an exact renormalization-group transformation. The renormalization-group analysis contains several interesting features including the fact that the parameter space of the Hamiltonian must be enlarged to six dimensions, yet remains finite. The connection of the model and transition treated here with the Zimm-Bragg model of the helix-coil transition and with the one-dimensional Ising model of magnetism is discussed.
NASA Astrophysics Data System (ADS)
Luo, Shu
2012-01-01
Enlightened by the idea of the 3×3 Cabibbo-Kobayashi-Maskawa angle matrix proposed recently by Harrison , we introduce the Dirac angle matrix Φ and the Majorana angle matrix Ψ in the lepton sector for Dirac and Majorana neutrinos, respectively. We show that in the presence of CP violation, the angle matrix Φ or Ψ is entirely equivalent to the complex Maki-Nakagawa-Sakata matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles and do not depend on any particular parametrization of V. In this paper, we further analyzed how the angle matrices evolve with the energy scale. The one-loop renormalization group equations of Φ, Ψ and some other rephasing invariant parameters are derived and a numerical analysis is performed to compare between the case of Dirac and Majorana neutrinos. Different neutrino mass spectra are taken into account in our calculation. We find that apparently different from the case of Dirac neutrinos, for Majorana neutrinos the renormalization group equation evolutions of Φ, Ψ and J strongly depend on the Majorana-type CP-violating parameters and are more sensitive to the sign of Δm312. They may receive significant radiative corrections in the minimal supersymmetric standard model with large tanβ if three neutrino masses are nearly degenerate.
Renormalization group calculation of the universal critical exponents of a polymer molecule
NASA Astrophysics Data System (ADS)
Belohorec, Peter
In this work the excluded volume problem of a linear flexible polymer molecule in a solution was investigated using a new method. The Domb-Joyce (DJ) lattice model (Domb C. and Joyce G. S. (1972). J. Phys. C: Solid State Phys. 5 956) was used to describe the polymer chain with a varying excluded volume parameterramateur w and bond number N. Monte Carlo (MC) generated data for the mean square end-to-end distance Rsbsp{N}{2} and the second virial coefficient Asb{2,N} were analyzed by a renormalization group technique that is a generalization of the one-parameter recursion model (Nickel B. G. (1991). Macromolecules 24, 1358). By defining the effective exponents nusb{R}(N,psi) and nusb{A}(N,psi ) using 2sp{2nusb{R}} = Rsbsp{2N}{2}/Rsbsp{N}{2} and 2sp{3nusb{A}} = Asb{2,2N}/Asb{2,N} where psi = {1/4}({6/pi})sp{3/2}{{Asb{2,N}}/{Rsbsp{N}{3}}} is the interpenetration function, the corrections varying as Nsp{-Delta} were eliminated from nusb{R}(N,psi) and nusb{A}(N,psi) and both universal critical exponents nu and Delta of the expected long chain behaviors Rsbsp{N}{2}~ asb{R}Nsp{2nu}(1 + bsb{R}Nsp{-Delta} +\\...) and Asb{2,N}~ asb{A}Nsp{3nu}(1 + bsb{A}Nsp{-Delta} +\\...) were determined very accurately. The problems encountered by standard methods when extracting the values of the leading exponent nu and the correction to scaling exponent Delta from the finite chain data were eliminated by the simultaneous use of many models (i.e., w in the range of 0 < omega ≤ 1) and by the use of the effective exponent transformation. Other universal quantities such as the asymptotic value psi* of the interpenetration function proportional to the dimensionless ratio of leading scaling amplitudes asb{A}/asbsp{R}{3/2} as well as the ratio of correction to scaling amplitudes bsb{A}/bsb{R} were also calculated with a very good precision. The results are nu = 0.58756(5),\\ Delta = 0.5310(33), psi* = 0.23221(11) and bsb{A}/bsb{R} = -.0.9028(132). The numerical solution of the DJ model
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem
Grusdt, F.; Shchadilova, Y. E.; Rubtsov, A. N.; Demler, E.
2015-01-01
When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed. PMID:26183614
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem.
Grusdt, F; Shchadilova, Y E; Rubtsov, A N; Demler, E
2015-01-01
When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed. PMID:26183614
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem
NASA Astrophysics Data System (ADS)
Grusdt, F.; Shchadilova, Y. E.; Rubtsov, A. N.; Demler, E.
2015-07-01
When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.
NASA Astrophysics Data System (ADS)
Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Sato, Daisuke
2014-04-01
We analyze dynamical chiral symmetry breaking (Dχ SB) in the Nambu-Jona-Lasinio model by using the non-perturbative renormalization group equation. The equation takes the form of a two-dimensional partial differential equation for the multi-fermion effective interactions V(x,t) where x is the bar {ψ }ψ operator and t is the logarithm of the renormalization scale. The Dχ SB occurs due to the quantum corrections, which means it emerges at some finite tc while integrating the equation with respect to t. At t_c some singularities suddenly appear in V which is compulsory in the spontaneous symmetry breakdown. Therefore there is no solution of the equation beyond tc. We newly introduce the notion of a weak solution to get the global solution including the infrared limit t rArr ∞ and investigate its properties. The obtained weak solution is global and unique, and it perfectly describes the physically correct vacuum even in the case of the first order phase transition appearing in a finite-density medium. The key logic of deduction is that the weak solution we defined automatically convexifies the effective potential when treating the singularities.
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-01
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
Decomposition of density matrix renormalization group states into a Slater determinant basis
NASA Astrophysics Data System (ADS)
Moritz, Gerrit; Reiher, Markus
2007-06-01
The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.
Decomposition of density matrix renormalization group states into a Slater determinant basis.
Moritz, Gerrit; Reiher, Markus
2007-06-28
The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants. PMID:17614539
NASA Astrophysics Data System (ADS)
Apte, Amit Shriram
This thesis presents numerical explorations of area-preserving nontwist maps, and a renormalization group framework for the destruction of invariant tori. We study the phenomena of bifurcation and reconnection, and the emergence of meandering tori which are non-KAM invariant curves. We also study the breakup of shearless invariant tori with noble winding numbers using improved numerical techniques to implement Greene's residue criterion. We interpret the breakup of invariant tori within a renormalization group framework by constructing renormalization group operators for the tori with winding numbers that are quadratic irrationals. We find the simple fixed points of these operators and interpret the map pairs with critical invariant tori as critical fixed points. We introduce coordinate transformations on the space of maps to relate these fixed points to each other. These transformations induce conjugacies between the corresponding operators, and provide a new perspective on the space of area-preserving maps.
NASA Astrophysics Data System (ADS)
Nghiem, H. T. M.; Costi, T. A.
2014-02-01
The time-dependent numerical renormalization group (TDNRG) method [Anders et al., Phys. Rev. Lett. 95, 196801 (2005), 10.1103/PhysRevLett.95.196801] offers the prospect of investigating in a nonperturbative manner the time dependence of local observables of interacting quantum impurity models at all time scales following a quantum quench. Here, we present a generalization of this method to arbitrary finite temperature by making use of the full density matrix approach [Weichselbaum et al., Phys. Rev. Lett. 99, 076402 (2007), 10.1103/PhysRevLett.99.076402]. We show that all terms in the projected full density matrix ρi →f=ρ+++ρ--+ρ+-+ρ-+ appearing in the time evolution of a local observable may be evaluated in closed form at finite temperature, with ρ+-=ρ-+=0. The expression for ρ-- is shown to be finite at finite temperature, becoming negligible only in the limit of vanishing temperatures. We prove that this approach recovers the short-time limit for the expectation value of a local observable exactly at arbitrary temperatures. In contrast, the corresponding long-time limit is recovered exactly only for a continuous bath, i.e., when the logarithmic discretization parameter Λ →1+. Since the numerical renormalization group approach breaks down in this limit, and calculations have to be carried out at Λ >1, the long-time behavior following an arbitrary quantum quench has a finite error, which poses an obstacle for the method, e.g., in its application to the scattering-states numerical renormalization group method for describing steady-state nonequilibrium transport through correlated impurities [Anders, Phys. Rev. Lett. 101, 066804 (2008), 10.1103/PhysRevLett.101.066804]. We suggest a way to overcome this problem by noting that the time dependence, in general, and the long-time limit, in particular, become increasingly more accurate on reducing the size of the quantum quench. This suggests an improved generalized TDNRG approach in which the system is time
Autocorrelations from the transfer-matrix density-matrix renormalization-group method
NASA Astrophysics Data System (ADS)
Naef, F.; Wang, X.; Zotos, X.; von der Linden, W.
1999-07-01
Extending the transfer-matrix density-matrix renormalization-group algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error <10-6) over a wide temperature range (0<βJ<20). After analytic continuation using the rules of probability theory along with the entropic prior (MaxEnt), we obtain real frequency spectra for the XY model, the isotropic Heisenberg, and the gapped Heisenberg-Ising model. Available exact results in some limits allow for a critical evaluation of the quality of answers expected from this procedure. We find that high-precision data are still insufficient for resolving specific line shapes such as low-frequency divergences. However, the method is appropriate for identifying low-temperature gaps and peak positions.
NASA Astrophysics Data System (ADS)
Codello, Alessandro; Tonero, Alberto
2016-07-01
We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2 -scalar theories. The idea is to perform the path integral by weighting the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we are integrating. We show that depending on the initial condition, or initial point in the phase diagram, we obtain different behaviors of the four-point function at the endpoint of the flow.
Kondo effect in the presence of van Hove singularities: A numerical renormalization group study
NASA Astrophysics Data System (ADS)
Zhuravlev, A. K.; Irkhin, V. Yu.
2011-12-01
A numerical renormalization-group investigation of the one-center t-t' Kondo problem is performed for the square lattice accounting for logarithmic Van Hove singularities (VHS) in the electron density of states near the Fermi level. The magnetic susceptibility, entropy, and specific heat are calculated. The temperature dependencies of the thermodynamic properties in the presence of VHS turn out to be nontrivial. When the distance Δ between VHS and the Fermi level decreases, the inverse logarithm of the corresponding Kondo temperature TK demonstrates a crossover from the standard linear to square-root dependence on the s-d exchange coupling. The low-temperature behavior of the magnetic susceptibility and specific heat are investigated, and the Wilson ratio is obtained. For Δ→0 the Fermi-liquid behavior is broken.
NASA Astrophysics Data System (ADS)
Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.
2016-04-01
We have studied a Fermi system with attractive U (r)-symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for r ≥ 4 the RG flux leaves the system's stability region - the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. The result of this analysis shows that for 3D systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism.
NASA Astrophysics Data System (ADS)
Katanin, A.
2013-12-01
We consider an effect of weak impurities on the electronic properties of graphene within the functional renormalization-group approach. The energy dependences of the electronic self-energy and density of states near the neutrality point are discussed. Depending on the symmetry of the impurities, the electronic damping Γ and density of states ρ can deviate substantially from those given by the self-consistent Born approximation. We investigate the crossover from the results of the self-consistent Born approximation, which are valid far from the neutrality point to the strong-coupling (diffusive) regime near the neutrality point. For impurities, which are diagonal in both valley and sublattice indices, we obtain a finite density of states at the Fermi level with values which are much bigger than the result of the self-consistent Born approximation.
Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene
NASA Astrophysics Data System (ADS)
Ardenghi, J. S.; Bechthold, P.; Jasen, P.; Gonzalez, E.; Juan, A.
2014-11-01
The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response functions are derived and computed in the Boltzmann limit showing that in the former case a minimum conductivity appears in the no-disorder limit. In turn, from the generalization of both functions, an exact relation can be obtained that relates both. Combining this result with the relation given by the continuity equation it is possible to obtain general functional behavior of the diffusion pole. Finally, a dynamical diffusion is computed in the quasistatic limit using the definition of relaxation function. A lower cutoff must be introduced to regularize infrared divergences which allow us to obtain a full renormalization group equation for the Fermi velocity, which is solved up to order O(ℏ2).
Disordered XYZ spin chain simulations using the spectrum bifurcation renormalization group
NASA Astrophysics Data System (ADS)
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2016-07-01
We study the disordered XYZ spin chain using the recently developed spectrum bifurcation renormalization group [Y.-Z. You et al., Phys. Rev. B 93, 104205 (2016), 10.1103/PhysRevB.93.104205] numerical method. With strong disorder, the phase diagram consists of three many-body localized (MBL) spin-glass phases. We argue that, with sufficiently strong disorder, these spin-glass phases are separated by marginally MBL critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin-glass order parameter, and find that the critical lines are characterized by an effective central charge c'=ln2 . Our data also suggest continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information [introduced in C.-M. Jian et al., arXiv:1508.07006] can distinguish these phases.
Multiscale renormalization group methods for effective potentials with multiple scalar fields
NASA Astrophysics Data System (ADS)
Wang, Zhi-Wei; Steele, Tom; McKeon, Gerry
2015-04-01
Conformally symmetric scalar extensions of the Standard Model are particular appealing to reveal the underlying mechanism for electroweak symmetry breaking and to provide dark matter candidates. The Gildener & Weinberg (GW) method is widely used in these models, but is limited to weakly coupled theories. In this talk, multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the GW method beyond the weak coupling limit. A model containing two interacting real scalar fields is used as an example to illustrate these multi-scale RG methods. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with O(M) × O(N) symmetry will also be discussed. Reseach funded by NSERC (Natural Sciences and Engineering Research Council of Canada).
Mohanty, S.; Bagtzoglou, C.
1994-12-31
Assessing the performance of the potential high-level waste repository at Yucca Mountain, Nevada, requires the determination of the rate of radionuclide transport via groundwater through the fractured zone to the accessible environment. An efficient methodology for the calculation of effective hydraulic properties is presented in this paper. The Real Space Renormalization Group (RSRG) approach is adapted and modified for application to fractured rock under unsaturated conditions. The conceptual models associated with this approach are discussed briefly and the implementation of the algorithm is presented in diagrammatic form. Some verification comparisons with direct numerical simulations are presented. The estimates of effective unsaturated hydraulic conductivity, as obtained with the RSRG method, compare very well with direct numerical simulation results for the fracture configurations considered in this work. The RSRG method also proves to be highly efficient in terms of computational requirements.
Renormalization group evolution of multi-gluon correlators in high energy QCD
Dumitru A.; Venugopalan R.; Jalilian-Marian, J.; Lappi, T.; Schenke, B.
2011-11-06
Many-body QCD in leading high energy Regge asymptotics is described by the Balitsky-JIMWLK hierarchy of renormalization group equations for the x evolution of multi-point Wilson line correlators. These correlators are universal and ubiquitous in final states in deeply inelastic scattering and hadronic collisions. For instance, recently measured di-hadron correlations at forward rapidity in deuteron-gold collisions at the Relativistic Heavy Ion Collider (RHIC) are sensitive to four and six point correlators of Wilson lines in the small x color fields of the dense nuclear target. We evaluate these correlators numerically by solving the functional Langevin equation that describes the Balitsky-JIMWLK hierarchy. We compare the results to mean-field Gaussian and large Nc approximations used in previous phenomenological studies. We comment on the implications of our results for quantitative studies of multi-gluon final states in high energy QCD.
Functional renormalization group approach to the Yang-Lee edge singularity
NASA Astrophysics Data System (ADS)
An, X.; Mesterházy, D.; Stephanov, M. A.
2016-07-01
We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ɛ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O({partial}^4) truncations of the scale-dependent effective action.
NASA Astrophysics Data System (ADS)
Wei, Tzu-Chieh
2010-06-01
We consider quantum states under the renormalization-group (RG) transformations introduced by Verstraete [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.94.140601 94, 140601 (2005)] and propose a quantification of entanglement under such RGs (via the geometric measure of entanglement). We examine the resulting entanglement under RG transformations for the ground states of “matrix-product-state” Hamiltonians constructed by Wolf [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.97.110403 97, 110403 (2006)] that possess quantum phase transitions. We find that near critical points, the ground-state entanglement exhibits singular behavior. The singular behavior within finite steps of the RG obeys a scaling hypothesis and reveals the correlation length exponent. However, under the infinite steps of RG transformation, the singular behavior is rendered different and is universal only when there is an underlying conformal-field-theory description of the critical point.
Renormalization group approach to spinor Bose-Fermi mixtures in a shallow optical lattice
Modak, S.; Sengupta, K.; Tsai, S.-W.
2011-10-01
We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the bosons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible broken-symmetry ground states at low temperatures and weak interactions.
Large Disorder Renormalization Group Study of the Anderson Model of Localization
NASA Astrophysics Data System (ADS)
Johri, Sonika; Bhatt, R. N.
2015-03-01
We describe a large disorder renormalization group (LDRG) scheme for the Anderson model of localization in one dimension which eliminates eigenstates based on the size of their wavefunctions rather than their energy (as done in RG models to date). We show that our LDRG scheme flows to infinite disorder, and thus becomes asymptotically exact. We use it to obtain the disorder-averaged inverse participation ratio and density of states and compare these with results obtained by exact numerical diagonalization for the entire spectrum. A modified method is formulated for higher dimensions, which is found to be less efficient, but capable of improvement. The possibility of extending this scheme to many-body localized states will be discussed. This work was supported by Department of Energy Grant No. DE-SC0002140.
NASA Astrophysics Data System (ADS)
Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.
2016-06-01
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.
Luo, Da-Wei; Xu, Jing-Bo
2015-03-15
We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs.
NASA Astrophysics Data System (ADS)
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d =2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d =3 or Kraichnan-Batchelor in d =2 ) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.
Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling
NASA Technical Reports Server (NTRS)
Longcope, D. W.; Sudan, R. N.
1991-01-01
The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.
Exact Renormalization Group Analysis of Turbulent Transport by the Shear Flow
NASA Astrophysics Data System (ADS)
E, Weinan; Shen, Hao
2013-11-01
The exact renormalization group (RG) method initiated by Wilson and further developed by Polchinski is used to study the shear flow model proposed by Avellaneda and Majda as a simplified model for the diffusive transport of a passive scalar by a turbulent velocity field. It is shown that this exact RG method is capable of recovering all the scaling regimes as the spectral parameters of velocity statistics vary, found by Avellaneda and Majda in their rigorous study of this model. This gives further confidence that the RG method, if implemented in the right way instead of using drastic truncations as in the Yakhot-Orszag’s approximate RG scheme, does give the correct prediction for the large scale behaviors of solutions of stochastic partial differential equations (PDE). We also derive the analog of the “large eddy simulation” models when a finite amount of small scales are eliminated from the problem.
NASA Astrophysics Data System (ADS)
Li, Dong-Peng; Chen, Shou-Wan; Niu, Zhong-Ming; Liu, Quan; Guo, Jian-You
2015-02-01
Following a recent letter [J.-Y. Guo, S.-W. Chen, Z.-M. Niu, D.-P. Li, and Q. Liu, Phys. Rev. Lett. 112, 062502 (2014), 10.1103/PhysRevLett.112.062502], we present more details for the relativistic symmetry research by using the similarity renormalization group. With the theoretical formalism expressed in detail, we explore the origin and breaking mechanism of relativistic symmetries for an axially deformed nucleus. By comparing the energy splitting between the (pseudo-) spin doublets, it is shown that the spin energy splitting arises almost completely from the spin-orbit coupling, while the pseudospin energy splitting arises from a combination of the nonrelativistic, dynamical, and spin-orbit terms. Furthermore, these splittings are correlated with nuclear deformation as well as with the quantum numbers of the doublets. The origin of relativistic symmetries is disclosed and the breaking mechanism of spin and pseudospin symmetries is clarified.
Density matrix renormalization group study of triangular Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Sota, Shigetoshi; Sjinjo, Kazuya; Shirakawa, Tomonori; Tohyama, Takami; Yunoki, Seiji
2015-03-01
Topological insulator has been one of the most active subjects in the current condensed matter physics. For most of topological insulators electron correlations are considered to be not essential. However, in the case where electron correlations are strong, novel phases such as a spin liquid phase can emerge in competition with a spin-orbit coupling. Here, using the density matrix renormalization group method, we investigate magnetic phase of a triangular Kitaev-Heisenberg (quantum compass) model that contains a spin-orbital interaction and spin frustration in the antiferromagnetic region. The triangular Kitaev-Heisenberg model is regarded as a dual model of the honeycomb Kitaev-Heisenberg model that is usually employed to discuss A2CuO3 (A=Na, K). Systematically calculating ground state energy, entanglement entropy, entanglement spectrum, and spin-spin correlation functions, we discuss the duality between the triangular and the honeycomb Kitaev-Heisenberg model as well as the ground state magnetic phases.
Wei, T.-C.
2010-06-15
We consider quantum states under the renormalization-group (RG) transformations introduced by Verstraete et al. [Phys. Rev. Lett. 94, 140601 (2005)] and propose a quantification of entanglement under such RGs (via the geometric measure of entanglement). We examine the resulting entanglement under RG transformations for the ground states of ''matrix-product-state'' Hamiltonians constructed by Wolf et al. [Phys. Rev. Lett. 97, 110403 (2006)] that possess quantum phase transitions. We find that near critical points, the ground-state entanglement exhibits singular behavior. The singular behavior within finite steps of the RG obeys a scaling hypothesis and reveals the correlation length exponent. However, under the infinite steps of RG transformation, the singular behavior is rendered different and is universal only when there is an underlying conformal-field-theory description of the critical point.
NASA Astrophysics Data System (ADS)
Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A.
2016-06-01
We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.
Exact renormalization group and loop variables: A background independent approach to string theory
NASA Astrophysics Data System (ADS)
Sathiapalan, B.
2015-11-01
This paper is a self-contained review of the loop variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space-time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.
Hu, Weifeng; Chan, Garnet Kin-Lic
2015-07-14
We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection. PMID:26575737
NASA Astrophysics Data System (ADS)
Stokes, James; Konik, Robert
2014-03-01
Using the Numerical Renormalization Group (NRG), the low energy sector of the Anderson Hamiltonian with two impurities in parallel has been previously argued to be consistent with an underscreened spin-1 Kondo effect (R. Zitko and J. Bonca, Phys. Rev. B 76, 241305 (2007); Logan et al., Phys. Rev. B 80, 125117 (2009)). Bethe Ansatz and slave boson calculations have given the ground state as a singlet (M. Kulkarni and R. M. Konik, Phys. Rev. B 83, 245121 (2011)). As an attempt to understand these differences, we have developed a modified NRG routine that takes into account the multiple channels arising from the logarithmic discretization of the Fermi sea. This could conceivably allow for more complicated screening processes suggested by the Bethe ansatz computations. Results of studies using this code for various numbers of impurities and channels will be presented and discussed in relationship to these conflicting views.
Hybrid-Space Density Matrix Renormalization Group Study of the Two-Dimensional Hubbard Model
NASA Astrophysics Data System (ADS)
Ehlers, Georg; Noack, Reinhard M.
We investigate the ground state of the two-dimensional Hubbard model on a cylinder geometry at intermediate coupling and weak doping. We study properties such as the behavior of the ground-state energy, pair-field correlations, and the appearance of stripes. We find striped ground states generically, with the width of the stripes depending on the filling, the boundary conditions, and the circumference of the cylinder. Furthermore, we analyse the interplay between the different stripe configurations and the decay of the pairing correlations. Our analysis is based on a hybrid-space density matrix renormalization group (DMRG) approach, which uses a momentum-space representation in the transverse and a real-space representation in the longitudinal direction. Exploiting the transverse momentum quantum number makes significant speedup and memory savings compared to the real-space DMRG possible. In particular, we obtain computational costs that are independent of the cylinder width for fixed size of the truncated Hilbert space.
Fermionic Renormalization Group Flow at All Scales: Breaking a Discrete Symmetry
NASA Astrophysics Data System (ADS)
Gersch, Roland; Honerkamp, Carsten; Rohe, Daniel; Metzner, Walter
2006-07-01
We extend the functional renormalization group technique in a modi cation of the one-particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry-broken phase of a charge-density wave mean- eld model. We study the half- lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry-breaking eld allows us to access the symmetry-broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature.
Computational difficulty of global variations in the density matrix renormalization group.
Eisert, J
2006-12-31
The density matrix renormalization group approach is arguably the most successful method to numerically find ground states of quantum spin chains. It amounts to iteratively locally optimizing matrix-product states, aiming at better and better approximating the true ground state. To date, both a proof of convergence to the globally best approximation and an assessment of its complexity are lacking. Here we establish a result on the computational complexity of an approximation with matrix-product states: The surprising result is that when one globally optimizes over several sites of local Hamiltonians, avoiding local optima, one encounters in the worst case a computationally difficult NP-hard problem (hard even in approximation). The proof exploits a novel way of relating it to binary quadratic programming. We discuss intriguing ramifications on the difficulty of describing quantum many-body systems. PMID:17280410
Pereira, E.; Procacci, A.
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.
Gorissen, Mieke; Hooyberghs, Jef; Vanderzande, Carlo
2009-02-01
Cumulants of a fluctuating current can be obtained from a free-energy-like generating function, which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the density-matrix renormalization group for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z . We also calculate the generating function of the dynamical activity (total number of configuration changes) near the absorbing-state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents. PMID:19391693
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less
Time-dependent perturbation theory in quantum mechanics and the renormalization group
NASA Astrophysics Data System (ADS)
Bhattacharjee, J. K.; Ray, D. S.
2016-06-01
Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.
NASA Astrophysics Data System (ADS)
Metaxas, Dimitrios
2007-02-01
I show that an application of renormalization group arguments may lead to significant corrections to the vacuum decay rate for phase transitions in flat and curved space-time. It can also give some information regarding its dependence on the parameters of the theory, including the cosmological constant in the case of decay in curved space-time.
NASA Astrophysics Data System (ADS)
Renklioglu, B.; Yalabik, M. C.
2012-12-01
Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T x and T y , and also different time-scale constants, α x and α y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.
NASA Astrophysics Data System (ADS)
Lo, Po-Wei; Guo, Guang-Yu; Anders, Frithjof B.
2014-05-01
Motivated by the recent observation of the Kondo effect in graphene in transport experiments, we investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemical potentials (μ). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudogap asymmetric Anderson impurity model which is solved by the accurate numerical renormalization group method. We find that although the Anderson impurity model considered here is a mixed-valence system, it can be driven into either the Kondo [μ >μc (critical value) >0], mixed-valency (μ ≈μc), or empty-orbital (μ <μc) regime by a gate voltage, giving rise to characteristic features in resistivity and dephasing rate in each regime. Specifically, in the case of μ <μc, the shapes of the resistivity (dephasing rate) curves for different μ are nearly identical. However, as temperature decreases, they start to increase to their maxima at a lower T /TK, but more rapidly [as (TK/T)3/2] than in normal metals [here, T (TK) denotes the (Kondo) temperature]. As T further decreases, after reaching the maximum, the dephasing rate drops more quickly than in normal metals, behaving as (T/TK)3 instead of (T/TK)2. Furthermore, the resistivity has a distinct peak above the saturation value near TK. In the case of μ >μc, in contrast, the resistivity curve has an additional broad shoulder above 10TK and the dephasing rate exhibits an interesting shoulder-peak shape. In the narrow boundary region (μ ≈μc), both the resistivity and dephasing rate curves are similar to the corresponding ones in normal metals. This explains the conventional Kondo-like resistivity from recent experiments on graphene with defects, although the distinct features in the resistivity in the other cases (μ <μc or μ >μc) were not seen in the experiments. The interesting features in the resistivity and dephasing rate are analyzed in
Sharma, Sandeep
2015-01-14
We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.
Density matrix renormalization group study of the Anyon-Hubbard model
NASA Astrophysics Data System (ADS)
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-02-01
Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.
Supersymmetry-breaking parameters from renormalization group invariants at the LHC
Carena, Marcela; Draper, Patrick; Shah, Nausheen R.; Wagner, Carlos E. M.
2011-02-01
We study renormalization group invariant (RGI) quantities in the minimal supersymmetric standard model and show that they are a powerful and simple instrument for testing high-scale models of supersymmetry (SUSY) breaking. For illustration, we analyze the frameworks of minimal and general gauge-mediated (MGM and GGM) SUSY breaking, with additional arbitrary soft Higgs mass parameters at the messenger scale. We show that if a gaugino and two first generation sfermion soft masses are determined at the LHC, the RGIs lead to MGM sum rules that yield accurate predictions for the other gaugino and first generation soft masses. RGIs can also be used to reconstruct the fundamental MGM parameters (including the messenger scale), calculate the hypercharge D-term, and find relationships among the third generation and Higgs soft masses. We then study the extent to which measurements of the full first generation spectrum at the LHC may distinguish different SUSY-breaking scenarios. In the case of the MGM model, although most deviations violate the sum rules by more than estimated experimental errors, we find a one-parameter family of GGM models that satisfy the constraints and produce the same first generation spectrum. The GGM-MGM degeneracy is lifted by differences in the third generation masses and the messenger scales.
Renormalization group study of the minimal Majoronic dark radiation and dark matter model
NASA Astrophysics Data System (ADS)
Chang, We-Fu; Ng, John N.
2016-07-01
We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos triangle Neff~ 0.05, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, ρ, of mass 1.5–4 TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, S, of mass in the 10–100 GeV range and its mixing with the standard model Higgs as large as 0.1 is also predicted. The dominant decay modes are S into bbar b and/or ωω. A sensitive search will come from rare Z decays via the chain Z → S+ fbar f, where f is a Standard Model fermion, followed by S into a pair of Majoron and/or b-quarks. The interesting consequences of dark matter bound state due to the sizable Sρ ρ-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at Mρ could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.
Nonlocal growth equations-a test case for dynamic renormalization group analysis
NASA Astrophysics Data System (ADS)
Schwartz, Moshe; Katzav, Eytan
2003-12-01
In this paper we discuss nonlocal growth equations such as the generalization of the Kardar-Parisi-Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar-Parisi-Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE) equation. We show that the steady-state strong coupling solution for nonlocal models such as NKPZ and NMBE can be obtained exactly in one dimension for some special cases, using the Fokker-Planck form of these equations. The exact results we derive do not agree with previous results obtained by Dynamic Renormalization Group (DRG) analysis. This discrepancy is important because DRG is a common method used extensively to deal with nonlinear field equations. While difficulties with this method for d>1 has been realized in the past, it has been believed so far that DRG is still safe in one dimension. Our result shows differently. The reasons for the failure of DRG to recover the exact one-dimensional results are also discussed.
Renormalization group flow of Hořava-Lifshitz gravity at low energies
NASA Astrophysics Data System (ADS)
Contillo, Adriano; Rechenberger, Stefan; Saueressig, Frank
2013-12-01
The functional renormalization group equation for projectable Hořava-Lifshitz gravity is used to derive the non-perturbative beta functions for the Newton's constant, cosmological constant and anisotropy parameter. The resulting coupled differential equations are studied in detail and exemplary RG trajectories are constructed numerically. The beta functions possess a non-Gaussian fixed point and a one-parameter family of Gaussian fixed points. One of the Gaussian fixed points corresponds to the Einstein-Hilbert action with vanishing cosmological constant and constitutes a saddle point with one IR-attractive direction. For RG trajectories dragged into this fixed point at low energies diffeomorphism invariance is restored. The emergence of general relativity from Hořava-Lifshitz gravity can thus be understood as a crossover-phenomenon where the IR behavior of the theory is controlled by this Gaussian fixed point. In particular RG trajectories with a tiny positive cosmological constant also come with an anisotropy parameter which is compatible with experimental constraints, providing a mechanism for the approximate restoration of diffeomorphism invariance in the IR. The non-Gaussian fixed point is UV-attractive in all three coupling constants. Most likely, this fixed point is the imprint of Asymptotic Safety at the level of Hořava-Lifshitz gravity.
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. PMID:27334156
A state interaction spin-orbit coupling density matrix renormalization group method
NASA Astrophysics Data System (ADS)
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.
Density matrix renormalization group study of Y-junction spin systems
NASA Astrophysics Data System (ADS)
Guo, Haihui
Junction systems are important to understand both from the fundamental and the practical point of view, as they are essential components in existing and future electronic and spintronic devices. With the continuous advance of technology, device size will eventual reach the atomic scale. Some of the most interesting and useful junction systems will be strongly correlated. We chose the Density Matrix Renormalization Group method to study two types of Y-junction systems, the Y and YDelta junctions, on strongly correlated spin chains. With new ideas coming from the quantum information field, we have made a very efficient. Y-junction DMRG algorithm, which improves the overall CUB cost from O(m6) to O(m4), where m is the number of states kept per block. We studied the ground state properties, the correlation length, and investigated the degeneracy problem on the Y and YDelta junctions. For the excited states, we researched the existence of magnon bound states for various conditions, and have shown that the bound state exists when the central coupling constant is small.
A driven similarity renormalization group approach to quantum many-body problems
Evangelista, Francesco A.
2014-08-07
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C{sub 2} and F{sub 2}. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.
NASA Astrophysics Data System (ADS)
Cvetič, G.; Kim, C. S.
We assume that the standard model (SM) breaks down around some energy Λ and is replaced there by a new (Higgsless) flavor gauge theory (FGT) with fewer input parameters in the interactions corresponding to the Yukawa sector of SM. This would imply more symmetry for the values of the Yukawa (running) parameters of SM at E Λ, possibly by a (approximate) flavor democracy (for the quark mass sector). We investigate this possibility by studying the renormalization group equations (RGE's) for the quark Yukawa couplings of SM with one and two Higgs doublets, by running them from the known physical values at low energies (E 1 GeV) to Λ (> 1 TeV) and comparing the resulting quark masses mq (E Λ) for various mt and υU/υD. Unlike previous investigations of these RGE's, we do not implement the requirement mt(Λpole) = ∞. We found that SM with two Higgs doublets (type 2) is most likely to experience a gradual transition to FGT. Our results also shed more light on the adequacy and deficiencies of the usual RGE approaches within TMSM and related models. We also found that, independent of the assumption of a transition mechanism to FGT, mt phy< ˜ 200 GeV for Λpole≪ ΛPlanck in most cases of SM with two Higgs doublets.
NASA Astrophysics Data System (ADS)
Wouters, Sebastian; Nakatani, Naoki; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2013-08-01
The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.070601 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
Extending the range of real time density matrix renormalization group simulations
NASA Astrophysics Data System (ADS)
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ > and operators A in the evaluation of ψ(t) = < ψ | A(t) | ψ > . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
Kondo insulators modeled by the one-dimensional Anderson lattice: A numerical-renormalization-group study
Guerrero, M.; Yu, C.C.
1995-04-15
In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half filling in one dimension using the density-matrix formulation of the numerical renormalization group. The asymmetric case is treated in the mixed-valence regime. We have calculated the charge gap, the spin gap, and the quasiparticle gap as a function of the repulsive interaction {ital U} using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all {ital U} for both the symmetric and asymmetric cases. Ruderman-Kittel-Kasuya-Yosida interactions are evident in the {ital f}-spin--{ital f}-spin correlation functions at large {ital U} in the symmetric case, but are suppressed in the asymmetric case as the {ital f} level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility {chi}({ital q}=2{ital k}{sub {ital F}}) and it is consistent with neutron scattering measurements of {chi}({ital q}) in CeNiSn.
NASA Astrophysics Data System (ADS)
Sai Venkata Ramana, A.
2016-01-01
In this paper, we have applied the seventh order version of coupling parameter expansion (CPE) method combined with global renormalization group theory (GRGT) to square well fluids of various ranges and have performed the following studies. Firstly, the convergence of the GRGT iteration scheme has been studied. It is observed that the point-wise convergence is non-uniform and slow in the coexistence region away from the critical point. However, the point-wise convergence improved as the critical temperature is approached. Secondly, we have obtained the liquid-vapor phase diagrams (LVPDs) for the square well fluids. The LVPDs obtained using GRGT corrected seventh order CPE are significantly accurate over those obtained from GRGT corrected 1-order thermodynamic perturbation theory (TPT). Also, excessive flatness of LVPDs close to the critical region as observed in GRGT corrected 1-order TPT has not been seen in the LVPDs of present method. Thirdly, the critical exponents have been obtained using present method. The exponents are seen to be of Ising universality class and follow the Rushbrooke and Griffiths equalities qualitatively. Finally, a study of Yang-Yang anomaly has been done using our method. It has been observed that the method predicts the existence of the anomaly but the predictions of the strength of anomaly differed from those of simulations. The reasons for the differences are analyzed.
NASA Astrophysics Data System (ADS)
Sun, Wen-Yang; Xu, Shuai; Liu, Cheng-Cheng; Ye, Liu
2016-05-01
In this paper, we study the anisotropy parameter and Dzyaloshinskii-Moriya (DM) interaction on negativity and quantum phase transition (QPT) by using the quantum renormalization-group (QRG) method in the spin model. In our model, the anisotropy parameter and DM interaction can influence the phase diagrams. Negativity can develop two different values which separated two phases i.e. Spin-fluid phase and the Néel phase with the number of QRG iterations increased, and can obviously exhibit QPT at the critical point. Then, we find that negativity of particles 1, 3 throughout is less than negativity of particles 1, 2 or particles 2, 3. Because of information between the three particle distributions, please see the conclusion. We find that the negativity difference value ( S) can also clearly detect QPT at the critical point. Most importantly, the maximum S max become more and more close to the critical point. So S max can be used as a criterion of the quantum phase transition occurrence when the spin chain is infinity ( N → ∞).
Operator evolution in the three-body space via the similarity renormalization group
NASA Astrophysics Data System (ADS)
Schuster, Micah; Quaglioni, Sofia; Johnson, Calvin; Jurgenson, Eric; Navratil, Petr
2014-03-01
Performing quantitative calculations of nuclear observables in terms of nucleons interacting through two- and three-nucleon forces is a guiding principle of ab initio nuclear theory. Computationally, this is complicated by the large model spaces needed to reach convergence in many-body approaches, such as the no-core shell model (NCSM). In recent years, the similarity renormalization group (SRG) has provided a powerful tool to soften interactions for ab initio structure calculations, thus leading to convergence within smaller model spaces. SRG has been very successful when applied to the Hamiltonian of the nuclear system. However, when computing observables other than spectra, one must evolve the relevant operators using the same transformation that was applied to the Hamiltonian. Here we compute the root mean square (RMS) radius of 3H to show that evolving the \\rcirc2 operator in the three-body space, thus including two- and three-body SRG induced terms, will yield an exactly unitary transformation. We then extend our calculations to 4He and compute the RMS radius and total strength of the dipole transition using operators evolved in the three-body space. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Support came from U.S. DOE/SC/NP (work proposal SCW1158), IMRR: LLNL-ABS-647982.
Renormalization-group theory for finite-size scaling in extreme statistics.
Györgyi, G; Moloney, N R; Ozogány, K; Rácz, Z; Droz, M
2010-04-01
We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation. PMID:20481705
Density-matrix renormalization group study of the extended Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Shinjo, Kazuya; Sota, Shigetoshi; Tohyama, Takami
2015-02-01
We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120∘ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.
Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group
Hergert, H.; Papakonstantinou, P.; Roth, R.
2011-06-15
We have developed a fully consistent framework for calculations in the quasiparticle random-phase approximation (QRPA) with NN interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter {lambda}. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.
Kloss, Thomas; Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2014-02-01
We investigate the scaling regimes of the Kardar-Parisi-Zhang (KPZ) equation in the presence of spatially correlated noise with power-law decay D(p) ∼ p(-2ρ) in Fourier space, using a nonperturbative renormalization group approach. We determine the full phase diagram of the system as a function of ρ and the dimension d. In addition to the weak-coupling part of the diagram, which agrees with the results from Europhys. Lett. 47, 14 (1999) and Eur. Phys. J. B 9, 491 (1999), we find the two fixed points describing the short-range- (SR) and long-range- (LR) dominated strong-coupling phases. In contrast with a suggestion in the references cited above, we show that, for all values of ρ, there exists a unique strong-coupling SR fixed point that can be continuously followed as a function of d. We show in particular that the existence and the behavior of the LR fixed point do not provide any hint for 4 being the upper critical dimension of the KPZ equation with SR noise. PMID:25353423
AdS/CFT and local renormalization group with gauge fields
NASA Astrophysics Data System (ADS)
Kikuchi, Ken; Sakai, Tadakatsu
2016-03-01
We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector β -functions, and some of their interesting properties are known to follow. We give a systematic rederivation of them on the basis of the flow equation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the flow equation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by determining a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.
Moritz, Gerrit; Reiher, Markus
2006-01-21
The application of the quantum-chemical density-matrix renormalization group (DMRG) algorithm is cumbersome for complex electronic structures with many active orbitals. The high computational cost is mainly due to the poor convergence of standard DMRG calculations. A factor which affects the convergence behavior of the calculations is the choice of the start-up procedure. In this start-up step matrix representations of operators have to be calculated in a guessed many-electron basis of the DMRG environment block. Different possibilities for the construction of these basis states exist, and we first compare four procedures to approximate the environment states using Slater determinants explicitly. These start-up procedures are applied to DMRG calculations on a sophisticated test system: the chromium dimer. It is found that the converged energies and the rate of convergence depend significantly on the choice of the start-up procedure. However, since already the most simple start-up procedure, which uses only the Hartree-Fock determinant, is comparatively good, Slater determinants, in general, appear not to be a good choice as approximate environment basis states for convergence acceleration. Based on extensive test calculations it is demonstrated that the computational cost can be significantly reduced if the number of total states m is successively increased. This is done in such a way that the environment states are built up stepwise from system states of previous truncated DMRG sweeps for slowly increasing m values. PMID:16438563
NASA Astrophysics Data System (ADS)
Moritz, Gerrit; Reiher, Markus
2006-01-01
The application of the quantum-chemical density-matrix renormalization group (DMRG) algorithm is cumbersome for complex electronic structures with many active orbitals. The high computational cost is mainly due to the poor convergence of standard DMRG calculations. A factor which affects the convergence behavior of the calculations is the choice of the start-up procedure. In this start-up step matrix representations of operators have to be calculated in a guessed many-electron basis of the DMRG environment block. Different possibilities for the construction of these basis states exist, and we first compare four procedures to approximate the environment states using Slater determinants explicitly. These start-up procedures are applied to DMRG calculations on a sophisticated test system: the chromium dimer. It is found that the converged energies and the rate of convergence depend significantly on the choice of the start-up procedure. However, since already the most simple start-up procedure, which uses only the Hartree-Fock determinant, is comparatively good, Slater determinants, in general, appear not to be a good choice as approximate environment basis states for convergence acceleration. Based on extensive test calculations it is demonstrated that the computational cost can be significantly reduced if the number of total states m is successively increased. This is done in such a way that the environment states are built up stepwise from system states of previous truncated DMRG sweeps for slowly increasing m values.
Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model
NASA Technical Reports Server (NTRS)
Yakhot, A.; Staroselsky, I.; Orszag, S. A.
1994-01-01
Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.
Brodsky, Stanley J.; Wu, Xing-Gang; /SLAC /Chongqing U.
2012-02-16
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal {beta}{sub i} terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of R{sub e{sup +}e{sup -}}(Q) up to four loops is presented. By using the world average {alpha}{sub s}{sup {ovr MS}}(MZ) = 0.1184 {+-} 0.0007, we obtain the asymptotic scale for the 't Hooft associated with the {ovr MS} scheme, {Lambda}{sub {ovr MS}}{sup 'tH} = 245{sub -10}{sup +9} MeV, and the asymptotic scale for the conventional {ovr MS} scheme, {Lambda}{sub {ovr MS}} = 213{sub -8}{sup +19} MeV.
A Renormalization-Group Interpretation of the Connection between Criticality and Multifractals
NASA Astrophysics Data System (ADS)
Chang, Tom
2014-05-01
Turbulent fluctuations in space plasmas beget phenomena of dynamic complexity. It is known that dynamic renormalization group (DRG) may be employed to understand the concept of forced and/or self-organized criticality (FSOC), which seems to describe certain scaling features of space plasma turbulence. But, it may be argued that dynamic complexity is not just a phenomenon of criticality. It is therefore of interest to inquire if DRG may be employed to study complexity phenomena that are distinctly more complicated than dynamic criticality. Power law scaling generally comes about when the DRG trajectory is attracted to the vicinity of a fixed point in the phase space of the relevant dynamic plasma parameters. What happens if the trajectory lies within a domain influenced by more than one single fixed point or more generally if the transformation underlying the DRG is fully nonlinear? The global invariants of the group under such situations (if they exist) are generally not power laws. Nevertheless, as we shall argue, it may still be possible to talk about local invariants that are power laws with the nonlinearity of transformation prescribing a specific phenomenon as crossovers. It is with such concept in mind that we may provide a connection between the properties of dynamic criticality and multifractals from the point of view of DRG (T. Chang, Chapter VII, "An Introduction to Space Plasma Complexity", Cambridge University Press, 2014). An example in terms of the concepts of finite-size scaling (FSS) and rank-ordered multifractal analysis (ROMA) of a toy model shall be provided. Research partially supported by the US National Science Foundation and the European Community's Seventh Framework Programme (FP7/ 2007-2013) under Grant agreement no. 313038/STORM.
NASA Astrophysics Data System (ADS)
Huang, Yu-Kun; Chen, Pochung; Kao, Ying-Jer; Xiang, Tao
2014-05-01
By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recently proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009), 10.1103/PhysRevLett.102.240603] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012), 10.1103/PhysRevLett.108.227206].
NASA Astrophysics Data System (ADS)
Guo, Jian-You; Chen, Shou-Wan; Niu, Zhong-Ming; Li, Dong-Peng; Liu, Quan
2014-02-01
Symmetry is an important and basic topic in physics. The similarity renormalization group theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity renormalization group theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system.
NASA Astrophysics Data System (ADS)
Anders, Frithjof B.; Schmitt, Sebastian
2010-04-01
Scattering states fulfill the correct boundary conditions of a current carrying open quantum system. Discretizing the energy continuum of these states allows for employing Wilson's numerical renormalization group approach without violating the boundary conditions by using a finite size system. We evolve the analytically known steady-state density operator for a non-interacting quantum-system at finite bias to the full interacting problem by the time-dependent numerical renormalization group after switching on the local charging energy. Using a newly developed algorithm for steady-state nonequilibrium Green functions, we can calculate the current I as function of bias voltage V for arbitrary temperature and magnetic field. A comparison with second-order and GW Kadanoff-Baym-Keldysh results shows excellent agreement for weak interaction strength U.
NASA Astrophysics Data System (ADS)
Calzetta, E. A.; Hu, B. L.; Mazzitelli, Francisco D.
2001-10-01
In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (CGEA)) and ideas (scaling, coarse-graining and backreaction) behind the treatment of quantum processes in dynamical background spacetimes and fields. We show how they are useful for the construction of renormalization group (RG) theories for studying these nonequilibrium processes and discuss the underlying issues. Examples are drawn from quantum field processes in an inflationary universe, semiclassical cosmology and stochastic gravity. In Part I (Sections /2, /3) we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) can be treated as static critical phenomena, while a `slow-roll' or power-law inflation can be treated as dynamical critical phenomena. In Part II (Sections /4, /5) we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger-DeWitt) CGEA devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III (Sections /6-/8) we present the CTP (in-in, or Schwinger-Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel; Fischer, Jan
2013-01-01
We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard “contour-improved” expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the τ lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, αs(Mτ2)=0.3189-0.0151+0.0173, which translates to αs(MZ2)=0.1184-0.0018+0.0021.
Physics implications of the diphoton excess from the perspective of renormalization group flow
NASA Astrophysics Data System (ADS)
Gu, Jiayin; Liu, Zhen
2016-04-01
A very plausible explanation for the recently observed diphoton excess at the 13 TeV LHC is a (pseudo)scalar with mass around 750 GeV, which couples to a gluon pair and to a photon pair through loops involving vectorlike quarks (VLQs). To accommodate the observed rate, the required Yukawa couplings tend to be large. A large Yukawa coupling would rapidly run up with the scale and quickly reach the perturbativity bound, indicating that new physics, possibly with a strong dynamics origin, is nearby. The case becomes stronger especially if the ATLAS observation of a large width persists. In this paper we study the implication on the scale of new physics from the 750 GeV diphoton excess using the method of renormalization group running with careful treatment of different contributions and perturbativity criterion. Our results suggest that the scale of new physics is generically not much larger than the TeV scale, in particular if the width of the hinted (pseudo)scalar is large. Introducing multiple copies of VLQs, lowering the VLQ masses, and enlarging VLQ electric charges help reduce the required Yukawa couplings and can push the cutoff scale to higher values. Nevertheless, if the width of the 750 GeV resonance turns out to be larger than about 1 GeV, it is very hard to increase the cutoff scale beyond a few TeVs. This is a strong hint that new particles in addition to the 750 GeV resonance and the vectorlike quarks should be around the TeV scale.
Short-range correlations in nuclei with similarity renormalization group transformations
NASA Astrophysics Data System (ADS)
Neff, T.; Feldmeier, H.; Horiuchi, W.
2015-08-01
Background: Realistic nucleon-nucleon interactions induce short-range correlations in nuclei. To solve the many-body problem unitary transformations like the similarity renormalization group (SRG) are often used to soften the interactions. Purpose: Two-body densities can be used to illustrate how the SRG eliminates short-range correlations in the wave function. The short-range information can however be recovered by transforming the density operators. Method: The many-body problem is solved for 4He in the no core shell model (NCSM) with SRG transformed AV 8 ' and chiral N3LO interactions. The NCSM wave functions are used to calculate two-body densities with bare and SRG transformed density operators in two-body approximation. Results: The two-body momentum distributions for AV 8 ' and N3LO have similar high-momentum components up to relative momenta of about 2.5 fm-1 , dominated by tensor correlations, but differ in their behavior at higher relative momenta. The contributions of many-body correlations are small for pairs with vanishing pair momentum but not negligible for the momentum distributions integrated over all pair momenta. Many-body correlations are induced by the strong tensor force and lead to a reshuffling of pairs between different spin-isospin channels. Conclusions: When using the SRG it is essential to use transformed operators for observables sensitive to short-range physics. Back-to-back pairs with vanishing pair momentum are the best tool to study short-range correlations.
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
NASA Astrophysics Data System (ADS)
Hergert, H.; Bogner, S. K.; Morris, T. D.; Schwenk, A.; Tsukiyama, K.
2016-03-01
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
Holographic renormalization group flow dual to attractor flow in extremal black holes
Hotta, Kyosuke
2009-05-15
We extend the discussion of the 'Kerr/CFT correspondence' and its recent developments to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow. It is conjectured that the extremal black hole space-time is holographically dual to the chiral two-dimensional field theory. Our example is a typical four-dimensional Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on four cycles of Calabi-Yau threefold. In the five-dimensional supergravity viewpoint, this near horizon geometry is AdS{sub 3}xS{sup 2}, and three-dimensional gravity coupled to moduli fields is effectively obtained after a dimensional reduction on S{sup 2}. Constructing the Hamilton-Jacobi equation, we define the holographic RG flow from the three-dimensional gravity. The central charge of the Virasoro algebra is calculable from the conformal anomaly at the point where the beta function defined from the gravity side becomes zero. In general, we can also identify the c function of the dual two-dimensional field theory. We show that these flow equations are completely equivalent to not only BPS but also non-BPS attractor flow equations of the moduli fields. The attractor mechanism by which the values of the moduli fields are fixed at the event horizon of the extremal black hole can be understood equivalently to the fact that the RG flows are fixed at the critical points in the dual field theory.