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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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}.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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
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}.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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}
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.
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.
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)
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)
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)
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.
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.
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.
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
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.
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.
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).
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
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.
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
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)
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.
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.
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.
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)
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.
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
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)
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.
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.
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
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.
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)
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.
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.
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.
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.
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.
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.
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.
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 → ∞).
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.
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
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.
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)
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)
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)
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)
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.
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.
Functional renormalization group analysis of the soft mode at the QCD critical point
NASA Astrophysics Data System (ADS)
Yokota, Takeru; Kunihiro, Teiji; Morita, Kenji
2016-07-01
We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral functions ρ_{σ, π}(ω, p) in the scalar (σ) and pseudoscalar (π) channels beyond the random phase approximation in the quark-meson model. At finite baryon chemical potential μ with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the σ channel has a support not only in the time-like (ω > p) but also in the space-like (ω < p) regions, which correspond to the mesonic and the particle-hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD critical point, which is a manifestation of the fact that the phonon mode is the soft mode associated with the second-order transition at the QCD critical point, as has been suggested by some authors. Moreover, our extensive calculation of the spectral function in the (ω, p) plane enables us to see that the mesonic and phonon modes have the respective definite dispersion relations ω_{σ.ph}(p), and it turns out that ω_{σ}(p) crosses the light-cone line into the space-like region, and then eventually merges into the phonon mode as the system approaches the critical point more closely. This implies that the sigma-mesonic mode also becomes soft at the critical point. We also provide numerical stability conditions that are necessary for obtaining the accurate effective potential from the flow equation.
A Renormalization Group Study of the Ising Model on the Hierarchical Hanoi Networks
NASA Astrophysics Data System (ADS)
Brunson, Clifton Trent
Despite all the remarkable breakthroughs in the area of complex networks over the last two decades, there still lacks a complete and general understanding of effects that occur when long-range connections are present in a system. This thesis explores the Ising model using recursive hierarchical networks called Hanoi networks (HN) as a substrate. Hanoi networks are purely synthetic and are not found in nature, so it is important to establish and not lose sight of why they worth studying. In essence, we are not strictly interested in HNs themselves, but the generalized statements about phase transitions on complex networks that they provide via the renormalization group (RG). The RG framework on HNs is established in this study and the thermodynamic observables for statistical models are derived from it. Traditionally, the RG has given physicists insight into the critical exponents of a system or model, which leads to universal behavior; however, hyperbolic networks, like the ones currently under investigation, do not contain constant exponents and do not exhibit universality. Instead, it is found that the scaling exponents are functions of the temperature. We ultimately want to answer the questions: What is it about long-range connections that create a break in universal behavior and can complex networks be designed to produce predicted and intended effects in phase behavior? The current state of research is several years or perhaps decades away from fully comprehending the answers to these questions. The research presented here is motivated by these questions, and our contribution here is intended to show a generalized picture of phase transitions on networks.
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.
Holography as a highly efficient renormalization group flow. I. Rephrasing gravity
NASA Astrophysics Data System (ADS)
Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan
2016-07-01
We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.
Holography as a highly efficient renormalization group flow. II. An explicit construction
NASA Astrophysics Data System (ADS)
Behr, Nicolas; Mukhopadhyay, Ayan
2016-07-01
We complete the reformulation of the holographic correspondence as a highly efficient renormalization group (RG) flow that can also determine the UV data in the field theory in the strong-coupling and large-N limit. We introduce a special way to define operators at any given scale in terms of appropriate coarse-grained collective variables, without requiring the use of the elementary fields. The Wilsonian construction is generalized by promoting the cutoff to a functional of these collective variables. We impose three criteria to determine the coarse-graining. The first criterion is that the effective Ward identities for local conservation of energy, momentum, etc. should preserve their standard forms, but in new scale-dependent background metric and sources which are functionals of the effective single-trace operators. The second criterion is that the scale-evolution equations of the operators in the actual background metric should be state-independent, implying that the collective variables should not explicitly appear in them. The final required criterion is that the end point of the scale-evolution of the RG flow can be transformed to a fixed point corresponding to familiar nonrelativistic equations with a finite number of parameters, such as incompressible nonrelativistic Navier-Stokes, under a certain universal rescaling of the scale and of the time coordinate. Using previous work, we explicitly show that in the hydrodynamic limit each such highly efficient RG flow reproduces a unique classical gravity theory with precise UV data that satisfy our IR criterion and also lead to regular horizons in the dual geometries. We obtain the explicit coarse-graining which reproduces Einstein's equations. In a simple example, we are also able to construct a low-energy effective action and compute the beta function. Finally, we show how our construction can be interpolated with the traditional Wilsonian RG flow at a suitable scale and can be used to develop new
Physics implications of the diphoton excess from the perspective of renormalization group flow
Gu, Jiayin; Liu, Zhen
2016-04-06
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 vector-like 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 near by. The case becomes stronger especially if the ATLAS observation of a large width persists. In this papermore » 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, lowing 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 vector-like quarks should be around the TeV scale.« less
NASA Astrophysics Data System (ADS)
Galley, Chad R.; Leibovich, Adam K.; Porto, Rafael A.; Ross, Andreas
2016-06-01
We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a "conservative" term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit—shrinking the binary to a point—which transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.
NASA Astrophysics Data System (ADS)
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Harris, Travis V.; Morokuma, Keiji; Kurashige, Yuki; Yanai, Takeshi
2014-02-07
The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe{sub 2}OCl{sub 6}]{sup 2−} and [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+}. After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe{sub 2}OCl{sub 6}]{sup 2−} with (16e,26o), and considerably improving the smaller active space results for [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+} with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.
NASA Astrophysics Data System (ADS)
Katzav, Eytan
2013-04-01
In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.
NASA Astrophysics Data System (ADS)
Chandre, C.; Govin, M.; Jauslin, H. R.
1998-02-01
We analyze the breakup of invariant tori in Hamiltonian systems with two degrees of freedom using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We consider a class of Hamiltonians quadratic in the action variables that is invariant under the chosen KAM transformations, following the approach of Thirring. The numerical implementation of the transformation shows that the KAM iteration converges up to the critical coupling at which the torus breaks up. By combining this iteration with a renormalization, consisting of a shift of resonances and rescalings of momentum and energy, we obtain a more efficient method that allows one to determine the critical coupling with high accuracy. This transformation is based on the physical mechanism of the breakup of invariant tori. We show that the critical surface of the transformation is the stable manifold of codimension one of a nontrivial fixed point, and we discuss its universality properties.
NASA Astrophysics Data System (ADS)
Freire, Hermann; Corrêa, Eberth
2012-02-01
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta et al. (in Phys. Rev. Lett. 85:4940, 2000), which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.
NASA Astrophysics Data System (ADS)
Rentrop, J. F.; Meden, V.; Jakobs, S. G.
2016-05-01
We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle-irreducible vertex functions, given a cutoff in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to nonconserving approximations introduced in an earlier publication [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015), 10.1088/1751-8113/48/14/145002]. We apply the different approximate flow equations to the single-impurity Anderson model in thermal equilibrium at vanishing temperature. Numerical results for the effective mass, the spin susceptibility, the charge susceptibility, and the linear conductance reflect the similarity of the methods to the fluctuation exchange approximation. We find the majority of the approximations to deviate stronger from the exact results than one-particle-irreducible functional renormalization group schemes. However, we identify a simple static two-particle-irreducible flow scheme which performs remarkably well and produces an exponential Kondo-like scale in the renormalized level position.
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2011-03-15
Nuclear effective field theory (NEFT) including pions in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, {Lambda}, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space up to including O(p{sup 2}), and find the nontrivial fixed points in the {sup 1}S{sub 0} and {sup 3}S{sub 1}-{sup 3}D{sub 1} channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems. PMID:27104687
Entanglement Renormalization and Wavelets
NASA Astrophysics Data System (ADS)
Evenbly, Glen; White, Steven R.
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Chan, Garnet Kin-Lic
2013-04-01
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
NASA Astrophysics Data System (ADS)
O'Malley, D.; Cushman, J. H.; Johnson, G.
2013-09-01
A random renormalization group technique is reviewed, and a related set of Bayesian scaling techniques are presented. The techniques are employed to study the motion of drifters in Lake Michigan on a time scale ranging from 30 min to 5 days and in the Gulf of Mexico on a time scale ranging from 8 h to 85 days. The scaling laws generalize the standard power law scalings. One of the advantages of the Bayesian approach is that scaling laws can be determined even with a paucity of data with the caveat that less data produce greater uncertainty in the scaling laws.
Liu, X M; Cheng, W W; Liu, J-M
2016-01-01
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions. PMID:26780973
NASA Astrophysics Data System (ADS)
Paeßens, Matthias; Schütz, Gunter M.
2002-08-01
The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculates the effects on the viscosity by the use of the density matrix renormalization group algorithm. Using input from Rouse theory, the rates for the constraint releases are determined in a self-consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.
NASA Astrophysics Data System (ADS)
Baldovin, F.; Robledo, A.
2002-10-01
We uncover the dynamics at the chaos threshold μ∞ of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for μ<μ∞. We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient λq. Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps.
NASA Astrophysics Data System (ADS)
Anders, Frithjof B.
2008-08-01
We propose a numerical renormalization group (NRG) approach to steady-state currents through nanodevices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left- and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias V. We employ the time-dependent NRG to evolve the known steady-state density operator for a noninteracting junction into the density operator of the fully interacting nanodevice at finite bias. We calculate the differential conductance as function of V, T, and the external magnetic field.
Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe
Shamir, Yigal
2007-03-01
I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to nonlocal effects in the fourth-root theory when the lattice spacing is nonzero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.
NASA Astrophysics Data System (ADS)
Khemani, Vedika; Pollmann, Frank; Sondhi, S. L.
2016-06-01
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
Liu, X. M.; Cheng, W. W.; Liu, J. -M.
2016-01-01
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions. PMID:26780973
Renormalization group study of a Fragile Fermi liquid in 1 + ɛ dimensions
NASA Astrophysics Data System (ADS)
Mai, Peizhi; Krishna-murthy, H. R.; Sriram Shastry, B.
2016-07-01
We present a calculation of the low energy Greens function of interacting fermions in 1 + ɛ dimensions using the method of extended poor man's scaling, developed here. We compute the wave function renormalization Z(ω) and also the decay rate near the Fermi energy. Despite the lack of ω2 damping characteristic of 3-dimensional Fermi liquids, we show that quasiparticles do exist in 1 + ɛ dimensions, in the sense that the quasiparticle weight Z is finite and that the damping rate is smaller than the energy. We explicitly compute the crossover from this behavior to a 1-dimensional type Tomonaga-Luttinger liquid behavior at higher energies.
NASA Astrophysics Data System (ADS)
Imada, Masatoshi; Kashima, Tsuyoshi
2000-09-01
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.
Monte Carlo simulations on marker grouping and ordering.
Wu, J; Jenkins, J; Zhu, J; McCarty, J; Watson, C
2003-08-01
Four global algorithms, maximum likelihood (ML), sum of adjacent LOD score (SALOD), sum of adjacent recombinant fractions (SARF) and product of adjacent recombinant fraction (PARF), and one approximation algorithm, seriation (SER), were used to compare the marker ordering efficiencies for correctly given linkage groups based on doubled haploid (DH) populations. The Monte Carlo simulation results indicated the marker ordering powers for the five methods were almost identical. High correlation coefficients were greater than 0.99 between grouping power and ordering power, indicating that all these methods for marker ordering were reliable. Therefore, the main problem for linkage analysis was how to improve the grouping power. Since the SER approach provided the advantage of speed without losing ordering power, this approach was used for detailed simulations. For more generality, multiple linkage groups were employed, and population size, linkage cutoff criterion, marker spacing pattern (even or uneven), and marker spacing distance (close or loose) were considered for obtaining acceptable grouping powers. Simulation results indicated that the grouping power was related to population size, marker spacing distance, and cutoff criterion. Generally, a large population size provided higher grouping power than small population size, and closely linked markers provided higher grouping power than loosely linked markers. The cutoff criterion range for achieving acceptable grouping power and ordering power differed for varying cases; however, combining all situations in this study, a cutoff criterion ranging from 50 cM to 60 cM was recommended for achieving acceptable grouping power and ordering power for different cases. PMID:12761620
NASA Astrophysics Data System (ADS)
Kachan, Devin; Levine, Alex; Bruinsma, Robijn
2014-03-01
Biology is rife with examples of active materials - soft matter systems driven into nonequilibrium steady states by energy input at the micro scale. For example, solutions of active micron scale swimmers produce active fluids showing phenomena reminiscent of turbulent convection at low Reynolds number; cytoskeletal networks driven by endogenous molecular motors produce active solids whose mechanics and low frequency strain fluctuations depend sensitively on motor activity. One hallmark of these systems is that they are driven at the micro scale by temporally correlated forces. In this talk, we study how correlated noise at the micro scale leads to novel long wavelength and long time scale dynamics at the macro scale in a simple model system. Specifically, we study the fluctuations of a ϕ4 scalar field obeying model A dynamics and driven by noise with a finite correlation time τ. We show that the effective dynamical system at long length and time scales is driven by white noise with a renormalized amplitude and renormalized transport coefficients. We discuss the implications of this result for a broad class of active matter systems driven at the micro scale by colored noise.
NASA Astrophysics Data System (ADS)
Li, Chenyang; Evangelista, Francesco A.
2016-04-01
The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder-state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker-Campbell-Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. 124, 194106 (2006)]. The resulting linearized MR-DSRG scheme with one- and two-body operators [MR-LDSRG(2)] contains only 39 terms and scales as O ( N 2 NP 2 NH 2 ) where NH, NP, and N correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrogen binding curves and the singlet-triplet splitting of p-benzyne yield results comparable in accuracy to those from multireference configuration interaction, Mukherjee multireference coupled cluster theory, and internally contracted multireference coupled cluster theory.
Li, Chenyang; Evangelista, Francesco A
2016-04-28
The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder-state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker-Campbell-Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. 124, 194106 (2006)]. The resulting linearized MR-DSRG scheme with one- and two-body operators [MR-LDSRG(2)] contains only 39 terms and scales as O(N(2)NP (2)NH (2)) where NH, NP, and N correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrogen binding curves and the singlet-triplet splitting of p-benzyne yield results comparable in accuracy to those from multireference configuration interaction, Mukherjee multireference coupled cluster theory, and internally contracted multireference coupled cluster theory. PMID:27131538
NASA Astrophysics Data System (ADS)
Antonov, N. V.; Kakin, P. I.
2016-02-01
We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t - t')/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction - the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa-Kardar model is irrelevant) and to the "pure" Hwa-Kardar model (the advection is irrelevant). For the special case ξ = 2(4 - d)/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.
NASA Astrophysics Data System (ADS)
Kashima, Tsuyoshi; Imada, Masatoshi
2001-08-01
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two procedures lead to a better approximation. The first is a numerical renormalization, which optimizes the chosen basis and projects onto the ground state within the fixed dimension, L, of the Hilbert space. The second is an increase of the dimension of the truncated Hilbert space, which enables the linear combination to converge to a better approximation. The extrapolation L→∞ after the convergence removes the approximation error systematically. This algorithm does not suffer from the negative sign problem and can be applied to systems in any spatial dimension and arbitrary lattice structure. The efficiency is tested and the implementation explained for two-dimensional Hubbard models where Slater determinants are employed as chosen basis. Our results with less than 400 chosen basis indicate good accuracy within the errorbar of the best available results as those of the quantum Monte Carlo for energy and other physical quantities.
Conserved quantities and renormalization group flows in two-dimensional field theory
NASA Astrophysics Data System (ADS)
Gerganov, Bogomil Enchev
2000-12-01
Several problems in two-dimensional field theory are investigated. The concepts of classical and quantum integrability in two space-time dimensions are presented in the Introduction and a number of algebraic structures associated with integrable systems are described. Some results of conformal field theory (CFT) and perturbed conformal field theory are reviewed. In Chapter 2, the problem of interaction of two-level atoms in fibrillar geometry with electro-magnetic radiation is studied in perturbation theory. A new formalism is developed, representing the atomic spin operators with elementary fermions, and a resemblance between the structures of this model and quantum electrodynamics is established. Although the system studied is not itself integrable, it can be shown that the integrable quantum sine-Gordon model has some validity as an approximate theory. The following two chapters study the properties of several multi-field generalizations of the sine-Gordon model. The Bukhvostov-Lipatov model is studied in Chapter 3. The classical integrability of the fermionic version of the model is established, both in the bulk and on the half line, by explicitly building a conserved charge of Lorentz spin 3. The quantum integrability of the more general double-cosine model is investigated using perturbed CFT. The analysis showed in particular that the conservation law is spoiled at the quantum level on the Bukhvostov-Lipatov submanifold of the parameter space. In Chapter 4 an N-field model is considered-its interaction term being a product of N cosines. For N >= 2 a conservation law of Lorentz spin 3 is found to first order in perturbed CFT on a manifold where the interaction becomes marginal. The integrability of the model on this manifold is further studied using renormalization techniques and for N = 2, 3, and 4, integrable points are found at which the model is equivalent to the bosonized Gross-Neveu model. Finally, the renormalization properties of a class of integrable
Antonov, N V; Gulitskiy, N M
2012-06-01
The field theoretic renormalization group and operator product expansion are applied to the Kazantsev-Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions. PMID:23005154
NASA Astrophysics Data System (ADS)
Katzav, Eytan
2002-06-01
In this paper I discuss a generalization of the well-known Kardar-Parisi-Zhang (KPZ) equation that includes long-range interactions. This Non-local Kardar-Parisi-Zhang (NKPZ) equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of colloids. I show that the steady state strong coupling solution for a subfamily of the NKPZ models can be solved exactly in one dimension, using the Fokker-Planck form of the equation, and yields a Gaussian distribution. This exact result does not agree with a previous result obtained by dynamic renormalization group (DRG) analysis. The reasons for this disagreement are not yet clear.
Vojta, Matthias; Mitchell, Andrew K; Zschocke, Fabian
2016-07-15
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit. PMID:27472132
NASA Astrophysics Data System (ADS)
Carballo-Rubio, Raúl; Barceló, Carlos; Garay, Luis J.
2015-04-01
There exists a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free massless particle with helicity ±2. We have recently shown that this theory can be understood as the result of self-coupling, in complete parallelism to the well-known case of general relativity. This special relativistic field theory of gravity exhibits a decoupling of vacuum zero-point energies of matter and passes all the known experimental tests in gravitation. It is explicitly demonstrated that there is no flow of the effective cosmological constant under the action of the renormalization group at one-loop level, while simple symmetry arguments show that this would continue to be true for higher-loop corrections. The important lesson is that just mild local assumptions concerning the nature of the particle mediating the gravitational interactions are enough to motivate theories which are free of the cosmological constant problem.
NASA Astrophysics Data System (ADS)
Chakrabarti, A.; Karmakar, S. N.; Moitra, R. K.
In this paper we present a study of the electronic properties of a one-dimensional Fibonacci chain with two hybridizing bands. Our study is motivated by recent experiments with quasicrystals in which transition metal atoms occupy positions of icosahedral symmetry. Using a recently proposed real space renormalization group scheme we make an exact analytical study of the two-band problem. We examine the effect of hybridization on the energy spectrum, the wave functions and the density of states of the Fibonacci chain. We find that the spectrum continues to remain a Cantor set even in the presence of hybridization. We conclude therefore this property of the spectrum is a purely structural effect. We present our results on the electronic density of states and show how hybridization produces additional structures in the energy spectrum.
NASA Astrophysics Data System (ADS)
Vojta, Matthias; Mitchell, Andrew K.; Zschocke, Fabian
2016-07-01
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.
Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle.
Pal, Tanmoy; Sadhukhan, Poulomi; Bhattacharjee, Somendra M
2015-04-01
A three-stranded DNA with short range base pairings only is known to exhibit a classical analog of the quantum Efimov effect, viz., a three-chain bound state at the two-chain melting point where no two are bound. By using a nonperturbative renormalization-group method for a rigid duplex DNA and a flexible third strand, with base pairings and strand exchange, we show that the Efimov-DNA is associated with a limit cycle type behavior of the flow of an effective three-chain interaction. The analysis also shows that thermally generated bubbles play an essential role in producing the effect. A toy model for the flow equations shows the limit cycle in an extended three-dimensional parameter space of the two-chain coupling and a complex three-chain interaction. PMID:25974437
NASA Astrophysics Data System (ADS)
Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A.
2016-05-01
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.
Jurgenson, E. D.; Maris, P.; Furnstahl, R. J.; Navratil, P.; Ormand, W. E.; Vary, J. P.
2013-05-13
The similarity renormalization group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While, in principle, the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. As a result, these calculations are used to assessmore » convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.« less
NASA Astrophysics Data System (ADS)
Yuan, Jing; Hu, Jiangping
2016-03-01
Pairing symmetries of iron-based superconductors are investigated systematically in a five-orbital model within the different regions of interaction parameters by functional renormalization group (FRG). Even for a fixed Fermi surface with both hole and electron pockets, it is found that depending on interaction parameters, a variety of pairing symmetries, including two types of d-wave and two types of s-wave pairing symmetries, can emerge. Only the dx^2-y^2 - and the s±-waves are robustly supported by the nearest-neighbor (NN) intra-orbital J 1 and the next-nearest-neighbor (NNN) intra-orbital J 2 antiferromagnetic (AFM) exchange couplings, respectively. This study suggests that the accurate initial input of the interaction parameters is essential to make FRG a useful method to determine the leading channel of superconducting instability.
Das, Mousumi
2014-03-28
We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties. PMID:24697451
Das, Mousumi
2014-03-28
We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties.
Jurgenson, E. D.; Maris, P.; Furnstahl, R. J.; Navratil, P.; Ormand, W. E.; Vary, J. P.
2013-05-13
The similarity renormalization group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While, in principle, the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. As a result, these calculations are used to assess convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.
NASA Astrophysics Data System (ADS)
Yi, Guang-Yu; Wang, Xiao-Qi; Gong, Wei-Jiang; Wu, Hai-Na; Chen, Xiao-Hui
2016-03-01
We investigate the Josephson effect in a triple-quantum-dot ring in which only one dot is coupled to the superconductors, by performing the numerical renormalization group calculations. As a result, two kinds of Josephson phase transitions arise. One is the phase transition accompanied by the sharp change of the current direction, whereas the other phase transition is only accompanied by the smooth change of the current direction. Our analysis shows that in this structure, the phase transitions are determined by the variation of interdot spin correlations. The geometry of triple-dot ring induces various spin-correlation modes, leading to the complicate phase transitions. What's notable is that a spin singlet can form between the two lateral dots, which is decoupled from the main channel of this structure. It is certain that such a structure provides an alternative proposal to manipulate the spin correlation between the lateral dots.
NASA Astrophysics Data System (ADS)
Kholodenko, A. L.; Freed, Karl F.
1983-06-01
We provide the first rigorous treatment of the electrostatic excluded volume for a polyelectrolyte chain which incorporates the effects of salt concentration. Our treatment involves an extension of the t'Hooft-Veltman method of dimensional regularization for polymer excluded volume, developed in the accompanying paper, to the case complicated by the presence of electrostatic interactions. The critical dimensionality for the polyelectrolyte chains with realistic interactions is shown to be four in sharp contrast to previous simplified analyses, which do not consider salt concentration effects explicitly and which lead to a critical dimensionality of six. Our results imply that expansions in ɛ=4-d (with d the dimensionality of space) can be applied, so the theory reduces to the limit of uncharged polymers with excluded volume when the electrostatic interactions become totally screened. Our renormalization group (RG) treatment indicates the absence of stable fixed points, so there is no simple scaling limit. The range of validity of the perturbation expansion is established on the basis of a RG analysis, and a physical meaning of the weak coupling limit is also determined. The predicted lack of universality for the polyelectrolyte chain is in accord with experimental information. Explicit renormalized expressions are derived for the mean squared end-to-end distance
NASA Astrophysics Data System (ADS)
Kumar, Manoranjan; Parvej, Aslam; Thomas, Simil; Ramasesha, S.; Soos, Z. G.
2016-02-01
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N =3 n +1 ≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB . The ground state (GS) and spin densities ρr=
NASA Astrophysics Data System (ADS)
Karndumri, Parinya
2016-08-01
We study various supersymmetric renormalization group (RG) flows of N =3 Chern-Simons-Matter theory in three dimensions by using four-dimensional N =3 gauged supergravity coupled to eight vector multiplets with S O (3 )×S U (3 ) gauge group. The AdS4 critical point preserving the full S O (3 )×S U (3 ) provides a gravity dual of N =3 superconformal field theory with flavor symmetry S U (3 ). We study the scalar potential and identify a new supersymmetric AdS4 critical point preserving the full N =3 supersymmetry and unbroken S O (3 )×U (1 ) symmetry. An analytic RG flow solution interpolating between S O (3 )×S U (3 ) and S O (3 )×U (1 ) critical points is explicitly given. We then investigate possible RG flows from these AdS4 critical points to nonconformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form AdS2×Σ2 with Σ2 being a two-sphere or a two-dimensional hyperbolic space and find a number of AdS2 geometries preserving four supercharges with S O (2 )×S O (2 )×S O (2 ) and S O (2 )×S O (2 ) symmetries.
NASA Astrophysics Data System (ADS)
Kikuchi, K.; Nagahama, H.
2013-12-01
A method to analyze self-affinities is introduced and applied to the large scale fold geometries of Quaternary and Tertiary sediments in the inner belt of the Northeast Honshu Arc, Japan (Kikuchi et al. 2013). Based on this analysis, their geometries are self-affine and can be differently scaled in different directions. They recognize the self-affinities for the amplitude and the wavelength of folds and a crossover from local to global altitude (vertical) variation of the geometries of folds in the Northeast Honshu Arc. Moreover, they discuss self-affinity for the crustal deformation is related to the b-value in Gutenberg-Richter's law, the fractal dimension and the uniformity of the crustal fragmentation. Softening behaviour can lead to localisation of fold packets in layered materials and a progression to chaos with fractal geometries (Hunt and Wadee, 1991). Why do fractal geometries exist and what is the control on the fractal dimension that is responsible for temperature and strain-rate dependence?(Ord and Hobbs, 2011). Shimamoto (1974) examined the conditions of similarity for geometrically similar systems of inhomogeneous viscous Newtonian fluids under similar boundary conditions, making use of the method of dimensional analysis (Buckingham's Pi-theorem). Then, based on the completely similarity, he vividly derived a relationship between the wavelength of fold and initial thickness of folded layer. Buckingham's Pi-theorem is sufficient to the first problems of fold systems. But the complete similarity can not give us the self-affinities of folds. A general renormalization-group argument is proposed to the applicability of the incomplete self-similarity theory (Barenblatt, 1979). So in this paper, based on the general renormalization-group argument, we derive the self-affinities for the amplitude and the wavelength of folds. Keywords: Fold, Self-Affinities, Dimensional Analysis, Pi-theorem, Incomplete self-similarity R e f e r e n c e s Barenblatt, G.I. (1979
NASA Astrophysics Data System (ADS)
van Enter, Aernout C. D.; Fernández, Roberto; Sokal, Alan D.
1993-09-01
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Our main results apply to local (in position space) RG maps acting on systems of bounded spins (compact single-spin space). Regarding regularity, we show that the RG map, defined on a suitable space of interactions (=formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce, and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension d⩾3, these pathologies occur in a full neighborhood { β> β 0, ¦h¦< ɛ( β)} of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension d⩾2, the pathologies occur at low temperatures for arbitrary magnetic field strength. Pathologies may also occur in the critical region for Ising models in dimension d⩾4. We discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems. In addition, we discuss critically the concept of Gibbs measure, which is at the heart of present-day classical statistical mechanics. We provide a careful, and, we hope, pedagogical, overview of the theory of Gibbsian measures as well as (the less familiar) non-Gibbsian measures, emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations. We give a rather complete catalogue of
NASA Astrophysics Data System (ADS)
Zhang, L.; Tang, G.; Xun, Z.; Han, K.; Chen, H.; Hu, B.
2008-05-01
The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-10-01
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on a density-matrix renormalization-group calculation, we provide a complete characterization of the universal properties of the bosonic Moore-Read state on a Haldane honeycomb lattice model at filling number ν =1 for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through simulating a flux-inserting experiment, it is found that two of the Abelian ground states can be adiabatically connected, whereas the ground state in the Ising anyon sector evolves back to itself, which reveals the fusion rules between different QPs in real space. Furthermore, we calculate the modular matrices S and U , which contain all the information for the anyonic QPs, such as quantum dimensions, fusion rule, and topological spins.
NASA Astrophysics Data System (ADS)
Takashima, Hirokazu; Ishihara, Sumio
2010-03-01
In order to study for novel spin and charge orders in strongly correlated electron systems in frustrated lattices,we investigated extended Hubbard model in 2 dimensional (2D) checkerboard and triangular lattices using the functional renormalization group method(fRG) with an improved algorithm [1]. In this method, both the quantum effect and the geometrical frustration effect at finite temperature are taken into account properly. Non-monotonic temperature dependence of the spin susceptibility was observed both in the models . In a 2D isotropic triangular lattice at half-filling, divergence of the particle-particle channel vertex functions was observed in a region of the intermediate value of the on-site Coulomb interaction. We have also investigated the extended Hubbard model with long-range Coulomb interactions. A possibility of the ferromagnetic order and calculations with including the self-energy correction will be introduced .[1] H. Takashima, R. Arita, K. Kuroki, and H. Aoki, J. Phys.: Conf. Ser, 150, 052261 (2009)
NASA Astrophysics Data System (ADS)
Miao, Jian-Jian; Zhang, Fu-Chun; Zhou, Yi
Motivated by recently discovered quasi-one-dimensional superconductor K2Cr3As3 with D3 h lattice symmetry, we study one-dimensional three-orbital Hubbard models with generic electron repulsive interaction described by intra-orbital repulsion U, inter-orbital repulsionU', and Hund's coupling J. As extracted from density functional theory calculation, two of the three atomic orbitals are degenerate and the third one is non-degenerate, and the system is presumed to be at incommensurate filling. With the help of bosonization, we have usual three-band Luttinger liquids in the normal state. Possible charge density wave (CDW), spin density wave (SDW) and superconducting instabilities are analyzed by one-loop renormalization group. The ground state depends on the ratio J / U . For the physical relevant parameter region, 0 < J / U < 1 / 2 , the ground states are superconducting states. When 0 < J / U < 1 / 3 , spin singlet superconducting state is favored. While spin triplet superconductor will be favored when 1 / 3 < J / U < 1 / 2 . The spin density wave state can be achieved only in the unphysical parameter region J / U > 1 / 2 .
Vernek, E.; Büsser, C. A.; Anda, E. V.; Feiguin, A. E.; Martins, G. B.
2014-03-31
A double quantum dot device, connected to two channels that only interact through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. Using a two-impurity Anderson model, and realistic parameter values [S. Amasha, A. J. Keller, I. G. Rau, A. Carmi, J. A. Katine, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Phys. Rev. Lett. 110, 046604 (2013)], it is shown that, by applying a moderate magnetic field and independently adjusting the gate potential of each quantum dot at half-filling, a spin-orbital SU(2) Kondo state can be achieved where the Kondo resonance originates from spatially separated parts of the device. Our results clearly link this spatial separation effect to currents with opposing spin polarizations in each channel, i.e., the device acts as a spin filter. In addition, an experimental probe of this polarization effect is suggested, pointing to the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.
Tsai, Y.S.
1983-01-01
Renormalization group technique is used to improve the accuracy of the lowest order radiative corrections in QED. The exponentiation of infrared terms comes automatically. It also leads to exponentiation of the vertex functions. It predicts the existence of conversion of photons into pairs and the result agrees with the Kroll-Wada relation. Kinoshita-Lee-Nauenberg cancellation of mass singularities occurs to all order in ..cap alpha.. in leading log approximation in the final state if we sum over all the final states. Higher order corrections to the order ..cap alpha../sup 3/ asymmetry is shown to be small. The results are used to derive useful formulas for the radiative corrections to processes such as e/sup +/e/sup -/ ..-->.. ..mu../sup +/..mu../sup -/, e/sup +/e/sup -/ ..-->.. ..mu../sup +/..mu../sup -/..gamma.., e/sup +/e/sup -/ ..-->.. hadron continuum, e/sup +/e/sup -/ ..-->.. very narrow resonance such as phi, and e/sup +/e/sup -/ ..-->.. not very narrow resonance such as Z/sup 0/.
NASA Astrophysics Data System (ADS)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2008-04-01
We study the polymer system consisting of two polymer chains situated in a fractal container that belongs to the three-dimensional Sierpinski gasket (3D SG) family of fractals. Each 3D SG fractal has four fractal impenetrable 2D surfaces, which are, in fact, 2D SG fractals. The two-polymer system is modeled by two interacting self-avoiding walks (SAW), one of them representing a 3D floating polymer, while the other corresponds to a chain confined to one of the four 2D SG boundaries (with no monomer in the bulk). We assume that the studied system is immersed in a poor solvent inducing the intra-chain interactions. For the inter-chain interactions we propose two models: in the first model (ASAW) the SAW chains are mutually avoiding, whereas in the second model (CSAW) chains can cross each other. By applying an exact renormalization group (RG) method, we establish the relevant phase diagrams for b = 2,3 and 4 members of the 3D SG fractal family for the model with avoiding SAWs, and for b = 2 and 3 fractals for the model with crossing SAWs. Also, at the appropriate transition fixed points we calculate the contact critical exponents, associated with the number of contacts between monomers of different chains. Throughout this paper we compare results obtained for the two models and discuss the impact of the topology of the underlying lattices on emerging phase diagrams.
Hannon, Kevin P; Li, Chenyang; Evangelista, Francesco A
2016-05-28
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples. PMID:27250283
NASA Astrophysics Data System (ADS)
Gour, Jeffrey R.; Piecuch, Piotr; Włoch, Marta
2010-10-01
The left-eigenstate completely renormalized (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as CR-EOMCC(2,3) [M. Włoch et al., Mol. Phys. 104, 2149 (2006); P. Piecuch et al., Int. J. Quantum Chem. 109, 3268 (2009)], and the companion ground-state CR-CC(2,3) methodology [P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005); P. Piecuch et al., Chem. Phys. Lett. 418, 467 (2006)] are used to determine the total electronic and adiabatic excitation energies corresponding to the ground and lowest three excited states of methylene. The emphasis is on comparing the CR-CC(2,3)/CR-EOMCC(2,3) results obtained with the large correlation-consistent basis sets of the aug-cc-pCV xZ (x = T, Q, 5) quality and the corresponding complete basis set (CBS) limits with the recently published variational and diffusion Quantum Monte Carlo (QMC) data [P. Zimmerman et al., J. Chem. Phys. 131, 124103 (2009)]. It is demonstrated that the CBS CR-CC(2,3)/CR-EOMCC(2,3) results are in very good agreement with the best QMC, i.e. diffusion MC (DMC) data, with errors in the total and adiabatic excitation energies of all calculated states on the order of a few millihartree and less than 0.1 eV, respectively, even for the challenging, strongly multi-reference C 1 A 1 state for which the basic EOMCC approach with singles and doubles completely fails. The agreement between the CBS CR-CC(2,3)/CR-EOMCC(2,3) and variational MC (VMC) results for the total energies is not as good as in the DMC case, but the excitation energies resulting from the CBS CR-CC(2,3)/CR-EOMCC(2,3) and VMC calculations agree very well.
Katanin, A. A.
2015-06-15
We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.
Stadler, K M; Yin, Z P; von Delft, J; Kotliar, G; Weichselbaum, A
2015-09-25
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales. PMID:26451570
NASA Astrophysics Data System (ADS)
Stadler, K. M.; Yin, Z. P.; von Delft, J.; Kotliar, G.; Weichselbaum, A.
2015-09-01
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1 /3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
NASA Astrophysics Data System (ADS)
Eberlein, Andreas
2015-12-01
We study the impact of the fermionic self-energy on one-loop functional renormalization group flows of the two-dimensional t -t' Hubbard model, with emphasis on electronic densities away from van Hove filling. In the presence of antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a flattening of the Fermi surface, shift magnetic phase boundaries, and significantly enhance critical scales. We trace back this effect to the presence of a magnetic first-order transition. For some parameters, the first-order character of the latter is reduced by self-energy effects. For reliably determining phase diagrams, the fermionic self-energy should be taken into account in functional renormalization group studies if scattering between hot spots is important.
Relating theories via renormalization
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.
2013-02-01
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of 150 years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behaviors separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. However, no renormalization gives a fully satisfactory formulation of field theory. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications, particularly to condensed-matter physics and particle physics, are summarized. This note is partially a
NASA Astrophysics Data System (ADS)
Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.
2014-11-01
We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.
Generation of SFR few-group constants using the Monte Carlo code Serpent
Fridman, E.; Rachamin, R.; Shwageraus, E.
2013-07-01
In this study, the Serpent Monte Carlo code was used as a tool for preparation of homogenized few-group cross sections for the nodal diffusion analysis of Sodium cooled Fast Reactor (SFR) cores. Few-group constants for two reference SFR cores were generated by Serpent and then employed by nodal diffusion code DYN3D in 2D full core calculations. The DYN3D results were verified against the references full core Serpent Monte Carlo solutions. A good agreement between the reference Monte Carlo and nodal diffusion results was observed demonstrating the feasibility of using Serpent for generation of few-group constants for the deterministic SFR analysis. (authors)
Roemelt, Michael
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
NASA Astrophysics Data System (ADS)
Žitko, Rok
2011-08-01
In the numerical renormalization-group (NRG) calculations of spectral functions of quantum impurity models, the results are always affected by discretization and truncation errors. The discretization errors can be alleviated by averaging over different discretization meshes (“z-averaging”), but since each partial calculation is performed for a finite discrete system, there are always some residual discretization and finite-size errors. The truncation errors affect the energies of the states and result in the displacement of the delta-peak spectral contributions from their correct positions. The two types of errors are interrelated: for coarser discretization, the discretization errors increase, but the truncation errors decrease since the separation of energy scales is enhanced. In this work, it is shown that by calculating a series of spectral functions for a range of the total number of states kept in the NRG truncation, it is possible to estimate the errors and determine the error bars for spectral functions, which is important when making accurate comparison to the results obtained by other methods and for determining the errors in the extracted quantities (such as peak positions, heights, and widths). The closely related problem of spectral broadening is also discussed: it is shown that the overbroadening contorts the results without, surprisingly, reducing the variance of the curves. It is thus important to determine the results in the limit of zero broadening. The method is applied to determine the error bounds for the Kondo peak splitting in an external magnetic field. For moderately strong fields, the results are consistent with the Bethe ansatz study by Moore and Wen [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.85.1722 85, 1722 (2000)]. We also discuss the regime of large U/Γ ratio. It is shown that in the strong-field limit, a spectral step is observed in the spectrum precisely at the Zeeman frequency until the field becomes so strong that
NASA Astrophysics Data System (ADS)
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-01
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
NASA Astrophysics Data System (ADS)
Roemelt, Michael
2015-07-01
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
Roemelt, Michael
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method. PMID:26233112
Symmetric blocking and renormalization in lattice N=4 super Yang-Mills
NASA Astrophysics Data System (ADS)
Giedt, Joel; Catterall, Simon
2015-04-01
The form of the long distance effective action of the twisted lattice N = 4 super Yang-Mills theory depends on having a real space renormalization group transformation that preserves the original lattice properties, both the symmetries and the geometric interpretation of the fields. We have found such a transformation and have exhibited its behavior through a preliminary Monte Carlo renormalization group calculation. Other results regarding the number of counterterms are also obtained by considering rescalings of the lattice fields. Supported by Department of Energy, Office of Science, Office of High Energy Physics Grants DE-FG02-08ER41575 and SC0009998.
NASA Astrophysics Data System (ADS)
Aoki, Ken-Ichi; Sato, Daisuke
The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DχSB) in QCD. We show that the DχSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.
Men'shenin, V. V.
2013-06-15
A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn{sub 2}O{sub 5} multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.
Revised methods for few-group cross sections generation in the Serpent Monte Carlo code
Fridman, E.; Leppaenen, J.
2012-07-01
This paper presents new calculation methods, recently implemented in the Serpent Monte Carlo code, and related to the production of homogenized few-group constants for deterministic 3D core analysis. The new methods fall under three topics: 1) Improved treatment of neutron-multiplying scattering reactions, 2) Group constant generation in reflectors and other non-fissile regions and 3) Homogenization in leakage-corrected criticality spectrum. The methodology is demonstrated by a numerical example, comparing a deterministic nodal diffusion calculation using Serpent-generated cross sections to a reference full-core Monte Carlo simulation. It is concluded that the new methodology improves the results of the deterministic calculation, and paves the way for Monte Carlo based group constant generation. (authors)
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz
NASA Astrophysics Data System (ADS)
Evenbly, G.; Vidal, G.
2015-11-01
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e-β H for infinite β . This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β , produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Improved convergence of Monte Carlo generated multi-group scattering moments
Nelson, A. G.; Martin, W. R.
2013-07-01
This paper introduces an improved method of obtaining multi-group scattering moments from a Monte Carlo neutron transport code for use in deterministic transport solvers. The new method increases the information obtained from scattering events and therefore has more useful convergence characteristics than the currently used analog techniques. A prototype of the improved method was implemented in the OpenMC Monte Carlo transport code to compare the accuracy and convergence characteristics of the new method. The prototype showed that accuracy was retained (or improved) while increasing the figure-of-merit for the generation of multi-group scattering moments. (authors)
NASA Astrophysics Data System (ADS)
Yunus, ćaǧın; Renklioǧlu, Başak; Keskin, Mustafa; Berker, A. Nihat
2016-06-01
The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d =3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d =3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.
Crisan, M.; Grosu, I.; Tifrea, I.; Bodea, D.
2005-11-01
We use the renormalization-group method to study the magnetic field influence on the Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems. We first considered a model with SU(2) symmetry (universality class z=1) and we obtain for the critical magnetic field a power law dependence on the critical temperature, [H{sub c}(T)-H{sub c}(0)]{approx}T{sup 2}. In the case of U(1) symmetry (universality class z=2) the dependence is different, and the magnetic critical field depends linearly on the critical temperature, [H{sub c}(T)-H{sub c}(0)]{approx}T. By considering a more relevant model, which includes also the system's anisotropy, we obtain for the same symmetry class a T{sup 3/2} dependence of the magnetic critical field on the critical temperature. We discuss these theoretical predictions of the renormalization group in connection with experimental results reported in the literature.
Phung, Quan Manh; Wouters, Sebastian; Pierloot, Kristine
2016-09-13
The complete active space second order perturbation theory (CASPT2) can be extended to larger active spaces by using the density matrix renormalization group (DMRG) as solver. Two variants are commonly used: the costly DMRG-CASPT2 with exact 4-particle reduced density matrix (4-RDM) and the cheaper DMRG-cu(4)-CASPT2 in which the 4-cumulant is discarded. To assess the accuracy and limitations of the latter variant DMRG-cu(4)-CASPT2 we study the spin state energetics of iron porphyrin Fe(P) and its model compound FeL2, a model for the active center of NiFe hydrogenase, and manganese-oxo porphyrin MnO(P)(+); a series of excited states of chromium hexacarbonyl Cr(CO)6; and the interconversion of two Cu2O2(2+) isomers. Our results clearly show that PT2 on top of DMRG is essential in order to obtain quantitative results for transition metal complexes. Good results were obtained with DMRG-cu(4)-CASPT2 as compared to full CASPT2 and DMRG-CASPT2 in calculations with small- and medium-sized active spaces. In calculations with large-sized active spaces (∼30 active orbitals), the performance of DMRG-cu(4)-CASPT2 is less impressive due to the errors originating from both the finite number of renormalized states m and the 4-RDM approximation. PMID:27547847
NASA Astrophysics Data System (ADS)
de Carvalho, Vanuildo S.; Freire, Hermann
2013-10-01
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O8 + δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.
Matsumoto, M.; Arafune, J. ); Tanaka, H. ); Shiraishi, K. )
1992-11-01
A minimal {ital N}=1 supergravity SU(5) grand unified theory (GUT) is studied for a heavy top-quark mass ({ital m}{sub {ital t}}{ge}90 GeV). Renormalization-group equations are solved without neglecting the Yukawa couplings for the third generation of quarks and leptons. The solutions for mass parameters are expressed as linear combinations of the initial-value parameters of the model at the GUT scale and the coefficients are numerically obtained. This semianalytical expression of the solutions makes it easy to use the results for low-energy phenomenology. Approximate analytical solutions valid for small tan{beta} ({lt}8) are also given. Combining theoretical considerations with experimental restrictions due to the CERN {ital e}{sup +}{ital e{minus}} collider LEP, the Collider Detector at Fermilab (CDF), and the proton decay experiments of Kamiokande, we can show that the very limited supersymmetric parameter space remains allowed.
Thermodynamics of the two-dimensional XY model from functional renormalization
NASA Astrophysics Data System (ADS)
Jakubczyk, P.; Eberlein, A.
2016-06-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ4-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.
Renormalized action improvements
Zachos, C.
1984-01-01
Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references.
Finch, W Holmes; Bolin, Jocelyn H; Kelley, Ken
2014-01-01
Classification using standard statistical methods such as linear discriminant analysis (LDA) or logistic regression (LR) presume knowledge of group membership prior to the development of an algorithm for prediction. However, in many real world applications members of the same nominal group, might in fact come from different subpopulations on the underlying construct. For example, individuals diagnosed with depression will not all have the same levels of this disorder, though for the purposes of LDA or LR they will be treated in the same manner. The goal of this simulation study was to examine the performance of several methods for group classification in the case where within group membership was not homogeneous. For example, suppose there are 3 known groups but within each group two unknown classes. Several approaches were compared, including LDA, LR, classification and regression trees (CART), generalized additive models (GAM), and mixture discriminant analysis (MIXDA). Results of the study indicated that CART and mixture discriminant analysis were the most effective tools for situations in which known groups were not homogeneous, whereas LDA, LR, and GAM had the highest rates of misclassification. Implications of these results for theory and practice are discussed. PMID:24904445
NASA Astrophysics Data System (ADS)
Dutta, Tirthankar; Ramasesha, S.
2012-01-01
In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)x-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)x-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)x-A, systems in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a “quasi-static” state.
Application de la methode des sous-groupes au calcul Monte-Carlo multigroupe
NASA Astrophysics Data System (ADS)
Martin, Nicolas
This thesis is dedicated to the development of a Monte Carlo neutron transport solver based on the subgroup (or multiband) method. In this formalism, cross sections for resonant isotopes are represented in the form of probability tables on the whole energy spectrum. This study is intended in order to test and validate this approach in lattice physics and criticality-safety applications. The probability table method seems promising since it introduces an alternative computational way between the legacy continuous-energy representation and the multigroup method. In the first case, the amount of data invoked in continuous-energy Monte Carlo calculations can be very important and tend to slow down the overall computational time. In addition, this model preserves the quality of the physical laws present in the ENDF format. Due to its cheap computational cost, the multigroup Monte Carlo way is usually at the basis of production codes in criticality-safety studies. However, the use of a multigroup representation of the cross sections implies a preliminary calculation to take into account self-shielding effects for resonant isotopes. This is generally performed by deterministic lattice codes relying on the collision probability method. Using cross-section probability tables on the whole energy range permits to directly take into account self-shielding effects and can be employed in both lattice physics and criticality-safety calculations. Several aspects have been thoroughly studied: (1) The consistent computation of probability tables with a energy grid comprising only 295 or 361 groups. The CALENDF moment approach conducted to probability tables suitable for a Monte Carlo code. (2) The combination of the probability table sampling for the energy variable with the delta-tracking rejection technique for the space variable, and its impact on the overall efficiency of the proposed Monte Carlo algorithm. (3) The derivation of a model for taking into account anisotropic
Chishtie, F. A.; Jia, J.; Hanif, T.; Mann, R. B.; McKeon, D. G. C.; Sherry, T. N.; Steele, T. G.
2011-05-15
We consider the effective potential V in the standard model with a single Higgs doublet in the limit that the only mass scale {mu} present is radiatively generated. Using a technique that has been shown to determine V completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to V using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling x, the quartic coupling of the Higgs field y, the SU(3) gauge coupling z, and the SU(2)xU(1) couplings r and s). We then employ the two loop RG functions with the three couplings x, y, z to sum the next-to-leading-log (NLL) contributions to V and then the three to five loop RG functions with one coupling y to sum all the N{sup 2}LL...N{sup 4}LL contributions to V. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the LL result is m{sub H}=219 GeV/c{sup 2} and decreases to m{sub H}=188 GeV/c{sup 2} at N{sup 2}LL order and m{sub H}=163 GeV/c{sup 2} at N{sup 4}LL order. No reasonable estimate of m{sub H} can be made at orders V{sub NLL} or V{sub N}{sup 3}{sub LL} since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for m{sub H} from the LL, N{sup 2}LL, and N{sup 4}LL approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of m{sub H}. The mass 163 GeV/c{sup 2} is argued to be an upper bound on m{sub H}.
DelGrande, J. Mark; Mathews, Kirk A.
2001-09-15
Conventional discrete ordinates transport calculations often produce negative fluxes due to unphysical negative scattering cross sections and/or as artifacts of spatial differencing schemes such as diamond difference. Inherently nonnegative spatial methods, such as the nonlinear, exponential characteristic spatial quadrature, eliminate negative fluxes while providing excellent accuracy, presuming the group-to-group, ordinate-to-ordinate cross sections are all nonnegative. A hybrid approach is introduced in which the flow from spatial cell to spatial cell uses discrete ordinates spatial quadratures, while anisotropic scattering of flux from one energy-angle bin (energy group and discrete element of solid angle) to another such bin is modeled using a Monte Carlo simulation to evaluate the bin-to-bin cross sections. The directional elements tile the sphere of directions; the ordinates for the spatial quadrature are at the centroids of the elements. The method is developed and contrasted with previous schemes for positive cross sections. An algorithm for evaluating the Monte Carlo (MC)-discrete elements (MC-DE) cross sections is described, and some test cases are presented. Transport calculations using MC-DE cross sections are compared with calculations using conventional cross sections and with MCNP calculations. In this testing, the new method is about as accurate as the conventional approach, and often is more accurate. The exponential characteristic spatial quadrature, using the MC-DE cross sections, is shown to provide useful results where linear characteristic and spherical harmonics provide negative scalar fluxes in every cell in a region.
NASA Astrophysics Data System (ADS)
Freire, Hermann; de Carvalho, Vanuildo
2015-03-01
The two-loop renormalization group (RG) calculation is considerably extended here for a two-dimensional (2D) fermionic effective field theory model, which includes only the so-called ``hot spots'' that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t -t' Hubbard model at low hole doping. We compute the Callan-Symanzik RG equation up to two loops describing the flow of the single-particle Green's function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that - in addition to clearly dominant SDW correlations - an approximate (pseudospin) symmetry relating a short-range incommensurate d-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates. We acknowledge financial support from CNPq under Grant No. 245919/2012-0 and FAPEG under Grant No. 201200550050248 for this project.
NASA Astrophysics Data System (ADS)
Tsuchiizu, Masahisa; Yamakawa, Youichi; Kontani, Hiroshi
2016-04-01
The discovery of the charge-density-wave formation in the high-Tc cuprate superconductors has activated intensive theoretical studies for the pseudogap states. However, the microscopic origin of the charge-density-wave state has been unknown so far since the many-body effects beyond the mean-field-level approximations, called the vertex corrections, are essential. Toward solving this problem, we employ the recently developed functional renormalization group method, by which we can calculate the higher-order vertex corrections in a systematic and unbiased way with high numerical accuracy. We discover the critical development of the p -orbital-density-wave (p -ODW) instability in the strong-spin-fluctuation region. The obtained p -ODW state possesses the key characteristics of the charge-ordering pattern in Bi- and Y-based superconductors, such as the wave vector parallel to the nearest Cu-Cu direction, and the d -symmetry form factor with the antiphase correlation between px and py orbitals in the same unit cell. In addition, from the observation of the beautiful scaling relation between the spin susceptibility and the p -ODW susceptibility, we conclude that the main driving force of the density wave is the Aslamazov-Larkin vertex correction that becomes very singular near the magnetic quantum-critical point.
NASA Astrophysics Data System (ADS)
Cherayil, Binny J.; Bhattacharyya, Pinaki
2014-06-01
The average time τr for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a "sink" term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of τr on N mirrors the behavior of the average time τc of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which τr ˜ N2.2. A simulation study by Cheng and Makarov [J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N2.2 behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react.
NASA Astrophysics Data System (ADS)
Wouters, Sebastian; Poelmans, Ward; Ayers, Paul W.; Van Neck, Dimitri
2014-06-01
The density matrix renormalization group (DMRG) has become an indispensable numerical tool to find exact eigenstates of finite-size quantum systems with strong correlation. In the fields of condensed matter, nuclear structure and molecular electronic structure, it has significantly extended the system sizes that can be handled compared to full configuration interaction, without losing numerical accuracy. For quantum chemistry (QC), the most efficient implementations of DMRG require the incorporation of particle number, spin and point group symmetries in the underlying matrix product state (MPS) ansatz, as well as the use of so-called complementary operators. The symmetries introduce a sparse block structure in the MPS ansatz and in the intermediary contracted tensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows to factorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. In addition, the fermion signs have to be carefully tracked. Because of these challenges, implementing DMRG efficiently for QC is not straightforward. Efficient and freely available implementations are therefore highly desired. In this work we present CheMPS2, our free open-source spin-adapted implementation of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented Hessian Newton-Raphson complete active space self-consistent field method, with exact Hessian. The bond dissociation curves of the 12 lowest states of the carbon dimer were obtained at the DMRG(28 orbitals, 12 electrons, DSU(2) = 2500)/cc-pVDZ level of theory. The contribution of 1 s core correlation to the X1Σg+ bond dissociation curve of the carbon dimer was estimated by comparing energies at the DMRG(36o, 12e, DSU(2) = 2500)/cc-pCVDZ and DMRG-SCF(34o, 8e, DSU(2) = 2500)/cc-pCVDZ levels of theory.
Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; Detmold, William; Pochinsky, Andrew V.
2015-12-29
In this study, we present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
NASA Astrophysics Data System (ADS)
Nelson, Adam
Multi-group scattering moment matrices are critical to the solution of the multi-group form of the neutron transport equation, as they are responsible for describing the change in direction and energy of neutrons. These matrices, however, are difficult to correctly calculate from the measured nuclear data with both deterministic and stochastic methods. Calculating these parameters when using deterministic methods requires a set of assumptions which do not hold true in all conditions. These quantities can be calculated accurately with stochastic methods, however doing so is computationally expensive due to the poor efficiency of tallying scattering moment matrices. This work presents an improved method of obtaining multi-group scattering moment matrices from a Monte Carlo neutron transport code. This improved method of tallying the scattering moment matrices is based on recognizing that all of the outgoing particle information is known a priori and can be taken advantage of to increase the tallying efficiency (therefore reducing the uncertainty) of the stochastically integrated tallies. In this scheme, the complete outgoing probability distribution is tallied, supplying every one of the scattering moment matrices elements with its share of data. In addition to reducing the uncertainty, this method allows for the use of a track-length estimation process potentially offering even further improvement to the tallying efficiency. Unfortunately, to produce the needed distributions, the probability functions themselves must undergo an integration over the outgoing energy and scattering angle dimensions. This integration is too costly to perform during the Monte Carlo simulation itself and therefore must be performed in advance by way of a pre-processing code. The new method increases the information obtained from tally events and therefore has a significantly higher efficiency than the currently used techniques. The improved method has been implemented in a code system
NASA Astrophysics Data System (ADS)
Patel, Niravkumar D.; Nocera, Alberto; Alvarez, Gonzalo; Arita, Ryotaro; Moreo, Adriana; Dagotto, Elbio
2016-08-01
The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe2S3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015), 10.1038/nmat4351] opens a broad avenue of research, because it represents the first report of pairing tendencies in a quasi-one-dimensional iron-based high-critical-temperature superconductor. Similarly, as in the case of the cuprates, ladders and chains can be far more accurately studied using many-body techniques and model Hamiltonians than their layered counterparts, particularly if several orbitals are active. In this publication, we derive a two-orbital Hubbard model from first principles that describes individual ladders of BaFe2S3 . The model is studied with the density matrix renormalization group. These first reported results are exciting for two reasons: (i) at half-filling, ferromagnetic order emerges as the dominant magnetic pattern along the rungs of the ladder, and antiferromagnetic order along the legs, in excellent agreement with neutron experiments; and (ii) with hole doping, pairs form in the strong coupling regime, as found by studying the binding energy of two holes doped on the half-filled system. In addition, orbital selective Mott phase characteristics develop with doping, with only one Wannier orbital receiving the hole carriers while the other remains half-filled. These results suggest that the analysis of models for iron-based two-leg ladders could clarify the origin of pairing tendencies and other exotic properties of iron-based high-critical-temperature superconductors in general.
NASA Astrophysics Data System (ADS)
Shirakawa, Tomonori; Yunoki, Seiji
2016-05-01
The density matrix renormalization group method is introduced in energy space to study Anderson impurity models. The method allows for calculations in the thermodynamic limit and is advantageous for studying not only the dynamical properties, but also the quantum entanglement of the ground state at the vicinity of an impurity quantum phase transition. This method is applied to obtain numerically exactly the ground-state phase diagram of the single-impurity Anderson model on the honeycomb lattice at half-filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase, but no Kondo screening phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model using the method introduced here. Although the high-energy excitations are obviously different, we find that the ground-state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single-impurity Anderson model on the honeycomb lattice, thus providing a quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally threefold degenerate at the valence fluctuating point. This should be contrasted with the degeneracy of the energy spectrum because the ground state is found to be always singlet. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
Renormalization in Periodically Driven Quantum Dots.
Eissing, A K; Meden, V; Kennes, D M
2016-01-15
We report on strong renormalization encountered in periodically driven interacting quantum dots in the nonadiabatic regime. Correlations between lead and dot electrons enhance or suppress the amplitude of driving depending on the sign of the interaction. Employing a newly developed flexible renormalization-group-based approach for periodic driving to an interacting resonant level we show analytically that the magnitude of this effect follows a power law. Our setup can act as a non-Markovian, single-parameter quantum pump. PMID:26824557
Sechopoulos, Ioannis; Ali, Elsayed S M; Badal, Andreu; Badano, Aldo; Boone, John M; Kyprianou, Iacovos S; Mainegra-Hing, Ernesto; McMillan, Kyle L; McNitt-Gray, Michael F; Rogers, D W O; Samei, Ehsan; Turner, Adam C
2015-10-01
The use of Monte Carlo simulations in diagnostic medical imaging research is widespread due to its flexibility and ability to estimate quantities that are challenging to measure empirically. However, any new Monte Carlo simulation code needs to be validated before it can be used reliably. The type and degree of validation required depends on the goals of the research project, but, typically, such validation involves either comparison of simulation results to physical measurements or to previously published results obtained with established Monte Carlo codes. The former is complicated due to nuances of experimental conditions and uncertainty, while the latter is challenging due to typical graphical presentation and lack of simulation details in previous publications. In addition, entering the field of Monte Carlo simulations in general involves a steep learning curve. It is not a simple task to learn how to program and interpret a Monte Carlo simulation, even when using one of the publicly available code packages. This Task Group report provides a common reference for benchmarking Monte Carlo simulations across a range of Monte Carlo codes and simulation scenarios. In the report, all simulation conditions are provided for six different Monte Carlo simulation cases that involve common x-ray based imaging research areas. The results obtained for the six cases using four publicly available Monte Carlo software packages are included in tabular form. In addition to a full description of all simulation conditions and results, a discussion and comparison of results among the Monte Carlo packages and the lessons learned during the compilation of these results are included. This abridged version of the report includes only an introductory description of the six cases and a brief example of the results of one of the cases. This work provides an investigator the necessary information to benchmark his/her Monte Carlo simulation software against the reference cases included here
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2015-11-10
We present an extended implementation of the multireference configuration interaction (MRCI) method combined with the quantum-chemical density matrix renormalization group (DMRG). In the previous study, we introduced the combined theory, referred to as DMRGMRCI, as a method to calculate high-level dynamic electron correlation on top of the DMRG wave function that accounts for active-space (or strong) correlation using a large number of active orbitals. The DMRG-MRCI method is built on the full internal-contraction scheme for the compact reference treatment and on the cumulant approximation for the treatment of the four-particle rank reduced density matrix (4-RDM). The previous implementation achieved the MRCI calculations with the active space (24e,24o), which are deemed the record largest, whereas the inherent Nact 8 × N complexity of computation was found a hindrance to using further large active space. In this study, an extended optimization of the tensor contractions is developed by explicitly incorporating the rank reduction of the decomposed form of the cumulant-approximated 4-RDM into the factorization. It reduces the computational scaling (to Nact7 × N) as well as the cache-miss penalty associated with direct evaluation of complex cumulant reconstruction. The present scheme, however, faces the increased complexity of factorization patterns for optimally implementing the tensor contraction terms involving the decomposed 4-RDM objects. We address this complexity using the enhanced symbolic manipulation computer program for deriving and coding programmable equations. The new DMRG-MRCI implementation is applied to the determination of the stability of the iron(IV)-oxo porphyrin relative to the iron(V) electronic isomer (electromer) using the active space (29e,29o) (including four second d-shell orbitals of iron) with triple-ζ-quality atomic orbital basis sets. The DMRG-cu(4)-MRCI+Q model is shown to favor the triradicaloid iron(IV)-oxo state as the lowest
Assassi, Valentin; Baumann, Daniel; Green, Daniel; Zaldarriaga, Matias E-mail: dbaumann@damtp.cam.ac.uk E-mail: matiasz@ias.edu
2014-08-01
This paper provides a systematic study of renormalization in models of halo biasing. Building on work of McDonald, we show that Eulerian biasing is only consistent with renormalization if non-local terms and higher-derivative contributions are included in the biasing model. We explicitly determine the complete list of required bias parameters for Gaussian initial conditions, up to quartic order in the dark matter density contrast and at leading order in derivatives. At quadratic order, this means including the gravitational tidal tensor, while at cubic order the velocity potential appears as an independent degree of freedom. Our study naturally leads to an effective theory of biasing in which the halo density is written as a double expansion in fluctuations and spatial derivatives. We show that the bias expansion can be organized in terms of Galileon operators which aren't renormalized at leading order in derivatives. Finally, we discuss how the renormalized bias parameters impact the statistics of halos.
Renormalization of stochastic lattice models: basic formulation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2007-10-01
We describe a general method for the multiscale analysis of stochastic lattice models. Beginning with a lattice Langevin formulation of site fluctuations, we derive stochastic partial differential equations by regularizing the transition rules of the model. Subsequent coarse graining is accomplished by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. The RG trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales. These continuum equations retain a quantitative connection over different scales, as well as to the underlying atomistic dynamics. This provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales. As an illustration we consider the one-dimensional (1D) Wolf-Villain (WV) model [Europhys. Lett. 13, 389 (1990)]. The RG analysis of this model, which we develop in detail, is generic and can be applied to a wide range of conservative lattice models. The RG trajectory of the 1D WV model shows a complex crossover sequence of linear and nonlinear stochastic differential equations, which is in excellent agreement with kinetic Monte Carlo simulations of this model. We conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems. PMID:17994944
Renormalizing Operator-Stable Lagrangian Velocities for Microbial Dynamics Simulations
NASA Astrophysics Data System (ADS)
Cushman, J. H.; Park, M.
2008-05-01
In previous works we've developed upscaling methodologies for stable Levy Lagrangian velocities in fractal media. The renormalization tools were generalized central limit theorems which are equivalent to a renormalization group approach. Here we extend these ides to operator-stable Lagrangian velocities and apply the results to microbial dynamics in multi-scale geologic formations. Renormalized Fokker-Planck equations are presented at each scale.
Trippe, T.G.; Lynch, G.R.
1987-11-01
The Berkeley Particle Data Group is considering providing a single standard numbering scheme for use in programs for high energy physics Monte Carlo event generation, detector simulation, and analysis. The purpose is to facilitate standardizing the interfaces between these programs, to reduce the possibility for errors, and to simplify code maintenance. Several schemes have been studied and a tentative proposal is given. The possibility of the Particle Data Group providing decay tables and material properties tables is discussed.
Remark on the subtractive renormalization of the quadratically divergent scalar mass
Fujikawa, Kazuo
2011-05-15
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We reexamine some technical aspects of the subtractive renormalization, in particular, the mass-independent renormalization of massive {lambda}{phi}{sup 4} theory with higher derivative regularization. We then discuss an unconventional scheme to introduce the notion of renormalization point {mu} to the subtractive renormalization in a theory defined by a large fixed cutoff M. The resulting renormalization group equation generally becomes inhomogeneous, but it is transformed to be homogeneous. The renormalized scalar mass consists of two components in this scheme, one with the ordinary anomalous dimension and the other which is proportional to the renormalization scale {mu}. This scheme interpolates between the theory defined by dimensional regularization and the theory with unsubtracted quadratic divergences.
Renormalization and plasma physics
Krommes, J.A.
1980-02-01
A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.
Renormalization for breakup of invariant tori
NASA Astrophysics Data System (ADS)
Apte, A.; Wurm, A.; Morrison, P. J.
2005-01-01
We present renormalization group operators for the breakup of invariant 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. Coordinate transformations on the space of maps relate these fixed points, and also induce conjugacies between the corresponding operators.
Renormalization of the neutrino mass matrix
NASA Astrophysics Data System (ADS)
Chiu, S. H.; Kuo, T. K.
2016-09-01
In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.
Renormalization of the quark mass matrix
NASA Astrophysics Data System (ADS)
Chiu, S. H.; Kuo, T. K.
2016-05-01
Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We also found approximate solutions to these equations if the quark masses are hierarchical or nearly degenerate.
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2014-11-15
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.
Renormalizing Entanglement Distillation
NASA Astrophysics Data System (ADS)
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens
2016-01-01
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
Somasundaram, E.; Palmer, T. S.
2013-07-01
In this paper, the work that has been done to implement variance reduction techniques in a three dimensional, multi group Monte Carlo code - Tortilla, that works within the frame work of the commercial deterministic code - Attila, is presented. This project is aimed to develop an integrated Hybrid code that seamlessly takes advantage of the deterministic and Monte Carlo methods for deep shielding radiation detection problems. Tortilla takes advantage of Attila's features for generating the geometric mesh, cross section library and source definitions. Tortilla can also read importance functions (like adjoint scalar flux) generated from deterministic calculations performed in Attila and use them to employ variance reduction schemes in the Monte Carlo simulation. The variance reduction techniques that are implemented in Tortilla are based on the CADIS (Consistent Adjoint Driven Importance Sampling) method and the LIFT (Local Importance Function Transform) method. These methods make use of the results from an adjoint deterministic calculation to bias the particle transport using techniques like source biasing, survival biasing, transport biasing and weight windows. The results obtained so far and the challenges faced in implementing the variance reduction techniques are reported here. (authors)
Renormalization and power counting of chiral nuclear forces
Long, Bingwei
2013-08-01
I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.
Nonperturbative renormalization of scalar quantum electrodynamics in d=3
Dimock, J.
2015-10-15
For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban’s approach to the renormalization group.
Multilogarithmic velocity renormalization in graphene
NASA Astrophysics Data System (ADS)
Sharma, Anand; Kopietz, Peter
2016-06-01
We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene. Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff scheme, we calculate the quasiparticle velocity, v (k ) , and the quasiparticle residue, Z , with frequency-dependent polarization. One of our most striking results is that v (k ) ∝ln[Ck(α ) /k ] where the momentum- and interaction-dependent cutoff scale Ck(α ) vanishes logarithmically for k →0 . Here k is measured with respect to one of the charge neutrality (Dirac) points and α =2.2 is the strength of dimensionless bare interaction. Moreover, we also demonstrate that the so-obtained multilogarithmic singularity is reconcilable with the perturbative expansion of v (k ) in powers of the bare interaction.
Nucleon-nucleon scattering within a multiple subtractive renormalization approach
Timoteo, V. S.; Frederico, T.; Delfino, A.; Tomio, Lauro
2011-06-15
We present a methodology to renormalize the nucleon-nucleon interaction in momentum space, using a recursive multiple subtraction approach that prescinds from a cutoff regularization, to construct the kernel of the scattering equation. The subtracted scattering equation is solved with the next-leading-order and next-to-next-leading-order interactions. The results are presented for all partial waves up to j=2, fitted to low-energy experimental data. In this renormalization group invariant approach, the subtraction energy emerges as a renormalization scale and the momentum associated with it comes to be about the QCD scale ({Lambda}{sub QCD}), irrespectively to the partial wave.
Renormalizing Entanglement Distillation.
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens
2016-01-15
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow. PMID:26824532
Hilbert space renormalization for the many-electron problem
NASA Astrophysics Data System (ADS)
Li, Zhendong; Chan, Garnet Kin-Lic
2016-02-01
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.
Renormalized Lie perturbation theory
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.
ERIC Educational Resources Information Center
Finch, W. Holmes
2016-01-01
Differential item functioning (DIF) assessment is a crucial component in test construction, serving as the primary way in which instrument developers ensure that measures perform in the same way for multiple groups within the population. When such is not the case, scores may not accurately reflect the trait of interest for all individuals in the…
Holographic entanglement renormalization of topological insulators
NASA Astrophysics Data System (ADS)
Wen, Xueda; Cho, Gil Young; Lopes, Pedro L. S.; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei
2016-08-01
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multiscale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the renormalization group to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. That is, if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales.
Multidimensional stochastic approximation Monte Carlo.
Zablotskiy, Sergey V; Ivanov, Victor A; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}). PMID:27415383
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Renormalization of stochastic lattice models: epitaxial surfaces.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2008-06-01
We present the application of a method [C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial additional technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the Edwards-Wilkinson (EW) model [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding
Renormalization of stochastic lattice models: Epitaxial surfaces
NASA Astrophysics Data System (ADS)
Haselwandter, Christoph A.; Vvedensky, Dimitri D.
2008-06-01
We present the application of a method [C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial additional technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the Edwards-Wilkinson (EW) model [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding
Carvalho, Vanuildo S de; Freire, Hermann
2014-09-15
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.
NASA Astrophysics Data System (ADS)
Patel, Niravkumar; Nocera, Alberto; Alvarez, Gonzalo; Arita, Ryotaro; Dagotto, Elbio
Iron based high-Tc superconductors have attracted considerable attention because of its unconventional superconducting properties. Here, we analyze the magnetic and pairing characteristics of the recently discovered two-leg ladder material BaFe2S3 that becomes superconducting by applying pressure, using a two-orbital Hubbard model studied via the Density Matrix Renormalization Group technique. The hopping parameters, which spans up-to the 2nd nearest-neighbor rungs, were obtained from the ab-initio downfolded band structure at ambient and high pressures. The magnetic phase diagram at a realistic Hund coupling J / U = 0 . 25 is presented varying the Hubbard U, at select values of the electronic fillings. At half-filling, we find a robust magnetic order in excellent agreement with experiments i.e. antiferromagnetic (ferromagnetic) along the leg (rung) directions. We also discuss a possible tendency for this system to form a paired bound state of holes in a small but finite window of Hubbard U. The symmetries of this tentative paired ground state will be discussed.
NASA Astrophysics Data System (ADS)
Siegel, J.; Siegel, Edward Carl-Ludwig
2011-03-01
Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!
A shape dynamical approach to holographic renormalization
NASA Astrophysics Data System (ADS)
Gomes, Henrique; Gryb, Sean; Koslowski, Tim; Mercati, Flavio; Smolin, Lee
2015-01-01
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities.
From dynamical systems to renormalization
Menous, Frédéric
2013-09-15
In this paper we study logarithmic derivatives associated to derivations on completed graded Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a Lie algebra and its Lie group. Such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non linearizability of a resonant vector fields corresponds to the non invertibility of a logarithmic derivative and to the existence of normal forms. These concepts, stemming from the theory of dynamical systems, can be rephrased in the abstract setting of Lie algebra and the same difficulties as in perturbative quantum field theory (pQFT) arise here. Surprisingly, one can adopt the same ideas as in pQFT with fruitful results such as new constructions of normal forms with the help of the Birkhoff decomposition. The analogy goes even further (locality of counter terms, choice of a renormalization scheme) and shall lead to more interactions between dynamical systems and quantum field theory.
NASA Astrophysics Data System (ADS)
Tang, Ho-Kin; Leaw, Jia Ning; Rodrigues, J. N. B.; Sengupta, P.; Assaad, F. F.; Adam, S.
In this work, we study the effects of realistic Coulomb interactions in graphene using a projective quantum Monte Carlo simulation of electrons at half-filing on a honeycomb lattice. We compute the quasiparticle residue, the renormalized Fermi velocity and the antiferromagnetic order parameter as a function of both the long-range and short-range components of the Coulomb potential. We find that the Mott insulator transition is determined mostly by the short-range interaction and is consistent with the Gross-Neveu-Yukawa critical theory. Far from the critical point and in the semi-metallic regime, we find that the Fermi-velocity and quasiparticle residue are influenced by the long-range tail of the Coulomb potential, and for very small interaction strength are consistent with predictions of first order perturbation theory. For experimentally relevant and stronger values of the long-range interaction, our numerical data contradicts prediction from both perturbation theory and the renormalization group approaches. This work was supported by Singapore National Research Foundation (NRF-NRFF2012-01 and CA2DM mid-size Centre), Singapore Ministry of Education(Yale-NUS College R-607-265-01312 and MOE2014-T2-2-112), and DFG Grant No. AS120/9-1.
Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
NASA Astrophysics Data System (ADS)
Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi
2016-03-01
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
Recursive renormalization group theory based subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE
1991-01-01
Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
Renormalization group running of neutrino parameters.
Ohlsson, Tommy; Zhou, Shun
2014-01-01
Neutrinos are the most elusive particles in our Universe. They have masses at least one million times smaller than the electron mass, carry no electric charge and very weakly interact with other particles, meaning that they are rarely captured in terrestrial detectors. Tremendous efforts in the past two decades have revealed that neutrinos can transform from one type to another as a consequence of neutrino oscillations--a quantum mechanical effect over macroscopic distances--yet the origin of neutrino masses remains puzzling. The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation. PMID:25322932
Renormalization group running of neutrino parameters
NASA Astrophysics Data System (ADS)
Ohlsson, Tommy; Zhou, Shun
2014-10-01
Neutrinos are the most elusive particles in our Universe. They have masses at least one million times smaller than the electron mass, carry no electric charge and very weakly interact with other particles, meaning that they are rarely captured in terrestrial detectors. Tremendous efforts in the past two decades have revealed that neutrinos can transform from one type to another as a consequence of neutrino oscillations—a quantum mechanical effect over macroscopic distances—yet the origin of neutrino masses remains puzzling. The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.
Dimensional renormalization: Ladders and rainbows
Delbourgo, R.; Kalloniatis, A.C.; Thompson, G.
1996-10-01
Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive the factors and renormalized Green{close_quote}s functions to {ital all} orders in perturbation theory for rainbow graphs and vertex (or scattering) diagrams at zero momentum transfer, in the context of dimensional regularization, and we prove that the correct anomalous dimensions for those processes emerge in the limit {ital D}{r_arrow}4. {copyright} {ital 1996 The American Physical Society.}
Monte Carlo methods in lattice gauge theories
Otto, S.W.
1983-01-01
The mass of the O/sup +/ glueball for SU(2) gauge theory in 4 dimensions is calculated. This computation was done on a prototype parallel processor and the implementation of gauge theories on this system is described in detail. Using an action of the purely Wilson form (tract of plaquette in the fundamental representation), results with high statistics are obtained. These results are not consistent with scaling according to the continuum renormalization group. Using actions containing higher representations of the group, a search is made for one which is closer to the continuum limit. The choice is based upon the phase structure of these extended theories and also upon the Migdal-Kadanoff approximation to the renormalizaiton group on the lattice. The mass of the O/sup +/ glueball for this improved action is obtained and the mass divided by the square root of the string tension is a constant as the lattice spacing is varied. The other topic studied is the inclusion of dynamical fermions into Monte Carlo calculations via the pseudo fermion technique. Monte Carlo results obtained with this method are compared with those from an exact algorithm based on Gauss-Seidel inversion. First applied were the methods to the Schwinger model and SU(3) theory.
Renormalization in Coulomb gauge QCD
NASA Astrophysics Data System (ADS)
Andraši, A.; Taylor, John C.
2011-04-01
In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.
High-order terms in the renormalized perturbation theory for the Anderson impurity model
NASA Astrophysics Data System (ADS)
Pandis, Vassilis; Hewson, Alex C.
2015-09-01
We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling U ˜. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized k -particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in U ˜, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.
Real-space renormalized dynamical mean field theory
NASA Astrophysics Data System (ADS)
Kubota, Dai; Sakai, Shiro; Imada, Masatoshi
2016-05-01
We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
LETTER: Fisher renormalization for logarithmic corrections
NASA Astrophysics Data System (ADS)
Kenna, Ralph; Hsu, Hsiao-Ping; von Ferber, Christian
2008-10-01
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogues. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.
RENORMALIZATION OF POLYAKOV LOOPS IN FUNDAMENTAL AND HIGHER REPRESENTATIONS
KACZMAREK,O.; GUPTA, S.; HUEBNER, K.
2007-07-30
We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal entent of the lattice and find that both prescriptions are equivalent, resulting in renormalization constants that depend on the bare coupling. Furthermore these renormalization constants show Casimir scaling for higher representations of the Polyakov loops. The analysis of Polyakov loops in different representations of the color SU(3) group indicates that a simple perturbative inspired relation in terms of the quadratic Casimir operator is realized to a good approximation at temperatures T{approx}>{Tc}, for renormalized as well as bare loops. In contrast to a vanishing Polyakov loop in representations with non-zero triality in the confined phase, the adjoint loops are small but non-zero even for temperatures below the critical one. The adjoint quark-antiquark pairs exhibit screening. This behavior can be related to the binding energy of glue-lump states.
Renormalization of the nonlinear O(3) model with θ-term
NASA Astrophysics Data System (ADS)
Flore, Raphael
2013-05-01
The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.
Renormalized reaction and relaxation rates
NASA Astrophysics Data System (ADS)
Gorbachev, Yuriy E.
2016-06-01
Impact of the non-equilibrium on the reaction and relaxation rates (called as generalized relaxation rates - GRR), for the spatially inhomogeneous gas mixture is considered. Discarding the assumption that the 'chemical' part of the collisional integral is a small correction to non-reactive part, the expression for the zero-order GRR is derived. They are represented as a renormalization of the traditional reaction and relaxation rates, which means mixing of all corresponding processes. Thus all reactions and relaxation processes are entangled.
Renormalization in momentum dependent resummations
Jakovac, Antal
2006-10-15
At finite temperature and in nonequilibrium environments we have to resum perturbation theory to avoid infrared divergences. Since resummation shuffles the perturbative orders, renormalizability is a nontrivial issue. In this paper we demonstrate that one can modify any type of resummations--even if it is momentum dependent, or it resums higher point functions - in a way that it is renormalizable with the usual zero temperature counterterms. To achieve this goal we reformulate resummation in form of a renormalization scheme. We apply this technique to perform a 2PI resummation in the six dimensional cubic scalar model in equilibrium.
RENORM predictions of diffraction at LHC confirmed
Goulianos, Konstantin
2015-04-10
The RENORM model predictions of diffractive, total, and total-inelastic cross sections at the LHC are confirmed by recent measurements. The predictions of several other available models are discussed, highlighting their differences from RENORM, mainly arising from the way rapidity gap formation, low- and high-mass diffraction, unitarization, and hadronization are implemented.
Renormalization of high-energy Lorentz-violating four-fermion models
Anselmi, Damiano; Ciuffoli, Emilio
2010-04-15
We study the one-loop renormalization of high-energy Lorentz-violating four-fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method to determine the asymptotic-freedom domain. We also point out that in some models the renormalization-group flow contains rational Zimmermann trajectories that might hide new symmetries.
NASA Astrophysics Data System (ADS)
Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.; Reboredo, Fernando A.
2016-05-01
We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.
Santana, Juan A; Krogel, Jaron T; Kent, Paul R C; Reboredo, Fernando A
2016-05-01
We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides. PMID:27155647
Constrained Path Monte Carlo with Matrix Product State trial wavefunctions
NASA Astrophysics Data System (ADS)
Chung, Chia-Min; Fishman, Matthew; White, Steven; Zhang, Shiwei
Constrained path Monte Carlo (CPMC) is a powerful method for simulating strongly correlated systems. By constraining the path with a trial wavefunction, CPMC circumvents the minus sign problem, but at the cost of introducing a bias. The Density Matrix Renormalization Group (DMRG) is an alternative simulation technique, which is immune to the minus sign problem, but which has an analogous ''dimensionality problem'' for two and three dimensions. Here we present a combination of these techniques, where we use a DMRG matrix product state as a trial wavefunction for CPMC. We demonstrate our method in two-dimensional Hubbard model, and show the comparison to DMRG alone and to CPMC with single-determinant trial functions.
Quantum Monte Carlo simulations with tensor-network states
NASA Astrophysics Data System (ADS)
Song, Jeong Pil; Clay, R. T.
2011-03-01
Matrix-product states, generated by the density-matrix renormalization group method, are among the most powerful methods for simulation of quasi-one dimensional quantum systems. Direct application of a matrix-product state representation fails for two dimensional systems, although a number of tensor-network states have been proposed to generalize the concept for two dimensions. We introduce a useful approximate method replacing a 4-index tensor by two matrices in order to contract tensors in two dimensions. We use this formalism as a basis for variational quantum Monte Carlo, optimizing the matrix elements stochastically. We present results on a two dimensional spinless fermion model including nearest- neighbor Coulomb interactions, and determine the critical Coulomb interaction for the charge density wave state by finite size scaling. This work was supported by the Department of Energy grant DE-FG02-06ER46315.
The Pion Renormalized Light-Cone Wave Function
NASA Astrophysics Data System (ADS)
Trawiński, Arkadiusz P.
2016-06-01
An approximate light-cone wave function for the pion effective quark-antiquark Fock sector corresponding to a small value of the renormalization group parameter is presented. The approximate wave function is motivated by the LF-holography and the quadratic confinement potential in the front form of Hamiltonian dynamics, which is in harmony with the linear confining potential in the instant form. The pion radius, decay constant and form-factor are also presented.
Bolin, Jocelyn Holden; Finch, W. Holmes
2014-01-01
Statistical classification of phenomena into observed groups is very common in the social and behavioral sciences. Statistical classification methods, however, are affected by the characteristics of the data under study. Statistical classification can be further complicated by initial misclassification of the observed groups. The purpose of this study is to investigate the impact of initial training data misclassification on several statistical classification and data mining techniques. Misclassification conditions in the three group case will be simulated and results will be presented in terms of overall as well as subgroup classification accuracy. Results show decreased classification accuracy as sample size, group separation and group size ratio decrease and as misclassification percentage increases with random forests demonstrating the highest accuracy across conditions. PMID:24616711
Renormalization effects on the MSSM from a calculable model of a strongly coupled hidden sector
Arai, Masato; Okada, Nobuchika
2011-10-01
We investigate possible renormalization effects on the low-energy mass spectrum of the minimal supersymmetric standard model (MSSM), using a calculable model of strongly coupled hidden sector. We model the hidden sector by N=2 supersymmetric quantum chromodynamics with gauge group SU(2)xU(1) and N{sub f}=2 matter hypermultiplets, perturbed by a Fayet-Iliopoulos term which breaks the supersymmetry down to N=0 on a metastable vacuum. In the hidden sector the Kaehler potential is renormalized. Upon identifying a hidden sector modulus with the renormalization scale, and extrapolating to the strongly coupled regime using the Seiberg-Witten solution, the contribution from the hidden sector to the MSSM renormalization group flows is computed. For concreteness, we consider a model in which the renormalization effects are communicated to the MSSM sector via gauge mediation. In contrast to the perturbative toy examples of hidden sector renormalization studied in the literature, we find that our strongly coupled model exhibits rather intricate effects on the MSSM soft scalar mass spectrum, depending on how the hidden sector fields are coupled to the messenger fields. This model provides a concrete example in which the low-energy spectrum of MSSM particles that are expected to be accessible in collider experiments is obtained using strongly coupled hidden sector dynamics.
Scaling relations and multicritical phenomena from functional renormalization.
Boettcher, Igor
2015-06-01
We investigate multicritical phenomena in O(N)+O(M) models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of functional renormalization. PMID:26172666
E-cigarette Marketing and Older Smokers: Road to Renormalization
Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas
2015-01-01
Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681
Rapidity renormalized TMD soft and beam functions at two loops
NASA Astrophysics Data System (ADS)
Lübbert, Thomas; Oredsson, Joel; Stahlhofen, Maximilian
2016-03-01
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p ⊥-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Signal inference with unknown response: calibration-uncertainty renormalized estimator.
Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa
2015-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them. PMID:25679743
Signal inference with unknown response: Calibration-uncertainty renormalized estimator
NASA Astrophysics Data System (ADS)
Dorn, Sebastian; Enßlin, Torsten A.; Greiner, Maksim; Selig, Marco; Boehm, Vanessa
2015-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.
Real-space renormalization in statistical mechanics
NASA Astrophysics Data System (ADS)
Efrati, Efi; Wang, Zhe; Kolan, Amy; Kadanoff, Leo P.
2014-04-01
This review compares the conceptualization and practice of early real-space renormalization group methods with the conceptualization of more recent real-space transformations based on tensor networks. For specificity, it focuses upon two basic methods: the "potential-moving" approach most used in the period 1975-1980 and the "rewiring method" as it has been developed in the last five years. The newer method, part of a development called the tensor renormalization group, was originally based on principles of quantum entanglement. It is specialized for computing approximations for tensor products constituting, for example, the free energy or the ground state energy of a large system. It can attack a wide variety of problems, including quantum problems, which would otherwise be intractable. The older method is formulated in terms of spin variables and permits a straightforward construction and analysis of fixed points in rather transparent terms. However, in the form described here it is unsystematic, offers no path for improvement, and of unknown reliability. The new method is formulated in terms of index variables which may be considered as linear combinations of the statistical variables. Free energies emerge naturally, but fixed points are more subtle. Further, physical interpretations of the index variables are often elusive due to a gauge symmetry which allows only selected combinations of tensor entries to have physical significance. In applications, both methods employ analyses with varying degrees of complexity. The complexity is parametrized by an integer called χ (or D in the recent literature). Both methods are examined in action by using them to compute fixed points related to Ising models for small values of the complexity parameter. They behave quite differently. The old method gives a reasonably good picture of the fixed point, as measured, for example, by the accuracy of the measured critical indices. This happens at low values of χ, but there is no
BOOK REVIEW: Renormalization Methods---A Guide For Beginners
NASA Astrophysics Data System (ADS)
Cardy, J.
2004-05-01
The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard phi4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent
Topological invariants and renormalization of Lorenz maps
NASA Astrophysics Data System (ADS)
Silva, Luis; Sousa Ramos, J.
2002-02-01
We prove that the invariants of the topological semiconjugation of Lorenz maps with β-transformations remains constant on the renormalization archipelagoes and analyze how the dynamics on the archipelagoes depends on its structure.
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Euclidean Epstein-Glaser renormalization
Keller, Kai J.
2009-10-15
In the framework of perturbative algebraic quantum field theory recently developed by Brunetti, Duetsch, and Fredenhagen (http://arxiv.org/abs/0901.2038) I give a general construction of so-called Euclidean time-ordered products, i.e., algebraic versions of the Schwinger functions, for scalar quantum field theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space [Epstein and Glaser, Ann. Inst. Henri Poincare 19, 211 (1973)]. An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of Euclidean quantum field theory have a unique singularity structure, i.e., they are unique up to a smooth part. Second, one needs to (re)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable.
Euclidean Epstein-Glaser renormalization
NASA Astrophysics Data System (ADS)
Keller, Kai J.
2009-10-01
In the framework of perturbative algebraic quantum field theory recently developed by Brunetti, Dütsch, and Fredenhagen (http://arxiv.org/abs/0901.2038) I give a general construction of so-called Euclidean time-ordered products, i.e., algebraic versions of the Schwinger functions, for scalar quantum field theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space [Epstein and Glaser, Ann. Inst. Henri Poincare 19, 211 (1973)]. An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-Δ+m2) of Euclidean quantum field theory have a unique singularity structure, i.e., they are unique up to a smooth part. Second, one needs to (re)introduce a (rather natural) "Euclidean causality" condition for the recursion of Epstein and Glaser to be applicable.
Gifford, Kent A; Wareing, Todd A; Failla, Gregory; Horton, John L; Eifel, Patricia J; Mourtada, Firas
2010-01-01
A patient dose distribution was calculated by a 3D multi-group S N particle transport code for intracavitary brachytherapy of the cervix uteri and compared to previously published Monte Carlo results. A Cs-137 LDR intracavitary brachytherapy CT data set was chosen from our clinical database. MCNPX version 2.5.c, was used to calculate the dose distribution. A 3D multi-group S N particle transport code, Attila version 6.1.1 was used to simulate the same patient. Each patient applicator was built in SolidWorks, a mechanical design package, and then assembled with a coordinate transformation and rotation for the patient. The SolidWorks exported applicator geometry was imported into Attila for calculation. Dose matrices were overlaid on the patient CT data set. Dose volume histograms and point doses were compared. The MCNPX calculation required 14.8 hours, whereas the Attila calculation required 22.2 minutes on a 1.8 GHz AMD Opteron CPU. Agreement between Attila and MCNPX dose calculations at the ICRU 38 points was within +/- 3%. Calculated doses to the 2 cc and 5 cc volumes of highest dose differed by not more than +/- 1.1% between the two codes. Dose and DVH overlays agreed well qualitatively. Attila can calculate dose accurately and efficiently for this Cs-137 CT-based patient geometry. Our data showed that a three-group cross-section set is adequate for Cs-137 computations. Future work is aimed at implementing an optimized version of Attila for radiotherapy calculations. PMID:20160682
Renormalization In Quantum Gauge Theory Using Zeta-Function Method
Chiritoiu, Viorel; Zet, Gheorghe
2009-05-22
It is possible to consider space-time symmetries (for example Poincare or de Sitter) as purely inner symmetries. A formulation of the de Sitter symmetry as purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the equations of structure using a constant deformation parameter {lambda}. Local gauge transformations and corresponding covariant derivative depending on gauge fields are obtained. The method of generalized zeta-function is used to realize the renormalization. An effective integral of action is obtained and a comparison with other results is given.
Three-body loss in lithium from functional renormalization
Floerchinger, S.; Schmidt, R.; Wetterich, C.
2009-05-15
We use functional-integral methods for an estimate of the three-body loss in a three-component {sup 6}Li ultracold atom gas. We advocate a simple picture where the loss proceeds by the formation of a three-atom bound trimer state, the trion. In turn, the effective amplitude for the trion formation from three atoms is estimated from a simple effective boson exchange process. The energy gap of the trion and other key quantities for the loss coefficient are computed in a functional renormalization-group framework.
Error estimates and specification parameters for functional renormalization
Schnoerr, David; Boettcher, Igor; Pawlowski, Jan M.; Wetterich, Christof
2013-07-15
We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.
On the Hyperbolicity of Lorenz Renormalization
NASA Astrophysics Data System (ADS)
Martens, Marco; Winckler, Björn
2014-01-01
We consider infinitely renormalizable Lorenz maps with real critical exponent α > 1 of certain monotone combinatorial types. We prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated two-dimensional strong unstable manifold. For monotone families of Lorenz maps we prove that each infinitely renormalizable combinatorial type has a unique representative within the family. We also prove that each infinitely renormalizable map has no wandering intervals, is ergodic, and has a uniquely ergodic minimal Cantor attractor of measure zero.
Novel formulations of CKM matrix renormalization
Kniehl, Bernd A.; Sirlin, Alberto
2009-12-17
We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.
Renormalized dissipation in plasmas with finite collisionality
Parker, S.E.; Carati, D.
1995-05-01
A nonlinear truncation procedure for Fourier-Hermite expansion of Boltzmann-type plasma equations is presented which eliminates fine velocity scale, taking into account its effect on coarser scales. The truncated system is then transformed back to (x, v) space which results in a renormalized Boltzmann equation. The resulting equation may allow for coarser velocity space resolution in kinetic simulations while reducing to the original Boltzmann equation when fine velocity scales are resolved. To illustrate the procedure, renormalized equations are derived for one dimensional electrostatic plasmas in which collisions are modeled by the Lenard-Bernstein operator.
Perturbative renormalization of the electric field correlator
NASA Astrophysics Data System (ADS)
Christensen, C.; Laine, M.
2016-04-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ∼ 12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Finite volume renormalization scheme for fermionic operators
Monahan, Christopher; Orginos, Kostas
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Renormalized Energy Concentration in Random Matrices
NASA Astrophysics Data System (ADS)
Borodin, Alexei; Serfaty, Sylvia
2013-05-01
We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, 2012; 1D log-gases and the renormalized energy, 2013). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.
Critical mass renormalization in renormalized ϕ4 theories in two and three dimensions
NASA Astrophysics Data System (ADS)
Pelissetto, Andrea; Vicari, Ettore
2015-12-01
We consider the O (N)-symmetric ϕ4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the ϕ4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative series in the massive renormalization scheme, taking into account their Borel summability and the known large-order behavior of the coefficients. The results are in good agreement with those obtained in lattice calculations.
Renormalization and destruction of 1/γ2 tori in the standard nontwist map
NASA Astrophysics Data System (ADS)
Apte, A.; Wurm, A.; Morrison, P. J.
2003-06-01
Extending the work of del-Castillo-Negrete, Greene, and Morrison [Physica D 91, 1 (1996); 100, 311 (1997)] on the standard nontwist map, the breakup of an invariant torus with winding number equal to the inverse golden mean squared is studied. Improved numerical techniques provide the greater accuracy that is needed for this case. The new results are interpreted within the renormalization group framework by constructing a renormalization operator on the space of commuting map pairs, and by studying the fixed points of the so constructed operator.
NASA Astrophysics Data System (ADS)
Young, Frederic; Siegel, Edward
Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!
Bose gases near resonance: Renormalized interactions in a condensate
Zhou, Fei Mashayekhi, Mohammad S.
2013-01-15
Bose gases at large scattering lengths or beyond the usual dilute limit for a long time have been one of the most challenging problems in many-body physics. In this article, we investigate the fundamental properties of a near-resonance Bose gas and illustrate that three-dimensional Bose gases become nearly fermionized near resonance when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose metastability. The instability and accompanying maximum are shown to be a precursor of the sign change of g{sub 2}, the renormalized two-body interaction between condensed atoms. g{sub 2} changes from effectively repulsive to attractive when approaching resonance from the molecular side, even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length. We carry out our studies of Bose gases via applying a self-consistent renormalization group equation which is further subject to a boundary condition. We also comment on the relation between the approach here and the diagrammatic calculation in an early article [D. Borzov, M.S. Mashayekhi, S. Zhang, J.-L. Song, F. Zhou, Phys. Rev. A 85 (2012) 023620]. - Highlights: Black-Right-Pointing-Pointer A Bose gas becomes nearly fermionized when its chemical potential approaches a maximum near resonance. Black-Right-Pointing-Pointer At the maximum, an onset instability sets in at a positive scattering length. Black-Right-Pointing-Pointer Condensates strongly influence the renormalization flow of few-body running coupling constants. Black-Right-Pointing-Pointer The effective two-body interaction constant changes its sign at a positive scattering length.
Bretscher, M.M.
1993-12-31
The WIMS-D4 code has been modified (WIMS-D4M) to produce microscopic isotopic cross sections in ISOTXS format for use in diffusion and transport calculations. Beginning with 69-group libraries based on ENDF/B-V data, numerous cell calculations have been made to prepare a set of broad group cross sections for use in diffusion calculations. Global calculations have been made for two control rod states of the Romanian steady state TRIGA reactor with 29 fresh HEU fuel clusters. Detailed Monte Carlo calculations also have been performed for the same reactor configurations using data based on ENDF/B-V. Results from these global calculations are compared with each other and with the measured excess reactivities. Although region-averaged macroscopic principal cross sections obtained from WIMS-D4M are in good agreement with the corresponding Monte Carlo values, problems exist with the high energy (E > 10 keV) microscopic hydrogen transport cross sections.
Collapse transition of randomly branched polymers: renormalized field theory.
Janssen, Hans-Karl; Stenull, Olaf
2011-05-01
We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse θ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse θ' transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions. PMID:21728509
Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
Brodsky, Stanley J.; Di Giustino, Leonardo; /SLAC
2011-08-19
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.
Renormalization of the jet-quenching parameter
NASA Astrophysics Data System (ADS)
Blaizot, Jean-Paul; Mehtar-Tani, Yacine
2014-09-01
We study the radiative processes that affect the propagation of a high energy gluon in a dense medium, such as a quark-gluon plasma. In particular, we investigate the role of the large double logarithmic corrections, ∼αsln2 L /τ0, that were recently identified in the study of p⊥-broadening by Liou, Mueller and Wu. We show that these large corrections can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L 2 + γ, with γ = 2√{αsNc / π }, as compared to the standard scaling in L2.
Renormalized vacuum polarization of rotating black holes
NASA Astrophysics Data System (ADS)
Ferreira, Hugo R. C.
2015-04-01
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.
Renormalized Resonance Quartets in Dispersive Wave Turbulence
NASA Astrophysics Data System (ADS)
Lee, Wonjung; Kovačič, Gregor; Cai, David
2009-07-01
Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distribution is in excellent agreement with the simulation of the full wave system in equilibrium.
Renormalization of gauge theories without cohomology
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-07-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
Entanglement renormalization and two dimensional string theory
NASA Astrophysics Data System (ADS)
Molina-Vilaplana, J.
2016-04-01
The entanglement renormalization flow of a (1 + 1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.
Brodsky, Stanley J.; Wu, Xing-Gang; /Chongqing U.
2012-04-02
The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal {l_brace}{beta}{sub i}{r_brace}-terms 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 renormalization scale {mu}{sub R}{sup PMC} and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale {mu}{sub R}{sup init}, consistent with renormalization group invariance. Moreover, after PMC scale-setting, the n!-growth of the pQCD expansion is eliminated. Even the residual scale-dependence at fixed order due to unknown higher-order {l_brace}{beta}{sub i}{r_brace}-terms is substantially suppressed. As an application, we apply the PMC procedure to obtain NNLO predictions for the t{bar t}-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for {sigma}{sub t{bar t}} is larger in magnitude in comparison with the conventional scale-setting method, and it agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
NASA Astrophysics Data System (ADS)
Cirrone, G. A. Pablo; Agodi, C.; Candiano, G.; Cuttone, G.; di Rosa, F.; Mongelli, E.; Lojacono, P.; Mazzaglia, S.; Russo, G.; Romano, F.; Valastro, L. M.; Lo Nigro, S.; Pittera, S.; Sabini, M. G.; Rafaele, L.; Salamone, V.; Morone, C.; Randazzo, N.; Sipala, V.; Bucciolini, M.; Bruzzi, M.; Menichelli, D.
2008-03-01
At the Italian Southern Laboratories (LNS) of the Italian National Institute for Nuclear Physics the first, and actually unique, Italian proton therapy center is installed and operating. Up to now, 140 patients have been treated. In this environment a big effort is devoted towards Monte Carlo simulation expeciallt with the GEANT4 Toolkit. The authors of this work belong to the Geant4 Collaboration and they use the toolkit in their research programs. They maintain a Monte Carlo application devoted to the complete simulation of a generic hadron-therapy beam line and take active part in the study of fragmentation processes. Moreover they are working in the development of a prototype of a proton Computed tomographic system. In this work we will report our results in the field of proton and carbon therapy either in the simulation as well in the experimental side of our activity.
Background independence in a background dependent renormalization group
NASA Astrophysics Data System (ADS)
Labus, Peter; Morris, Tim R.; Slade, Zöe H.
2016-07-01
Within the derivative expansion of conformally reduced gravity, the modified split Ward identities are shown to be compatible with the flow equations if and only if either the anomalous dimension vanishes or the cutoff profile is chosen to have a power-law form. No solutions exist if the Ward identities are incompatible. In the compatible case, a clear reason is found for why Ward identities can still forbid the existence of fixed points; however, for any cutoff profile, a background independent (and parametrization independent) flow equation is uncovered. Finally, expanding in vertices, the combined equations are shown generically to become either overconstrained or highly redundant beyond the six-point level.
The δN formula is the dynamical renormalization group
Dias, Mafalda; Seery, David; Ribeiro, Raquel H. E-mail: RaquelHRibeiro@case.edu
2013-10-01
We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix
Kniehl, Bernd A.; Sirlin, Alberto
2006-12-01
We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave function renormalization contributions, and to implement the on-shell renormalization of the former with nondiagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.
Renormalization of a two-loop neutrino mass model
Babu, K. S.; Julio, J.
2014-01-01
We analyze the renormalization group structure of a radiative neutrino mass model consisting of a singly charged and a doubly charged scalar fields. Small Majorana neutrino masses are generated by the exchange of these scalars via two-loop diagrams. We derive boundedness conditions for the Higgs potential and show how they can be satisfied to energies up to the Planck scale. Combining boundedness and perturbativity constraints with neutrino oscillation phenomenology, new limits on the masses and couplings of the charged scalars are derived. These in turn lead to lower limits on the branching ratios for certain lepton flavor violating (LFV) processes such as μ→eγ, μ→3e and μ – e conversion in nuclei. Improved LFV measurements could test the model, especially in the case of inverted neutrino mass hierarchy where these are more prominent.
Renormalization of a two-loop neutrino mass model
NASA Astrophysics Data System (ADS)
Babu, K. S.; Julio, J.
2014-06-01
We analyze the renormalization group structure of a radiative neutrino mass model consisting of a singly charged and a doubly charged scalar fields. Small Majorana neutrino masses are generated by the exchange of these scalars via two-loop diagrams. We derive boundedness conditions for the Higgs potential and show how they can be satisfied to energies up to the Planck scale. Combining boundedness and perturbativity constraints with neutrino oscillation phenomenology, new limits on the masses and couplings of the charged scalars are derived. These in turn lead to lower limits on the branching ratios for certain lepton flavor violating (LFV) processes such as μ→eγ, μ→3e and μ - e conversion in nuclei. Improved LFV measurements could test the model, especially in the case of inverted neutrino mass hierarchy where these are more prominent.
NASA Astrophysics Data System (ADS)
Ovidiu Vlad, Marcel
1992-07-01
A new stochastic renormalization approach for multi-step decay phenomena is developed. A simple physical interpretation of the renormalization method is suggested. It consists in grouping successions of variable numbers of decay events into blocks. The law of probability multiplication leads to an exponential random process Y = YX1 + X2 + …0 where both the exponents X1, X2,… and the basis Y0 are random variables. The physically consistent solution of the model corresponds to a “super-strong” renormalization regime. The dependence of the moments of the decay parameter on the number of decay steps q can be exactly determined. It consists in a linear superposition of inverse power laws in q modulated by periodic functions in In q, having different periods. The theory is applied to the renormalization of the bronchial tree. Our computation shows that the lung structure is very tolerant to fluctuations. This result supports the mechanism of morphogenesis of fractal biological organs suggested by West (Ann. Biomed. Eng. 18 (1990) 135). The possibilities of application to the scattering phenomena in one-dimensional disordered media are also investigated.
The standard model and its generalizations in the Epstein-Glaser approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2000-12-01
We continue our study of non-Abelian gauge theories in the framework of the Epstein-Glaser approach to renormalization theory. We consider the case when massive spin-1 bosons are present in the theory and we modify appropriately the analysis of the origin of the gauge invariance performed in a preceding paper in the case of null-mass spin-1 bosons. Then we are able to extend a result of Dütsch and Scharf concerning the uniqueness of the standard model, consistent with renormalization theory. In fact we consider the most general case, i.e. the consistent interaction of r spin-1 bosons, and we do not impose any restrictions on the gauge group and the mass spectrum of the theory. We show that, besides the natural emergence of a group structure (as in the massless case), we obtain new conditions of a group theoretical nature, namely the existence of a certain representation of the gauge group associated to the Higgs fields. Some other mass relations connecting the structure constants of the gauge group and the masses of the bosons emerge naturally. The proof is carried out using the Epstein-Glaser approach to renormalization theory.
Handley, G. R.; Masters, L. C.; Stachowiak, R. V.
1981-04-10
Validation of the Monte Carlo criticality code, KENO IV, and the Hansen-Roach sixteen-energy-group cross sections was accomplished by calculating the effective neutron multiplication constant, k/sub eff/, of 29 experimentally critical assemblies which had uranium enrichments of 92.6% or higher in the uranium-235 isotope. The experiments were chosen so that a large variety of geometries and of neutron energy spectra were covered. Problems, calculating the k/sub eff/ of systems with high-uranium-concentration uranyl nitrate solution that were minimally reflected or unreflected, resulted in the separate examination of five cases.
Electronic states on a fractal: Exact Green's-function renormalization approach
NASA Astrophysics Data System (ADS)
Andrade, R. F. S.; Schellnhuber, H. J.
1991-12-01
A nontrivial tight-binding model for electron dynamics on the fractal Koch curve is investigated within the framework of the Green's-function formalism. The key result is the construction of a multiple exact renormalization group that allows one to derive all the rather unusual properties of the model. This group is generated by four nonequivalent decimation operations, which define distinct transformation rules for the 48 relevant parameters to be renormalized. The calculation of the density of states confirms the crucial results that were obtained recently using transfer-matrix methods: local self-affinity, dense gap structure, and singular electronic levels with infinite degeneracy. This demonstrates that the Green's-function approach is not inferior to other techniques even in topologically one-dimensional situations.
NASA Astrophysics Data System (ADS)
Cheon, M.; Chang, I.
1999-04-01
The scaling behavior for a binary fragmentation of critical percolation clusters is investigated by a large-cell Monte Carlo real-space renormalization group method in two and three dimensions. We obtain accurate values of critical exponents λ and phi describing the scaling of fragmentation rate and the distribution of fragments' masses produced by a binary fragmentation. Our results for λ and phi show that the fragmentation rate is proportional to the size of mother cluster, and the scaling relation σ = 1 + λ - phi conjectured by Edwards et al. to be valid for all dimensions is satisfied in two and three dimensions, where σ is the crossover exponent of the average cluster number in percolation theory, which excludes the other scaling relations.
NASA Astrophysics Data System (ADS)
Ghoshal, Nababrata; Shabnam, Sabana; DasGupta, Sudeshna; Roy, Soumen Kumar
2016-05-01
Extensive Monte Carlo simulations are performed to investigate the critical properties of a special singular point usually known as the Landau point. The singular behavior is studied in the case when the order parameter is a tensor of rank 2. Such an order parameter is associated with a nematic-liquid-crystal phase. A three-dimensional lattice dispersion model that exhibits a direct biaxial nematic-to-isotropic phase transition at the Landau point is thus chosen for the present study. Finite-size scaling and cumulant methods are used to obtain precise values of the critical exponent ν =0.713 (4 ) , the ratio γ /ν =1.85 (1 ) , and the fourth-order critical Binder cumulant U*=0.6360 (1 ) . Estimated values of the exponents are in good agreement with renormalization-group predictions.
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N_{C} → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower
Importance of proper renormalization scale-setting for QCD testing at colliders
NASA Astrophysics Data System (ADS)
Wu, Xing-Gang; Wang, Sheng-Quan; Brodsky, Stanley J.
2016-02-01
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant α s to eliminate all non-conformal { β i } terms in the pQCD series. The { β i } terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the "increasing-decreasing" behavior observed by the D0 collaboration for increasing t overline t invariant mass. At
NASA Astrophysics Data System (ADS)
Chandre, C.; Jauslin, H. R.
1998-12-01
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for 3 degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.
Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; Ma, Hong -Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-06-26
The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R_{δ}-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R_{e+e–} and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β_{i}}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.
NASA Astrophysics Data System (ADS)
Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-09-01
The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.
Anomalies, equivalence and renormalization of cosmological frames
NASA Astrophysics Data System (ADS)
Herrero-Valea, Mario
2016-05-01
We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments, we claim that equivalence is broken in the presence of anomalous symmetries in one of the frames. This is particularized to the case of the relation between the Einstein and Jordan frames in scalar-tensor theories used to describe early Universe dynamics. Although in this case a regularization that cancels the anomaly exists, the renormalized theory always develops a nonvanishing contribution to the S matrix that is present only in the Jordan frame, promoting the different frames to different physical theories that must be UV completed in a different way.
Semihard processes with BLM renormalization scale setting
Caporale, Francesco; Murdaca, Beatrice; Papa, Alessandro
2015-04-10
We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.
Charge renormalization in nominally apolar colloidal dispersions
NASA Astrophysics Data System (ADS)
Evans, Daniel J.; Hollingsworth, Andrew D.; Grier, David G.
2016-04-01
We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.
A site-renormalized molecular fluid theory
NASA Astrophysics Data System (ADS)
Dyer, Kippi M.; Perkyns, John S.; Pettitt, B. Montgomery
2007-11-01
The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.
Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions
NASA Astrophysics Data System (ADS)
Wang, Lei; Iazzi, Mauro; Corboz, Philippe; Troyer, Matthias
2015-06-01
We present the ground state extension of the efficient continuous-time quantum Monte Carlo algorithm for lattice fermions of M. Iazzi and M. Troyer, Phys. Rev. B 91, 241118 (2015), 10.1103/PhysRevB.91.241118. Based on continuous-time expansion of an imaginary-time projection operator, the algorithm is free of systematic error and scales linearly with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless t -V model as an example and compare the numerical results with exact diagonalization, density matrix renormalization group, and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.
2010-10-20
The "Monte Carlo Benchmark" (MCB) is intended to model the computatiional performance of Monte Carlo algorithms on parallel architectures. It models the solution of a simple heuristic transport equation using a Monte Carlo technique. The MCB employs typical features of Monte Carlo algorithms such as particle creation, particle tracking, tallying particle information, and particle destruction. Particles are also traded among processors using MPI calls.
Critical temperature and superfluid gap of the unitary Fermi gas from functional renormalization
NASA Astrophysics Data System (ADS)
Boettcher, Igor; Pawlowski, Jan M.; Wetterich, Christof
2014-05-01
We investigate the superfluid transition of the unitary Fermi gas by means of the functional renormalization group, aiming at quantitative precision. We extract Tc/μ=0.38(2) and Δ /μ=1.04(15) for the critical temperature and the superfluid gap at zero temperature, respectively, within a systematic improvement of the truncation for the effective average action. The key ingredient in comparison to previous approaches consists in the use of regulators which cut off both frequencies and momenta. We incorporate renormalization effects on both the bosonic and the fermionic propagators, include higher-order bosonic scattering processes, and investigate the regulator and specification parameter dependence for an error estimate. The ratio Δ /Tc=2.7(3) becomes less sensitive to the relative cutoff scale of bosons and fermions when improving the truncation. The techniques developed in this work are easily carried over to the cases of finite scattering length, lower dimensionality, and spin imbalance.
Chetty, Indrin J.; Curran, Bruce; Cygler, Joanna E.; DeMarco, John J.; Ezzell, Gary; Faddegon, Bruce A.; Kawrakow, Iwan; Keall, Paul J.; Liu, Helen; Ma, C.-M. Charlie; Rogers, D. W. O.; Seuntjens, Jan; Sheikh-Bagheri, Daryoush; Siebers, Jeffrey V.
2007-12-15
The Monte Carlo (MC) method has been shown through many research studies to calculate accurate dose distributions for clinical radiotherapy, particularly in heterogeneous patient tissues where the effects of electron transport cannot be accurately handled with conventional, deterministic dose algorithms. Despite its proven accuracy and the potential for improved dose distributions to influence treatment outcomes, the long calculation times previously associated with MC simulation rendered this method impractical for routine clinical treatment planning. However, the development of faster codes optimized for radiotherapy calculations and improvements in computer processor technology have substantially reduced calculation times to, in some instances, within minutes on a single processor. These advances have motivated several major treatment planning system vendors to embark upon the path of MC techniques. Several commercial vendors have already released or are currently in the process of releasing MC algorithms for photon and/or electron beam treatment planning. Consequently, the accessibility and use of MC treatment planning algorithms may well become widespread in the radiotherapy community. With MC simulation, dose is computed stochastically using first principles; this method is therefore quite different from conventional dose algorithms. Issues such as statistical uncertainties, the use of variance reduction techniques, the ability to account for geometric details in the accelerator treatment head simulation, and other features, are all unique components of a MC treatment planning algorithm. Successful implementation by the clinical physicist of such a system will require an understanding of the basic principles of MC techniques. The purpose of this report, while providing education and review on the use of MC simulation in radiotherapy planning, is to set out, for both users and developers, the salient issues associated with clinical implementation and
Renormalization-scheme-invariant perturbation theory: Miracle or mirage
Chyla, J.
1985-05-15
A recently proposed solution to the renormalization-scheme ambiguity in perturbation theory is critically analyzed and shown to possess another kind of ambiguity closely related to the one it is supposed to cure.
The renormalized Jellium model of colloidal suspensions with multivalent counterions
NASA Astrophysics Data System (ADS)
Colla, Thiago E.; Levin, Yan
2010-12-01
An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.
Renormalization of the Polyakov loop with gradient flow
NASA Astrophysics Data System (ADS)
Petreczky, P.; Schadler, H.-P.
2015-11-01
We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2 +1 flavor QCD with highly improved staggered quarks and lattices with temporal extents of Nτ=6 , 8, 10 and 12 we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from T =116 MeV up to T =815 MeV , with small errors not only for the Polyakov loop in fundamental representation, but also for the Polyakov loops in higher representations. We compare our results with standard renormalization schemes and discuss the Casimir scaling of the Polyakov loops.
Renormalization of the Brazilian chiral nucleon-nucleon potential
Da Rocha, Carlos A.; Timoteo, Varese S.
2013-03-25
In this work we present a renormalization of the Brazilian nucleon-nucleon (NN) potential using a subtractive method. We show that the exchange of correlated two pion is important for isovector channels, mainly in tensor and central potentials.
Renormalization in Coulomb-gauge QCD within the Lagrangian formalism
Niegawa, A.
2006-08-15
We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)
Renormalization of curvature elastic constants for elastic and fluid membranes
NASA Astrophysics Data System (ADS)
Ami, S.; Kleinert, H.
1987-02-01
We study the fluctuations of membranes with area and curvature elasticity and calculate the renormalization of the curvature elastic constants due to thermal fluctuations. For the mean curvature elastic constant the result is the same as obtained previously for “ideal membranes” which resist only to curvature deformations. The renormalization of the gaussian curvature, on the other hand, depends on the elastic contants. In an incompressible membrane, it is five times weaker than in an ideal membrane.
Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves
2014-01-01
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221
Goh, Segun; Lee, Keumsook; Choi, MooYoung; Fortin, Jean-Yves
2014-01-01
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221
Grassman-number tensor network states and its renormalization
NASA Astrophysics Data System (ADS)
Gu, Zhengcheng; Verstraete, Frank; Wen, Xiaogang
2010-03-01
Traditional condensed matter physics is based on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Mean-field theory is a powerful method to describe symmetry breaking phases and phase transitions by assuming the ground state wavefunctions for many- body systems can be approximately described by direct product states. The Fermi liquid theory is another powerful method to study electron systems by assuming that the ground state wavefunctions for the electrons can be approximately described by Slater determinants. In this paper, we propose a new class of states: Grassman-number tensor product states. These states only need polynomial amount of information to approximately encode many-body ground states. Many classes of states, such as matrix/tensor product states (M/TPS), Slater determinant states, etc., are subclasses of Grassman-number tensor product states. However, calculating the physical quantities for these state can be exponential hard in general. To solve this difficulty, we develop the Grassman-tensor- entanglement renormalization group (GTERG) method to efficiently calculate the physical quantities. We demonstrate our algorithm by studying several simple fermion/boson models.
2006-05-09
The Monte Carlo example programs VARHATOM and DMCATOM are two small, simple FORTRAN programs that illustrate the use of the Monte Carlo Mathematical technique for calculating the ground state energy of the hydrogen atom.
NASA Astrophysics Data System (ADS)
Geneste, Grégory; Bellaiche, L.; Kiat, Jean-Michel
2016-06-01
The radio-frequency dielectric response of the lead-free Ba (Zr0.5Ti0.5)O3 relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.
Geneste, Grégory; Bellaiche, L; Kiat, Jean-Michel
2016-06-17
The radio-frequency dielectric response of the lead-free Ba(Zr_{0.5}Ti_{0.5})O_{3} relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors. PMID:27367408
Tensor hypercontraction. II. Least-squares renormalization.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2012-12-14
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry. PMID:23248986
Tensor hypercontraction. II. Least-squares renormalization
NASA Astrophysics Data System (ADS)
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2012-12-01
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.
Calibration of the Top-Quark Monte Carlo Mass
NASA Astrophysics Data System (ADS)
Kieseler, Jan; Lipka, Katerina; Moch, Sven-Olaf
2016-04-01
We present a method to establish, experimentally, the relation between the top-quark mass mtMC as implemented in Monte Carlo generators and the Lagrangian mass parameter mt in a theoretically well-defined renormalization scheme. We propose a simultaneous fit of mtMC and an observable sensitive to mt, which does not rely on any prior assumptions about the relation between mt and mtMC. The measured observable is independent of mtMC and can be used subsequently for a determination of mt. The analysis strategy is illustrated with examples for the extraction of mt from inclusive and differential cross sections for hadroproduction of top quarks.
Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays
NASA Technical Reports Server (NTRS)
Chiu, H. H.
1989-01-01
The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.
Renormalization of massless Feynman amplitudes in configuration space
NASA Astrophysics Data System (ADS)
Nikolov, Nikolay M.; Stora, Raymond; Todorov, Ivan
2014-05-01
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincaré covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-10-23
We present how the surface-state correspondence, conjectured by Miyaji and Takayanagi, works in the setup of AdS(3)/CFT(2) by generalizing the formulation of a continuous multiscale entanglement renormalization group ansatz. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on AdS(3) and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it reproduces the time slice of AdS(3). PMID:26551098
Peripheral NN scattering from subtractive renormalization of chiral interactions
Batista, E. F.; Szpigel, S.; Timóteo, V. S.
2014-11-11
We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm{sup −1} and 1 fm{sup −1}. In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E{sub lab} = 150 MeV, with a cutoff at Λ = 30 fm{sup −1}.
Renormalizations and Wandering Jordan Curves of Rational Maps
NASA Astrophysics Data System (ADS)
Cui, Guizhen; Peng, Wenjuan; Tan, Lei
2016-05-01
We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.
Renormalizations and Wandering Jordan Curves of Rational Maps
NASA Astrophysics Data System (ADS)
Cui, Guizhen; Peng, Wenjuan; Tan, Lei
2016-04-01
We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.
Dimension-5 C P -odd operators: QCD mixing and renormalization
NASA Astrophysics Data System (ADS)
Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; Mereghetti, Emanuele; Yoon, Boram
2015-12-01
We study the off-shell mixing and renormalization of flavor-diagonal dimension-five T - and P -odd operators involving quarks, gluons, and photons, including quark electric dipole and chromoelectric dipole operators. We present the renormalization matrix to one loop in the MS ¯ scheme. We also provide a definition of the quark chromoelectric dipole operator in a regularization-independent momentum-subtraction scheme suitable for nonperturbative lattice calculations and present the matching coefficients with the MS ¯ scheme to one loop in perturbation theory, using both the naïve dimensional regularization and 't Hooft-Veltman prescriptions for γ5.
Renormalized dissipation in the nonconservatively forced Burgers equation
Krommes, J.A.
2000-01-19
A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.
Screening of heterogeneous surfaces: charge renormalization of Janus particles.
Boon, N; Carvajal Gallardo, E; Zheng, S; Eggen, E; Dijkstra, M; van Roij, R
2010-03-17
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles. PMID:21389438
On the renormalization of the Gibbons-Hawking boundary term
NASA Astrophysics Data System (ADS)
Jacobson, Ted; Satz, Alejandro
2014-03-01
The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the gravitational action are generally renormalized differently when integrating out quantum fluctuations. The former is affected by nonminimal couplings, while the latter is affected by boundary conditions. We use the heat kernel method to analyze this behavior for a nonminimally coupled scalar field, the Maxwell field, and the graviton field. Allowing for Robin boundary conditions, we examine in which cases the renormalization preserves the ratio of boundary and bulk terms required for the effective action to possess a stationary point. The implications for field theory and black hole entropy computations are discussed.
Quantum Monte Carlo for atoms and molecules
Barnett, R.N.
1989-11-01
The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H{sub 2}, LiH, Li{sub 2}, and H{sub 2}O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li{sub 2}, and H{sub 2}O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations, the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions.
Brown, F.B.; Sutton, T.M.
1996-02-01
This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.
Pseudo-ε expansion and renormalized coupling constants at criticality.
Sokolov, A I; Nikitina, M A
2014-05-01
Universal values of dimensional effective coupling constants g(2k) that determine nonlinear susceptibilities χ(2k) and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ε expansion approach. Pseudo-ε expansions for g(6) and g(8) at criticality are derived for arbitrary n. Analogous series for ratios R(6) = g(6)/g(4)(2) and R(8) = g(8)/g(4)(3) that figure in the equation of state are also found, and the pseudo-ε expansion for Wilson fixed point location g(4)(*) descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0 ≤ n ≤ 64, with the most attention paid to the physically important cases n = 0,1,2,3. Pseudo-ε expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g(4)(*) and R(6)(*) that are almost as accurate as those provided by the Padé technique. Pseudo-ε expansion estimates for g(8)(*) and R(8)(*) are found to be much worse than those for lower-order couplings independently of the resummation method employed. The numerical effectiveness of the pseudo-ε expansion approach in two dimensions is also studied. Pseudo-ε expansion for g(4)(*) originating from the five-loop RG series for the β function of two-dimensional λϕ(4) field theory is used to get numerical estimates for n ranging from 0 to 64. The approach discussed gives accurate enough values of g(4)(*) down to n = 2 and leads to fair estimates for Ising and polymer (n = 0) models. PMID:25353759
Pseudo-ɛ expansion and renormalized coupling constants at criticality
NASA Astrophysics Data System (ADS)
Sokolov, A. I.; Nikitina, M. A.
2014-05-01
Universal values of dimensional effective coupling constants g2k that determine nonlinear susceptibilities χ2k and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for g6 and g8 at criticality are derived for arbitrary n. Analogous series for ratios R6=g6/g42 and R8=g8/g43 that figure in the equation of state are also found, and the pseudo-ɛ expansion for Wilson fixed point location g4* descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0≤n≤64, with the most attention paid to the physically important cases n =0,1,2,3. Pseudo-ɛ expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g4* and R6* that are almost as accurate as those provided by the Padé technique. Pseudo-ɛ expansion estimates for g8* and R8* are found to be much worse than those for lower-order couplings independently of the resummation method employed. The numerical effectiveness of the pseudo-ɛ expansion approach in two dimensions is also studied. Pseudo-ɛ expansion for g4* originating from the five-loop RG series for the β function of two-dimensional λϕ4 field theory is used to get numerical estimates for n ranging from 0 to 64. The approach discussed gives accurate enough values of g4* down to n =2 and leads to fair estimates for Ising and polymer (n =0) models.
Analytical band Monte Carlo analysis of electron transport in silicene
NASA Astrophysics Data System (ADS)
Yeoh, K. H.; Ong, D. S.; Ooi, C. H. Raymond; Yong, T. K.; Lim, S. K.
2016-06-01
An analytical band Monte Carlo (AMC) with linear energy band dispersion has been developed to study the electron transport in suspended silicene and silicene on aluminium oxide (Al2O3) substrate. We have calibrated our model against the full band Monte Carlo (FMC) results by matching the velocity-field curve. Using this model, we discover that the collective effects of charge impurity scattering and surface optical phonon scattering can degrade the electron mobility down to about 400 cm2 V‑1 s‑1 and thereafter it is less sensitive to the changes of charge impurity in the substrate and surface optical phonon. We also found that further reduction of mobility to ∼100 cm2 V‑1 s‑1 as experimentally demonstrated by Tao et al (2015 Nat. Nanotechnol. 10 227) can only be explained by the renormalization of Fermi velocity due to interaction with Al2O3 substrate.
NASA Astrophysics Data System (ADS)
Sato, Ryo; Yokoyama, Hisatoshi
2016-07-01
Band renormalization effects (BRE) are comprehensively studied for a mixed state of dx2 - y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders, in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In a weakly correlated regime (U/t ≲ 6), BRE are negligible on all the states studied. As previously shown, the effective band of d-SC is greatly renormalized but the modifications of physical quantities, including energy improvement, are negligible. In contrast, BRE on the AF state considerably affects various features of the system. Because the energy is markedly improved for t'/t < 0, the AF state occupies almost the whole underdoped regime in phase diagrams. A doped metallic AF state undergoes a kind of Lifshitz transition at t' = t'{L} ˜ - 0.05t as t'/t varies, irrespective of the values of U/t and δ (doping rate). Pocket Fermi surfaces arise around (π ,0) [(π /2,π /2)] for t' > t'{L} [t' < t'{L}], which corresponds to the electron-hole asymmetry observed in angle-resolved photoemission spectroscopy (ARPES) spectra. The coexistent state of the two orders is possible basically for t' > t'{L}, because the existence of Fermi surfaces near (π ,0) is a requisite for the electron scattering of {q} = (π ,π ). Actually, the coexistent state appears mainly for t'{L}/t < t'/t ≲ 0.2 in the mixed state. Nevertheless, the AF and coexisting states become unstable toward phase separation for - 0.05 ≲ t'/t ≲ 0.2 but become stable at other values of t'/t owing to the energy reduction by the diagonal hopping of doped holes. We show that this instability does not directly correlate with the strength of d-SC.