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Sample records for carlo renormalization group

  1. 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.

  2. Fourier Monte Carlo renormalization-group approach to crystalline membranes.

    PubMed

    Tröster, A

    2015-02-01

    The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.

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

    SciTech Connect

    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).

  4. 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.

  5. Renormalization scheme dependence with renormalization group summation

    NASA Astrophysics Data System (ADS)

    McKeon, D. G. C.

    2015-08-01

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

  6. No-core Monte Carlo shell model calculations with unitary correlation operator method and similarity renormalization group

    NASA Astrophysics Data System (ADS)

    Liu, Lang

    2015-05-01

    The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for 3H and 4He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM. Supported by Fundamental Research Funds for the Central Universities (JUSRP1035), National Natural Science Foundation of China (11305077)

  7. Renormalization group functional equations

    SciTech Connect

    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.

  8. 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.

  9. 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.

  10. 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.

  11. Gutzwiller renormalization group

    DOE PAGES

    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

  12. Fermionic quantum criticality in honeycomb and π -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Parisen Toldin, Francesco; Hohenadler, Martin; Assaad, Fakher F.; Herbut, Igor F.

    2015-04-01

    We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π -flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

  13. Renormalization group in internal space

    SciTech Connect

    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.

  14. 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.

  15. Contractor renormalization group and the Haldane conjecture

    SciTech Connect

    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.

  16. 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.

  17. 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.

  18. Renormalization Group Trajectories Between Two Fixed Points

    NASA Astrophysics Data System (ADS)

    Abdesselam, Abdelmalek

    2010-03-01

    We report on our recent rigorous construction of complete renormalization group trajectories between two fixed points for the three-dimensional phi-four model with modified propagator considered by Brydges, Mitter and Scoppola (BMS). These are discrete critical trajectories which connect the ultraviolet Gaussian fixed point to the nontrivial BMS infrared fixed point which is an analogue of the Wilson-Fisher fixed point. The renormalization group map is defined rigorously and nonperturbatively, without using the hierarchical approximation. The trajectories are constructed by a fixed point argument in a suitable Banach space of sequences, where one perturbs a nonlinear one-dimensional iteration.

  19. Cosmology is not a renormalization group flow.

    PubMed

    Woodard, R P

    2008-08-22

    A critical examination is made of two simple implementations of the idea that cosmology can be viewed as a renormalization group (RG) flow. Both implementations are shown to fail when applied to a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. Cosmological evolution in this model is not driven by any RG screening of couplings but rather by inflationary particle production gradually filling an initially empty universe with a sea of long wavelength scalars.

  20. Black Hole Entropy and the Renormalization Group

    NASA Astrophysics Data System (ADS)

    Satz, Alejandro; Jacobson, Ted

    2015-01-01

    Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least an important contribution to the total Bekenstein-Hawking entropy, and that the divergences in the entanglement entropy should be absorbed in the renormalization of the gravitational couplings. In this talk, we describe how an improved understanding of black hole entropy is obtained by combining these notions with the renormalization group. By introducing an RG flow scale, we investigate whether the total entropy of the black hole can be partitioned in a "gravitational" part related to the flowing gravitational action, and a "quantum" part related to the unintegrated degrees of freedom. We describe the realization of this idea for free fields, and the complications and qualifications arising for interacting fields.

  1. 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.

  2. 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.

  3. Renormalization group flows and continual Lie algebras

    NASA Astrophysics Data System (ADS)

    Bakas, Ioannis

    2003-08-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

  4. Nonuniversal quantities from dual renormalization group transformations.

    PubMed

    Meurice, Y; Niermann, S

    1999-09-01

    Using a simplified version of the renormalization group (RG) transformation of Dyson's hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena. PMID:11970062

  5. 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.

  6. The Renormalization Group in Nuclear Physics

    NASA Astrophysics Data System (ADS)

    Furnstahl, R. J.

    2012-07-01

    Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.

  7. 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.

  8. Renormalization group analysis in nonrelativistic QCD for colored scalars

    SciTech Connect

    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.

  9. 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.

  10. Advanced density matrix renormalization group method for nuclear structure calculations

    NASA Astrophysics Data System (ADS)

    Legeza, Ã.-.; Veis, L.; Poves, A.; Dukelsky, J.

    2015-11-01

    We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous 400 keV discrepancy in the ground state energy of 56Ni. We then report the first DMRG results in the p f +g 9 /2 shell model space for the ground 0+ and first 2+ states of 64Ge which are benchmarked with reference data obtained from a Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.

  11. 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.

  12. Polarizable Embedding Density Matrix Renormalization Group.

    PubMed

    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

  13. Quark lepton complementarity and renormalization group effects

    SciTech Connect

    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.

  14. Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale

    SciTech Connect

    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 {βRi}-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.

  15. 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.

  16. 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.

  17. The ab-initio density matrix renormalization group in practice

    SciTech Connect

    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.

  18. The ab-initio density matrix renormalization group in practice

    NASA Astrophysics Data System (ADS)

    Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

    2015-01-01

    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.

  19. Renormalization group and the superconducting susceptibility of a Fermi liquid

    SciTech Connect

    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.

  20. Renormalization of the periodic scalar field theory by Polchinski's renormalization group method

    NASA Astrophysics Data System (ADS)

    Nándori, I.; Sailer, K.; Jentschura, U. D.; Soff, G.

    2002-04-01

    The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this paper, we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.

  1. Background field functional renormalization group for absorbing state phase transitions.

    PubMed

    Buchhold, Michael; Diehl, Sebastian

    2016-07-01

    We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions. PMID:27575107

  2. Background field functional renormalization group for absorbing state phase transitions

    NASA Astrophysics Data System (ADS)

    Buchhold, Michael; Diehl, Sebastian

    2016-07-01

    We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.

  3. From infinite to two dimensions through the functional renormalization group.

    PubMed

    Taranto, C; Andergassen, S; Bauer, J; Held, K; Katanin, A; Metzner, W; Rohringer, G; Toschi, A

    2014-05-16

    We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling. PMID:24877952

  4. Communication: Four-component density matrix renormalization group

    SciTech Connect

    Knecht, Stefan Reiher, Markus; Legeza, Örs

    2014-01-28

    We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.

  5. 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.

  6. Renormalization group flows, cycles, and c-theorem folklore.

    PubMed

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

    2012-03-30

    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.

  7. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.

    PubMed

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice

  8. 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

  9. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.

    PubMed

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice

  10. Renormalization group analysis of graphene with a supercritical Coulomb impurity

    NASA Astrophysics Data System (ADS)

    Nishida, Yusuke

    2016-08-01

    We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial-wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power-law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.

  11. More on the renormalization group limit cycle in QCD

    SciTech Connect

    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.

  12. New applications of renormalization group methods in nuclear physics.

    PubMed

    Furnstahl, R J; Hebeler, K

    2013-12-01

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

  13. Renormalization-group calculation of excitation properties for impurity models

    NASA Astrophysics Data System (ADS)

    Yoshida, M.; Whitaker, M. A.; Oliveira, L. N.

    1990-05-01

    The renormalization-group method developed by Wilson to calculate thermodynamical properties of dilute magnetic alloys is generalized to allow the calculation of dynamical properties of many-body impurity Hamiltonians. As a simple illustration, the impurity spectral density for the resonant-level model (i.e., the U=0 Anderson model) is computed. As a second illustration, for the same model, the longitudinal relaxation rate for a nuclear spin coupled to the impurity is calculated as a function of temperature.

  14. Towards a complete renormalization group trajectory between two fixed points

    NASA Astrophysics Data System (ADS)

    Abdesselam, Abdelmalek

    2007-12-01

    We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.

  15. Wilsonian renormalization group equation for nuclear current operators

    SciTech Connect

    Kvinikhidze, A. N.; Blankleider, B.

    2007-12-15

    We present the solution to the recently derived Wilsonian renormalization group (RG) equation for nuclear current operators. To eliminate the present ambiguity in the RG equation itself, we introduce a new condition specifying the cutoff independence of the five-point Green function corresponding to the two-body propagator with current operator insertion. The resulting effective current operator is then shown to obey a modified Ward-Takahashi identity that differs from the usual one, but that nevertheless leads to current conservation.

  16. Subtractive Renormalization Group Invariance: Pionless EFT at NLO

    SciTech Connect

    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}.

  17. Dynamical renormalization group resummation of finite temperature infrared divergences

    SciTech Connect

    Boyanovsky, D.; de Vega, H.J. ); Boyanovsky, D.; de Vega, H.J.; Simionato, M. et Denis Diderot , Tour 16, 1er. etage, 4, Place Jussieu, 75252 Paris, Cedex 05 ); Holman, R. ); Simionato, M. )

    1999-09-01

    We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e[sup [minus][alpha] hthinsp;T hthinsp;t hthinsp;ln[t/t[sub 0

  18. Adaptive random renormalization group classification of multiscale dispersive processes

    NASA Astrophysics Data System (ADS)

    Cushman, John; O'Malley, Dan

    2013-04-01

    Renormalization group operators provide a detailed classification tool for dispersive processes. We begin by reviewing a two-scale renormalization group classification scheme. Repeated application of one operator is associated with long time behavior of the process while repeated application of the other is associated with short time behavior. This approach is shown to be robust even in the presence of non-stationary increments and/or infinite second moments. Fixed points of the operators can be used for further sub classification of the processes when appropriate limits exist. As an example we look at advective dispersion in an ergodic velocity field. Let X(t) be a fixed point of the long-time renormalization group operator (RGO) RX(t)=X(rt)/r^p. Scaling laws for the probability density, mean first passage times, and finite-size Lyapunov exponents of such fixed points are reviewed in anticipation of more general results. A generalized RGO, Rp, where the exponent in R above is now a random variable is introduced. Scaling laws associated with these random RGOs (RRGOs) are demonstrated numerically and applied to a process modeling the transition from sub-dispersion to Fickian dispersion. The scaling laws for the RRGO are not simple power laws, but instead are a weighted average of power laws. The weighting in the scaling laws can be determined adaptively via Bayes' theorem.

  19. Infrared Yang-Mills theory: A renormalization group perspective

    NASA Astrophysics Data System (ADS)

    Weber, Axel; Dall’Olio, Pietro; Astorga, Francisco

    2016-05-01

    We describe a technically very simple analytical approach to the deep infrared regime of Yang-Mills theory in the Landau gauge via Callan-Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson-Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

  20. Infrared Renormalization-Group Flow for Heavy-Quark Masses

    SciTech Connect

    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.

  1. 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.

  2. Constraint on Defect and Boundary Renormalization Group Flows.

    PubMed

    Jensen, Kristan; O'Bannon, Andy

    2016-03-01

    A conformal field theory (CFT) in dimension d≥3 coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" b that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that b must decrease or remain constant from the ultraviolet to the infrared. Our result applies also to a CFT in d=3 flat space with a planar boundary. PMID:26991169

  3. Density matrix renormalization group numerical study of the kagome antiferromagnet.

    PubMed

    Jiang, H C; Weng, Z Y; Sheng, D N

    2008-09-12

    We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.

  4. Density matrix renormalization group approach to the massive Schwinger model

    NASA Astrophysics Data System (ADS)

    Byrnes, T. M.; Sriganesh, P.; Bursill, R. J.; Hamer, C. J.

    2002-07-01

    The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field θ=π is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located and demonstrated to belong in the 2D Ising universality class.

  5. Precise estimate of correlation length exponents from simple real-space renormalization group analysis

    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.

  6. Elliptical galaxies kinematics within general relativity with renormalization group effects

    SciTech Connect

    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)

  7. 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.

  8. 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.

  9. Determining the structure of supersymmetry breaking with renormalization group invariants

    SciTech Connect

    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.

  10. Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

    PubMed

    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.

  11. 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 .

  12. Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

    PubMed

    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

  13. The large-N{sub c} renormalization group

    SciTech Connect

    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}.

  14. Unique determination of the effective potential in terms of renormalization group functions

    SciTech Connect

    Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.

    2008-03-15

    The perturbative effective potential V in the massless {lambda}{phi}{sup 4} model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d{sup 4}V/d{phi}{sup 4})|{sub {phi}}{sub ={mu}}={lambda} is used, where {mu} represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.

  15. Renormalization Group for Critical Phenomena in Complex Networks

    PubMed Central

    Boettcher, S.; Brunson, C. T.

    2011-01-01

    We discuss the behavior of statistical models on a novel class of complex “Hanoi” networks. Such modeling is often the cornerstone for the understanding of many dynamical processes in complex networks. Hanoi networks are special because they integrate small-world hierarchies common to many social and economical structures with the inevitable geometry of the real world these structures exist in. In addition, their design allows exact results to be obtained with the venerable renormalization group (RG). Our treatment will provide a detailed, pedagogical introduction to RG. In particular, we will study the Ising model with RG, for which the fixed points are determined and the RG flow is analyzed. We show that the small-world bonds result in non-universal behavior. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of hierarchical networks generally, and we provide a general theory to describe our findings. PMID:22194725

  16. 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.

  17. Random Renormalization Group Operators Applied to Stochastic Dynamics

    NASA Astrophysics Data System (ADS)

    O'Malley, Daniel; Cushman, John H.

    2012-11-01

    Let X( t) be a fixed point the renormalization group operator (RGO), R p, r X( t)= X( rt)/ r p . Scaling laws for the probability density, mean first passage times, finite-size Lyapunov exponents of such fixed points are reviewed in anticipation of more general results. A generalized RGO, {R}_{P,n} where P is a random variable, is introduced. Scaling laws associated with these random RGOs (RRGOs) are demonstrated numerically and applied to subdiffusion in bacterial cytoplasm and a process modeling the transition from subdiffusion to classical diffusion. The scaling laws for the RRGO are not simple power laws, but are a weighted average of power laws. The weighting used in the scaling laws can be determined adaptively via Bayes' theorem.

  18. 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.

  19. Renormalization group analysis of a fermionic hot-spot model

    NASA Astrophysics Data System (ADS)

    Whitsitt, Seth; Sachdev, Subir

    2014-09-01

    We present a renormalization group (RG) analysis of a fermionic "hot-spot" model of interacting electrons on the square lattice. We truncate the Fermi-surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wave vector (π,π). This is motivated by the importance of these Fermi-surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether or not the hot spots are perfectly nested, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and J,V interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with J,V interactions have competing singlet dx2-y2 superconducting and d-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wave vectors, and find dominant d-form factor enhancement for a range of couplings.

  20. Renormalization group optimized perturbation theory at finite temperatures

    NASA Astrophysics Data System (ADS)

    Kneur, Jean-Loïc; Pinto, Marcus B.

    2015-12-01

    A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar λ ϕ4 field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-N results of the O (N ) model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard thermal loop perturbation theory. The latter approaches exhibit a sensibly degrading scale dependence at higher orders, which we identify as a consequence of missing RG invariance. In contrast RGOPT gives a considerably reduced scale dependence at two-loop level, even for relatively large coupling values √{λ /24 }˜O (1 ), making results much more stable as compared with standard perturbation theory, with expected similar properties for thermal QCD.

  1. 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.

  2. Renormalization group calculations with k∥ dependent couplings in a ladder

    NASA Astrophysics Data System (ADS)

    Abramovici, G.

    2006-05-01

    We investigate the phase diagram of a ladder system (two chains, with a Hubbard interaction U and an interband coupling t⊥). It is already known [M. Fabrizio, Phys. Rev. B 48 (1993) 15838] that backward interband scattering (gb) plays a particular role in this system. Moreover, some authors (for instance [ H.J. Schulz, Phys. Rev. B 53 (1996) R2959]) have early pointed out that, because of this coupling gb, parallel momentum (k∥) dependence could not be neglected. So we have introduced an original method to include k∥ dependence of couplings, in a RG calculation using the one particle irreducible (OPI) scheme. We calculate different susceptibilities, which are classified according to their symmetries. Our results depend on whether we include k∥ dependence or not. When we include this dependence, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small t⊥, followed by a superconducting region with a simultaneous divergence of the spin density waves channel. The region with only spin density wave fluctuations disappears, when k∥ dependence is neglected. Altogether, our results prove that k∥ is an influential variable in the renormalization group flow, for a ladder.

  3. Renormalization group evolution of the universal theories EFT

    DOE PAGES

    Wells, James D.; Zhang, Zhengkang

    2016-06-21

    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, butmore » 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. Finally, 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.« less

  4. Bimetric renormalization group flows in quantum Einstein gravity

    SciTech Connect

    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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

    SciTech Connect

    Pogorelov, A. A.; Suslov, I. M.

    2007-08-15

    According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.

  11. Renormalization-group approach to the vulcanization transition

    PubMed

    Peng; Goldbart

    2000-04-01

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

  12. Communication: Active space decomposition with multiple sites: Density matrix renormalization group algorithm

    SciTech Connect

    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.

  13. Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

    PubMed

    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

  14. Noncompact lattice QED with two charges: Phase diagram and renormalization group flow

    SciTech Connect

    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.}

  15. Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity

    SciTech Connect

    Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand E-mail: Bertrand.Chauvineau@oca.eu

    2015-09-01

    We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.

  16. Strong disorder renormalization group primer and the superfluid-insulator transition

    NASA Astrophysics Data System (ADS)

    Refael, Gil; Altman, Ehud

    2013-10-01

    This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

  17. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

    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.

  18. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

    PubMed

    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.

  19. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

    PubMed

    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

  20. 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.

  1. Renormalization group estimates of transport coefficients in the advection of a passive scalar by incompressible turbulence

    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.

  2. Decoherence in a double-dot Aharonov-Bohm interferometer: Numerical renormalization group study

    NASA Astrophysics Data System (ADS)

    Kubala, Björn; Roosen, David; Sindel, Michael; Hofstetter, Walter; Marquardt, Florian

    2014-07-01

    Coherence in electronic interferometers is typically believed to be restored fully in the limit of small voltages, frequencies, and temperatures. However, it is crucial to check this essentially perturbative argument by nonperturbative methods. Here we use the numerical renormalization group to study ac transport and decoherence in an experimentally realizable model interferometer, a parallel double quantum dot coupled to a phonon mode. The model allows us to clearly distinguish renormalization effects from decoherence. We discuss finite-frequency transport and confirm the restoration of coherence in the dc limit.

  3. Density matrix renormalization group with efficient dynamical electron correlation through range separation

    SciTech Connect

    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.

  4. 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.

  5. 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

  6. Approaching many-body localization from disordered Luttinger liquids via the functional renormalization group

    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.

  7. Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

    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.

  8. Logarithms of alpha in QED bound states from the renormalization group

    PubMed

    Manohar; Stewart

    2000-09-11

    The velocity renormalization group is used to determine lnalpha contributions to QED bound state energies. The leading-order anomalous dimension for the potential gives the alpha(5)lnalpha Lamb shift. The next-to-leading-order anomalous dimension determines the alpha(6)lnalpha, alpha(7)ln (2)alpha, and alpha(8)ln (3)alpha corrections to the energy. These are used to obtain the alpha(8)ln (3)alpha Lamb shift and alpha(7)ln (2)alpha hyperfine splitting for hydrogen, muonium, and positronium, as well as the alpha(2)lnalpha and alpha(3)ln (2)alpha corrections to the ortho- and parapositronium lifetimes. This shows for the first time that these logarithms can be computed from the renormalization group.

  9. Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

    PubMed

    Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

    2010-01-14

    We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+). PMID:20095661

  10. Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group

    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.

  11. Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group

    NASA Astrophysics Data System (ADS)

    Weichselbaum, Andreas; von Delft, Jan

    2007-08-01

    We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.

  12. New applications of the renormalization group method in physics: a brief introduction.

    PubMed

    Meurice, Y; Perry, R; Tsai, S-W

    2011-07-13

    The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

  13. The Density Matrix Renormalization Group for Strongly Correlated Electron Systems: A Generic Implementation

    SciTech Connect

    Alvarez, Gonzalo

    2009-01-01

    The purpose of this paper is (1) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (2) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks.

  14. The Magnus expansion and the in-medium similarity renormalization group

    SciTech Connect

    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.

  15. 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.

  16. Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

    NASA Astrophysics Data System (ADS)

    Seiler, Christian; Evers, Ferdinand

    2016-10-01

    A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

  17. Advances in the Application of the Similarity Renormalization Group to Strongly Interacting Systems

    NASA Astrophysics Data System (ADS)

    Wendt, Kyle Andrew

    The Similarity Renormalization Group (SRG) as applied in nuclear physics is a tool to soften and decouple inter-nucleon interactions. The necessity for such a tool is generated by the strong coupling of high- and low-momentum degrees of freedom in modern precision interactions. In recent years the SRG have been used with great success in enhancing few (2-12) nucleon calculations, but there are still many open questions about the nature of the SRG, and how it affects chiral forces. This thesis focuses on three topics within the study of the SRG as it applies to nuclear few-body interactions, with a focus on nuclear forces from chiral effective field theory. The typical SRG applied to nuclear physics is the T̂ rel-SRG, which uses the relative kinetic energy to generate a renormalizing flow. However, this generator explicitly violates criteria that ensure the SRG will decouple the interaction. Previous study of this generator found for a simple model that as the resolution is lowered past the momentum scales associated with a bound state, the T̂rel-SRG enhances coupling near the bound state whereas the classical Wegner generator completely decouples the bound state. In practice, this has not been an issue because the only two-body bound state is very shallow, and therefore well below the SRG softening scales. This study is extended to use leading order chiral effective field theory with large cutoffs to explore this decoupling. This builds in the same low energy physics while including spurious high energy details, including high energy bound states. The evolutions with T̂rel-SRG are compared to the evolution with Wegner's generator. During the decoupling process, the SRG can induce new non-local contributions to the interactions, which inhibits its application using Quantum Monte Carlo (QMC) methods. Separating out the non-local terms is numerically difficult. Instead an approximate separation is applied to T̂ rel-SRG evolved interactions and the nature of the

  18. 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.

  19. A renormalization group analysis of lattice models of two-dimensional membranes

    SciTech Connect

    Ambjoern, J.; Durhuus, B.; Froehlich, J.; Joensson, T. )

    1989-04-01

    The authors study lattice models of two-dimensional membranes of interest in statistical physics. The energy functional of a membrane is expressed as a sum of terms proportional to the surface area of the membrane, an extrinsic curvature and an intrinsic curvature quantity, respectively, but they neglect excluded volume effects. They introduce a renormalization transformation for these models which preserves the form of the energy functional, up to nonlocal terms. Their renormalization group construction is used to analyze the phase diagram and the different critical regimes of their models. They find evidence for a crumpling transition, separating a regime where surfaces are crystalline from one where the surfaces collapse to branched polymers, and they find a third genuine random-surface regime.

  20. 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.

  1. Chiral dynamics in a magnetic field from the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Kamikado, Kazuhiko; Kanazawa, Takuya

    2014-03-01

    We investigate the quark-meson model in a magnetic field using the functional renormalization group equation beyond the local-potential approximation. Our truncation of the effective action involves anisotropic wave function renormalization for mesons, which allows us to investigate how the magnetic field distorts the propagation of neutral mesons. Solving the flow equation numerically, we find that the transverse velocity of mesons decreases with the magnetic field at all temperatures, which is most prominent at zero temperature. The meson screening masses and the pion decay constants are also computed. The constituent quark mass is found to increase with magnetic field at all temperatures, resulting in the crossover temperature that increases monotonically with the magnetic field. This tendency is consistent with most model calculations but not with the lattice simulation performed at the physical point. Our work suggests that the strong anisotropy of meson propagation may not be the fundamental origin of the inverse magnetic catalysis.

  2. Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices.

    PubMed

    Huang, Yu-Kun

    2011-03-01

    A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special E·S·E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.

  3. Renormalization group improved pQCD prediction for Υ(1 S) leptonic decay

    NASA Astrophysics Data System (ADS)

    Shen, Jian-Ming; Wu, Xing-Gang; Ma, Hong-Hao; Bi, Huan-Yu; Wang, Sheng-Quan

    2015-06-01

    The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to Υ(1 S) leptonic decay rate Γ(Υ(1 S) → ℓ+ℓ-) has been finished by Beneke et al. [8]. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for Γ(Υ(1 S) → ℓ+ℓ-) by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of β-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for Υ(1 S) leptonic decay, i.e. keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.

  4. Interplay of the scaling limit and the renormalization group: Implications for symmetry restoration

    NASA Astrophysics Data System (ADS)

    Konik, Robert M.; Saleur, Hubert; Ludwig, Andreas W.

    2002-08-01

    Symmetry restoration is usually understood as a renormalization-group induced phenomenon. In this context, the issue of whether one-loop renormalization-group equations can be trusted in predicting symmetry restoration has recently been the subject of much debate. Here we advocate a more pragmatic point of view and expand the definition of symmetry restoration to encompass all situations where the physical properties have only a weak dependence upon an anisotropy in the bare couplings. Moreover we concentrate on universal properties, and so take a scaling limit where the physics is well described by a field theory. In this context, we find a large variety of models that exhibit, for all practical purposes, symmetry restoration: even if symmetry is not restored in a strict sense, physical properties are surprisingly insensitive to the remaining anisotropy. Although we have adopted an expanded notion of symmetry restoration, we nonetheless emphasize that the scaling limit also has implications for symmetry restoration as a renormalization-group induced phenomenon. In all the models we considered, the scaling limit turns out only to permit bare couplings which are nearly isotropic and small. Then the one-loop β function should contain all the physics and higher loop orders can be neglected. We suggest that this feature generalizes to more complex models. We exhibit a large class of theories with current-current perturbations [of which the SO(8) model of interest in two-leg Hubbard ladders and armchair carbon nanotubes is one] where the one-loop β functions indicate symmetry restoration; thus we argue that these results can be trusted within the scaling limit.

  5. 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

  6. Apker Award Recipient: Renormalization-Group Study of Helium Mixtures Immersed in a Porous Medium

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna

    1998-03-01

    Superfluidity and phase separation in ^3He-^4He mixtures immersed in aerogel are studied by renormalization-group theory. Firstly, the theory is applied to jungle-gym (non-random) aerogel.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 55, 3798 (1997).) This calculation is conducted via the coupled renormalization-group mappings of interactions near and away from aerogel. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfludity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. Secondly, the theory is applied to true aerogel, which has quenched disorder at both atomic and geometric levels.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 56, 11865 (1997).) This calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of quenched probability distributions of random interactions. Random-bond effects on superfluidity onset and random-field effects on superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general prediction and experiments. Based on these studies, the experimentally observed(S.B. Kim, J. Ma, and M.H.W. Chan, Phys. Rev. Lett. 71, 2268 (1993); N. Mulders and M.H.W. Chan, Phys. Rev. Lett. 75, 3705 (1995).) distinctive characteristics of ^3He-^4He mixtures in aerogel are related to the aerogel properties of connectivity, tenuousness, and atomic and geometric randomness.

  7. Renormalization group invariants and sum rules in the deflected mirage mediation supersymmetry breaking

    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.

  8. A simpler derivation of Feigenbaum's renormalization group equation for the period-doubling bifurcation sequence

    NASA Astrophysics Data System (ADS)

    Coppersmith, S. N.

    1999-01-01

    One interesting and important property of nonlinear dynamical systems is that they can exhibit universality—behavior that is quantitatively identical for a broad class of systems. The first and most famous example of universality in a dynamical system was identified by Feigenbaum [M. J. Feigenbaum, J. Stat. Phys. 19, 25-52 (1978), 21, 669-706 (1979)] in the period-doubling route to chaos. This note presents a new derivation of Feigenbaum's renormalization group equation, used to understand this universality. The argument, designed for incorporation into an undergraduate dynamical systems course, is simpler than those in standard textbooks.

  9. 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.

  10. Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

    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.

  11. Renormalization-group-invariant partial sum of Feynman diagrams and its application to phase transitions

    NASA Astrophysics Data System (ADS)

    Hong, Seok-In

    1995-08-01

    The phase transition of the three-dimensional (3D) φ4 theory is considered in terms of the two-dimensional (2D) effective φ4 theory for sufficiently high temperatures. Instead of the effective potential, we use the renormalization-group-(RG-) invariant mass parameter Γ(2)(p=0) directly. For practical use, we find that superdaisy diagrams are a RG-invariant subset of Feynman diagrams for Γ(2)(p=0). The parameters of the effective theory are related to the original ones by certain matching conditions. The resulting critical temperature is the same as that obtained by Einhorn and Jones.

  12. Renormalization-group theory for the phase-field crystal equation

    NASA Astrophysics Data System (ADS)

    Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.

    2006-07-01

    We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

  13. Order parameter evolution in scalar QFT: Renormalization group resummation of secular terms

    SciTech Connect

    de Vega, H.J.; Salgado, J.F.

    1997-11-01

    The quantum evolution equations for the field expectation value are analytically solved to cubic order in the field amplitude and to one-loop level in the {lambda}{phi}{sup 4} model. We adapt and use the renormalization group (RG) method for such nonlinear and nonlocal equations. The time dependence of the field expectation value is explicitly derived integrating the RG equations. It is shown that the field amplitude for late times approaches a finite limit as O(t{sup {minus}3/2}). This limiting value is expressed as a function of the initial field amplitude. {copyright} {ital 1997} {ital The American Physical Society}

  14. 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

  15. Two-dimensional N=(2,2) Wess-Zumino model in the functional renormalization group approach

    SciTech Connect

    Synatschke-Czerwonka, Franziska; Fischbacher, Thomas; Bergner, Georg

    2010-10-15

    We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum-dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations are reproduced with high accuracy. But in the regime with intermediate couplings higher-order operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.

  16. Diffusion on a one-dimensional disordered lattice: A renormalization-group approach

    NASA Astrophysics Data System (ADS)

    Guyer, R. A.

    1984-04-01

    Diffusion of a particle on a one-dimensional disordered lattice is studied using the renormalization-group (RG) procedure of Goncalves da Silva and Koiller

    [Solid State Commun. 40, 215 (1981)]
    . The RG equations are derived and their physical content is discussed. Several examples are studied using the RG equations and a disorder-averaging procedure that permits stepwise averaging of the RG equations. Values of the diffusion constant so calculated, while qualitatively correct, are in poor agreement with the known correct answer. The RG equations are shown to be derivable from a dedecoration carried out on a replica-trick description of the diffusion process. Employing the relationship of the RG equations to dedecoration, a stepwise disorder-averaging procedure is constructed that yields values of the diffusion constant in excellent agreement with expectations. The relationships of the RG equations to the renormalization-group treatment of Machta
    [Phys. Rev. B 24, 5260 (1981)]
    and to the logistic equation are discussed.

  17. From short to long distances with Gell-Mann--Low Renormalization group

    NASA Astrophysics Data System (ADS)

    Dunjko, Vanja; Olshanii, Maxim

    2004-05-01

    Computing correlation functions is an important and formidable problem of many-body physics. For 1D gapless systems, Haldane's theory gives exponents of large distance expansions, model details entering through speed of sound. The prefactors depend on high-energy cutoffs, and it is unclear which model-dependent parameters set them. ..We present a method very well-suited for the approximate computation of the leading order prefactor, with short-distance expansion as an input. Our basis is the Gell-Mann--Low Renormalization Group, and optimism about sufficient analyticity of correlation functions. In the test case of Tonks-Girardeau gas, a rare model where both short and long-distance expansions are known, already the first non-zero subleading term of the short-distance expansion gives the long-distance prefactor to within 15%. ..While Wilson's Renormalization Group makes high energy cutoffs irrelevant, we actually determine them for Haldane model. A byproduct of our method is an interpolation between short and long-distance behaviors, which we use to treat interaction-induced decoherence in atom interferometers.

  18. 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

  19. Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem

    PubMed Central

    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

  20. Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem.

    PubMed

    Grusdt, F; Shchadilova, Y E; Rubtsov, A N; Demler, E

    2015-07-17

    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.

  1. Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

    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.

  2. Dynamic structure factor of a Fibonacci lattice: A renormalization-group approach

    NASA Astrophysics Data System (ADS)

    Karmakar, S. N.; Chakrabarti, Arunava; Moitra, R. K.

    1992-08-01

    We present a real-space renormalization-group method for evaluating the exact dynamic structure factor S(q,ω) of a quasiperiodic Fibonacci chain. Contrary to earlier work that takes account only of the global aspects of the symmetry of the chain, our method additionally takes care of the local environmental aspects of the symmetry by separating the original lattice into a finite number of self-similar interpenetrating sublattices, followed by elimination of the coupling between them. Our method also yields correctly the positions of the Bragg peaks of the Fibonacci chain. Moreover, the present method allows the sites of the chain to be grouped into classes following a ``genealogical'' classification, the members of a given class being equivalent up to a certain length scale. Based on this classification, the proof of the existence of a key site, which has only been conjectured in our earlier work using numerical search, has been given.

  3. Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group

    NASA Astrophysics Data System (ADS)

    Weichselbaum, Andreas; von Delft, Jan

    2007-03-01

    We show how spectral functions for quantum impurity models, i.e. nanosystem embedded in fermionic or bosonic environment, can be calculated very accurately using a complete set of ``discarded'' numerical renormalization group (NRG) eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our rigorous derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods including state of the art DM-NRG. The resulting procedure based on the full density matrix of the system (FDM-NRG) ensures that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.

  4. Nonperturbative renormalization group and momentum dependence of n-point functions. I

    SciTech Connect

    Blaizot, Jean-Paul; Mendez-Galain, Ramon; Wschebor, Nicolas

    2006-11-15

    We present an approximation scheme to solve the nonperturbative renormalization group equations and obtain the full momentum dependence of the n-point functions. It is based on an iterative procedure where, in a first step, an initial ansatz for the n-point functions is constructed by solving approximate flow equations derived from well motivated approximations. These approximations exploit the derivative expansion and the decoupling of high momentum modes. The method is applied to the O(N) model. In leading order, the self-energy is already accurate both in the perturbative and the scaling regimes. A stringent test is provided by the calculation of the shift {delta}T{sub c} in the transition temperature of the weakly repulsive Bose gas, a quantity which is particularly sensitive to all momentum scales. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%.

  5. Quantum phase transition by employing trace distance along with the density matrix renormalization group

    SciTech Connect

    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.

  6. Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram

    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.

  7. Renormalization group improvement and dynamical breaking of symmetry in a supersymmetric Chern-Simons-matter model

    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.

  8. Many-body localization phase transition: A simplified strong-randomness approximate renormalization group

    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.

  9. 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.

  10. 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.

  11. Multichannel Numerical Renormalization Group study of the Anderson Hamiltonian with multiple impurities

    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.

  12. Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution

    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.

  13. Renormalization group evolution of multi-gluon correlators in high energy QCD

    NASA Astrophysics Data System (ADS)

    Dumitru, A.; Jalilian-Marian, J.; Lappi, T.; Schenke, B.; Venugopalan, R.

    2011-12-01

    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.

  14. Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution.

    PubMed

    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. PMID:27415353

  15. Density-matrix renormalization-group study of current and activity fluctuations near nonequilibrium phase transitions.

    PubMed

    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

  16. Numerical study of renormalization group flows of nuclear effective field theory without pions on a lattice

    NASA Astrophysics Data System (ADS)

    Harada, Koji; Sasabe, Satoru; Yahiro, Masanobu

    2016-08-01

    We formulate the next-to-leading-order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice and investigate nonperturbative renormalization group flows in the strong-coupling region by diagonalizing the Hamiltonian numerically. The cutoff (proportional to the inverse of the lattice constant) dependence of the coupling constants is obtained by changing the lattice constant with the binding energy and the asymptotic normalization constant for the ground state being fixed. We argue that the critical line can be obtained by looking at the finite-size dependence of the ground-state energy. We determine the relevant operator and locate the nontrivial fixed point, as well as the physical flow line corresponding to the deuteron in the two-dimensional plane of dimensionless coupling constants. It turns out that the location of the nontrivial fixed point is very close to the one obtained by the corresponding analytic calculation, but the relevant operator is quite different.

  17. 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).

  18. 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.

  19. 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.

  20. Effect of weak impurities on electronic properties of graphene: Functional renormalization-group analysis

    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.

  1. 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.

  2. Electronic quasiparticles in the quantum dimer model: Density matrix renormalization group results

    NASA Astrophysics Data System (ADS)

    Lee, Junhyun; Sachdev, Subir; White, Steven R.

    2016-09-01

    We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates. The model contains bosonic dimers, representing a spin-singlet valence bond between a pair of electrons, and fermionic dimers, representing a quasiparticle with spin-1/2 and charge +e . By density matrix renormalization group calculations on a long but finite cylinder, we obtain the ground-state density distribution of the fermionic dimers for a number of different total densities. From the Friedel oscillations at open boundaries, we deduce that the Fermi surface consists of small hole pockets near (π /2 ,π /2 ) , and this feature persists up to a doping density of 1/16. We also compute the entanglement entropy and find that it closely matches the sum of the entanglement entropies of a critical boson and a low density of free fermions. Our results support the existence of a fractionalized Fermi liquid in this model.

  3. Symmetry-conserving purification of quantum states within the density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Nocera, A.; Alvarez, G.

    2016-01-01

    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 and using canonical approaches. We furthermore explore its applicability beyond spins systems to t -J and Hubbard models.

  4. Symmetry-conserving purification of quantum states within the density matrix renormalization group

    DOE PAGES

    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

  5. Random interface growth in a random environment: Renormalization group analysis of a simple model

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Kakin, P. I.

    2015-10-01

    We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known Kardar-Parisi-Zhang model. The turbulent advecting velocity field is modeled by the Kraichnan rapid-change ensemble: Gaussian statistics with the correlation function < vv> ∝ δ( t - tς ) k - d-ξ, where k is the wave number and ξ is a free parameter, 0 < ξ < 2. We study the effects of the fluid compressibility. Using the field theory renormalization group, we show that depending on the relation between the exponent ξ and the spatial dimension d, the system manifests different types of large-scale, long-time asymptotic behavior associated with four possible fixed points of the renormalization group equations. In addition to the known regimes (ordinary diffusion, the ordinary growth process, and a passively advected scalar field), we establish the existence of a new nonequilibrium universality class. We calculate the fixed-point coordinates and their stability regions and critical dimensions to the first order of the double expansion in ξ and ɛ = 2 - d (one-loop approximation). It turns out that for an incompressible fluid, the most realistic values ξ = 4/3 or ξ = 2 and d = 1 or d = 2 correspond to the case of a passive scalar field, where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant and the interface growth is completely determined by the turbulent transfer. If the compressibility becomes sufficiently strong, then a crossover occurs in the critical behavior, and these values of d and ξ are in the stability region of the new regime, where the advection and nonlinearity are both important. But the coordinates of the fixed point for this regime are in the unphysical region, and its physical interpretation hence remains an open problem.

  6. Spin-adapted density matrix renormalization group algorithms for quantum chemistry

    NASA Astrophysics Data System (ADS)

    Sharma, Sandeep; Chan, Garnet Kin-Lic

    2012-03-01

    We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)], 10.1209/epl/i2002-00393-0 to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of hat{S}^2, and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)], 10.1103/PhysRevE.61.3199 where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe2S2, [Fe2S2(SCH3)4]2-, and Cr2 systems. In the case of Fe2S2, the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe2S2(SCH3)4]2-, we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr2 we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.

  7. Application of the renormalization group to the calculation of the vacuum decay rate in flat and curved space-time

    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.

  8. Gate-tunable Kondo resistivity and dephasing rate in graphene studied by numerical renormalization group calculations

    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

  9. A general non-Abelian density matrix renormalization group algorithm with application to the C{sub 2} dimer

    SciTech Connect

    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.

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

    SciTech Connect

    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.

  11. Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.

    PubMed

    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.

  12. 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.

  13. A state interaction spin-orbit coupling density matrix renormalization group method.

    PubMed

    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

  14. Thouless theorem for matrix product states and subsequent post density matrix renormalization group methods

    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.

  15. 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.

  16. Density-matrix renormalization group algorithm with multi-level active space.

    PubMed

    Ma, Yingjin; Wen, Jing; Ma, Haibo

    2015-07-21

    The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field (SCF) variant ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that ML-type DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values. PMID:26203012

  17. Renormalization group scale-setting from the action—a road to modified gravity theories

    NASA Astrophysics Data System (ADS)

    Domazet, Silvije; Štefančić, Hrvoje

    2012-12-01

    The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

  18. Turbulent magnetic Prandtl number in helical kinematic magnetohydrodynamic turbulence: two-loop renormalization group result.

    PubMed

    Jurčišinová, E; Jurčišin, M; Remecký, R; Zalom, P

    2013-04-01

    Using the field theoretic renormalization group technique, the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl number in the kinematic magnetohydrodynamic turbulence is investigated in the two-loop approximation. It is shown that the presence of helicity decreases the value of the turbulent magnetic Prandtl number and, at the same time, the two-loop helical contribution to the turbulent magnetic Prandtl number is at most 4.2% (in the case with the maximal helicity) of its nonhelical value. These results demonstrate, on one hand, the potential importance of the presence of asymmetries in processes in turbulent environments and, on the other hand, the rather strong stability of the properties of diffusion processes of the magnetic field in the conductive turbulent environment with the spatial parity violation in comparison to the corresponding systems without the spatial parity violation. In addition, obtained results are compared to the corresponding results found for the two-loop turbulent Prandtl number in the model of passively advected scalar field. It is shown that the turbulent Prandtl number and the turbulent magnetic Prandtl number, which are the same in fully symmetric isotropic turbulent systems, are essentially different when one considers the spatial parity violation. It means that the properties of the diffusion processes in the turbulent systems with a given symmetry breaking can considerably depend on the internal tensor structure of advected quantities.

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

    NASA Astrophysics Data System (ADS)

    Katanin, A.

    2011-12-01

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

  20. Thermodynamics of weakly coupled Falicov-Kimball chains from renormalization-group theory.

    PubMed

    Sznajd, Jozef

    2015-06-01

    The linear perturbation renormalization group is used to study spinless two-band fermion chains at half-filling. The model consists of two species of spinless fermions, namely localized f and extended p, and it takes into account the following: the kinetic energy of fermions p, the on-site Coulomb repulsion V between p and f fermions, chemical potentials μ(p) and μ(f) adjusted in such a way that the average of the site occupation 〈n(f)(i)〉+〈n(p)(i)〉=1, and a weak interchain hopping t(x). The average occupation number, the specific heat, and the correlation functions are studied as functions of temperature. For a single chain the occupation number is a smooth function of T and the specific heat displays two maxima. The weak interchain hopping triggers a discontinuity in the occupation number of fermions as a function of temperature. A long-standing controversy on whether the Falicov-Kimball model can describe a discontinuous transition of n(f) is also addressed.

  1. Radiatively induced first-order phase transitions the necessity of the renormalization group

    NASA Astrophysics Data System (ADS)

    Alford, Mark; March-Russell, John

    1994-04-01

    We advocate a (Wilson) renormalization-group (RG) treatment of finite-temperature first-order phase transitions, in particular those driven by radiative corrections such as occur in the standard model, and other spontaneously broken gauge theories. We introduce the scale-dependent coarse-grained free energy SΛ[ φ] which we explicitly calculate, using the Wilson RG and a (4 - ɛ)-expansion, for a scalar toy model that shares many features of the gauged case. As argued by Langer and others, the dynamics of the phase transition are described by SΛ[ φ] with 1/Λ of order the bubble wall thickness, and not by the usual (RG-improved) finite-temperature effective action which is reproduced by SΛ[ φ] for Λ → 0. We argue that for weakly first-order transitions (such as that in the he (4 - ɛ)-expansion is necessary to control an inevitable growth of the effective scale-dependent coupling towards the strong-coupling regime, and that diagrammatic resummation techniques are unlikely to be appropriate.

  2. A driven similarity renormalization group approach to quantum many-body problems

    SciTech Connect

    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.

  3. 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.

  4. 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.

  5. Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point

    NASA Astrophysics Data System (ADS)

    Vosk, Ronen; Altman, Ehud

    2013-02-01

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

  6. Many-body localization in one dimension as a dynamical renormalization group fixed poin

    NASA Astrophysics Data System (ADS)

    Vosk, Ronen; Altman, Ehud

    2013-03-01

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

  7. Tensor Renormalization Group Study of the General Spin-S Blume-Capel Model

    NASA Astrophysics Data System (ADS)

    Yang, Li-Ping; Xie, Zhi-Yuan

    2016-10-01

    We focus on the special situation of D = 2J in the general spin-S Blume-Capel model on a square lattice. Under an infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are investigated by the newly developed tensor renormalization group method. We clearly demonstrate the phase transition process: in the case of an integer spin-S, there are S first-order phase transitions with the stepwise magnetizations M = S,S - 1, ldots ,0; in the case of a half-odd integer spin-S, there are S - 1/2 first-order phase transitions with corresponding M = S,S - 1, ldots ,1/2 in addition to one continuous phase transition due to spin-flip Z2 symmetry breaking. At low temperatures, all first-order phase transitions are accompanied by the successive disappearance of the spin-component pairs (±s); furthermore, the transition temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of a magnetic field, a visualization parameter characterizing the intrinsic degeneracy of the different phases provides a different reference for the phase transition process.

  8. Dynamical renormalization group study for a class of non-local interface equations

    NASA Astrophysics Data System (ADS)

    Nicoli, Matteo; Cuerno, Rodolfo; Castro, Mario

    2011-10-01

    We provide a detailed dynamic renormalization group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) nonlinearity, which nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, which agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent of the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems such as the Lai-Das Sarma-Villain equation, in which vertex cancellation is known not to imply an associated symmetry of the equation.

  9. A state interaction spin-orbit coupling density matrix renormalization group method.

    PubMed

    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.

  10. 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.

  11. Theory of fully developed hydrodynamic turbulent flow: Applications of renormalization-group methods

    NASA Astrophysics Data System (ADS)

    Yuan, Jian-Yang; Ronis, David

    1992-04-01

    A model for randomly stirred or homogeneous turbulent fluids is analyzed using renormalization-group methods on a path-integral representation of the Navier-Stokes equations containing a spatially and temporally colored noise source. For moderate Reynolds numbers and certain values of the dynamic exponent governing the noise correlation, an additional scaling regime is found at wave vectors k beyond those where the Kolmogorov 5/3 law holds. In this case, the energy spectrum decays as k-1-z, where 1

  12. 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.

  13. Supersymmetry-breaking parameters from renormalization group invariants at the LHC

    SciTech Connect

    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.

  14. Renormalization group equation study of the scalar sector of the minimal B-L extension of the standard model

    SciTech Connect

    Basso, Lorenzo; Moretti, Stefano; Pruna, Giovanni Marco

    2010-09-01

    We present the complete set of renormalization group equations at one loop for the nonexotic minimal U(1) extension of the standard model (SM). It includes all models that are anomaly-free with the SM fermion content augmented by one right-handed neutrino per generation. We then pursue the numerical study of the pure B-L model, deriving the triviality and vacuum stability bounds on an enlarged scalar sector comprising one additional Higgs singlet field with respect to the SM.

  15. Study on vapor-liquid equilibria and surface tensions for nonpolar fluids by renormalization group theory and density gradient theory.

    PubMed

    Fu, Dong

    2006-10-01

    An equation of state (EOS) applicable for both the uniform and nonuniform fluids is established by using the density-gradient theory (DGT). In the bulk phases, the EOS reduces to statistical associating fluid theory (SAFT). By combining the EOS with the renormalization group theory (RGT), the vapor-liquid-phase equilibria and surface tensions for 10 nonpolar chainlike fluids are investigated from low temperature up to the critical point. The obtained results agree well with the experimental data.

  16. Renormalized entanglement entropy

    NASA Astrophysics Data System (ADS)

    Taylor, Marika; Woodhead, William

    2016-08-01

    We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement en-tropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renor-malization group flows. The renormalized entanglement entropy for disk regions in AdS 4 spacetimes agrees precisely with the holographically renormalized action for AdS 4 with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deforma-tions by operators of dimension 3 /2 < Δ < 5 /2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entangle-ment entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

  17. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

    NASA Astrophysics Data System (ADS)

    DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

    2008-06-01

    For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

  18. Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

    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.

  19. Many-body localization and transition by density matrix renormalization group and exact diagonalization studies

    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.

  20. Ab initio density matrix renormalization group study of magnetic coupling in dinuclear iron and chromium complexes

    SciTech Connect

    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.

  1. Renormalization-group analysis of layered sine-Gordon type models

    NASA Astrophysics Data System (ADS)

    Nándori, I.; Nagy, S.; Sailer, K.; Jentschura, U. D.

    2005-10-01

    We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two "normal", massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the "mass corrections". The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J→0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

  2. Physics implications of the diphoton excess from the perspective of renormalization group flow

    DOE PAGES

    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

  3. 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.

  4. Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Münder, W.; Weichselbaum, A.; Holzner, A.; von Delft, Jan; Henley, C. L.

    2010-07-01

    A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix (CDM). For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all the correlations between the two clusters. We show how to extract from the CDM a survey of the relative strengths of the system's correlations in different symmetry sectors and the nature of their decay with distance (power law or exponential), as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To achieve this goal, we introduce a new method of analysing the CDM, termed the dominant operator basis (DOB) method, which identifies in an unbiased fashion a small set of operators for each cluster that serve as a basis for the dominant correlations of the system. We illustrate this method by analysing the CDM for a spinless extended Hubbard model that features a competition between charge density correlations and pairing correlations, and show that the DOB method successfully identifies their relative strengths and dominant correlators. To calculate the ground state of this model, we use the density matrix renormalization group, formulated in terms of a variational matrix product state (MPS) approach within which subsequent determination of the CDM is very straightforward. In an extended appendix, we give a detailed tutorial introduction to our variational MPS approach for ground state calculations for one-dimensional quantum chain models. We present in detail how MPSs overcome the problem of large Hilbert space dimensions in these models and describe all the techniques needed for handling them in practice.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

    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.

  10. Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.

    PubMed

    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.

  11. The density matrix renormalization group for strongly correlated electron systems: A generic implementation

    NASA Astrophysics Data System (ADS)

    Alvarez, G.

    2009-09-01

    The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks. Program summaryProgram title: DMRG++ Catalogue identifier: AEDJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: See file LICENSE No. of lines in distributed program, including test data, etc.: 15 795 No. of bytes in distributed program, including test data, etc.: 83 454 Distribution format: tar.gz Programming language: C++, MPI Computer: PC, HP cluster Operating system: Any, tested on Linux Has the code been vectorized or parallelized?: Yes RAM: 1 GB (256 MB is enough to run included test) Classification: 23 External routines: BLAS and LAPACK Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice. Solution method: The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the

  12. Size distributions of shocks and static avalanches from the functional renormalization group.

    PubMed

    Le Doussal, Pierre; Wiese, Kay Jörg

    2009-05-01

    Interfaces pinned by quenched disorder are often used to model jerky self-organized critical motion. We study static avalanches, or shocks, defined here as jumps between distinct global minima upon changing an external field. We show how the full statistics of these jumps is encoded in the functional-renormalization-group fixed-point functions. This allows us to obtain the size distribution P(S) of static avalanches in an expansion in the internal dimension d of the interface. Near and above d=4 this yields the mean-field distribution P(S) approximately S;{-3/2}e;{-S4S_{m}} , where S_{m} is a large-scale cutoff, in some cases calculable. Resumming all one-loop contributions, we find P(S) approximately S;{-tau}exp(C(SS_{m});{1/2}-B/4(S/S_{m});{delta}) , where B , C , delta , and tau are obtained to first order in =4-d . Our result is consistent to O() with the relation tau=tau_{zeta}:=2-2/d+zeta , where zeta is the static roughness exponent, often conjectured to hold at depinning. Our calculation applies to all static universality classes, including random-bond, random-field, and random-periodic disorders. Extended to long-range elastic systems, it yields a different size distribution for the case of contact-line elasticity, with an exponent compatible with tau=2-1/d+zeta to O(=2-d) . We discuss consequences for avalanches at depinning and for sandpile models, relations to Burgers turbulence and the possibility that the relation tau=tau_{zeta} be violated to higher loop order. Finally, we show that the avalanche-size distribution on a hyperplane of codimension one is in mean field (valid close to and above d=4 ) given by P(S) approximately K_{13}(S)S , where K is the Bessel- K function, thus tau_{hyperplane}=4/3 .

  13. Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics

    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.

  14. Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach.

    PubMed

    Khemani, Vedika; Pollmann, Frank; Sondhi, S L

    2016-06-17

    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. PMID:27367405

  15. Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction

    PubMed Central

    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

  16. Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

    SciTech Connect

    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.

  17. Renormalization group for centrosymmetric gauge transformations of the dynamic motion for a Markov-ordered polymer chain

    SciTech Connect

    Mikhailov, I.D.; Zhuravskii, L.V.

    1987-11-01

    A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for along polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type.

  18. Renormalization-Group Theory Study of Superfluidity and Phase Separation of Helium Mixtures Immersed in Jungle-Gym Aerogel

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna; Berker, A. Nihat

    1997-03-01

    Superfluidity and phase separation in ^3He-^4He mixtures immersed in jungle-gym (non-random) aerogel are studied by renormalization-group theory.(Phys. Rev. B, in press (1996)) Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena, and trends with respect to aerogel concentration, are explained by the connectivity and tenuousness of jungle-gym aerogel.

  19. Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a nonrandom aerogel

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna; Nihat Berker, A.

    1997-02-01

    Superfluidity and phase separation in 3-4He mixtures immersed in a jungle-gym (nonrandom) aerogel are studied by renormalization-group theory. Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low 4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena and trends with respect to aerogel concentration are explained by the connectivity and tenuousness of a jungle-gym aerogel.

  20. Monte Carlo simulations on marker grouping and ordering.

    PubMed

    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.

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

    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.

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

    PubMed

    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

  3. Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.

    PubMed

    Sasaki, Akira; Kojo, Masashi; Hirose, Kikuji; Goto, Hidekazu

    2011-11-01

    The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

  4. Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model.

    PubMed

    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.

  5. Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group

    DOE PAGES

    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

  6. Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening.

    PubMed

    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

  7. Two-Band Fibonacci Quasicrystal with Hybridization:. Exact Local GREEN’S Function Using the Renormalization-Group Method

    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.

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

    PubMed

    Hewson, Alex C; Bauer, Johannes

    2010-03-24

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

  9. Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group

    SciTech Connect

    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.

  10. Communication: Novel quantum states of electron spins in polycarbenes from ab initio density matrix renormalization group calculations.

    PubMed

    Mizukami, Wataru; Kurashige, Yuki; Yanai, Takeshi

    2010-09-01

    An investigation into spin structures of poly(m-phenylenecarbene), a prototype of magnetic organic molecules, is presented using the ab initio density matrix renormalization group method. It is revealed by achieving large-scale multireference calculations that the energy differences between high-spin and low-spin states (spin-gaps) of polycarbenes decrease with increasing the number of carbene sites. This size-dependency of the spin-gaps strikingly contradicts the predictions with single-reference methods including density functional theory. The wave function analysis shows that the low-spin states are beyond the classical spin picture, namely, much of multireference character, and thus are manifested as strongly correlated quantum states. The size dependence of the spin-gaps involves an odd-even oscillation, which cannot be explained by the integer-spin Heisenberg model with a single magnetic-coupling constant.

  11. t-Jz ladder: Density-matrix renormalization group and series expansion calculations of the phase diagram

    NASA Astrophysics Data System (ADS)

    Weisse, A.; Bursill, R. J.; Hamer, C. J.; Weihong, Zheng

    2006-04-01

    The phase diagram of the two-leg t-Jz ladder is explored, using the density-matrix renormalization group method. Results are obtained for energy gaps, electron density profiles, and correlation functions for the half filled and quarter filled cases. The effective Lagrangian velocity parameter vρ is shown to vanish at half filling. The behavior of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full t-J ladder, but scaled up by a factor of about 2 in coupling. Near half filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter filling the system appears to be in a Tomonaga-Luttinger phase.

  12. Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening

    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.

  13. Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle

    NASA Astrophysics Data System (ADS)

    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.

  14. Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle.

    PubMed

    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.

  15. An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory.

    PubMed

    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.

  16. Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory.

    PubMed

    Mi, Jianguo; Tang, Yiping; Zhong, Chongli; Li, Yi-Gui

    2005-11-01

    Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.

  17. Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the 'Standard Values'

    SciTech Connect

    Pogorelov, A. A.; Suslov, I. M.

    2008-06-15

    New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standard values and for a further increase in accuracy.

  18. Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle.

    PubMed

    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

  19. Low-lying excited states in armchair polyacene within Pariser-Parr-Pople model: A density matrix renormalization group study

    SciTech Connect

    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.

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

    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= at site r are quite different for junctions with S =1 /2 , 1, 3/2, and 2. The GS has finite total spin SG=2 S (S ) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0 (<0 ) at sites of the larger (smaller) sublattice. S =1 /2 junctions have delocalized states and decreasing spin densities with increasing N . S =1 junctions have four localized Sz=1 /2 states at the end of each arm and centered on the junction, consistent with localized states in S =1 chains with finite Haldane gap. The GS of S =3 /2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S =1 /2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S =3 /2 or 2 junctions.

  1. Holographic renormalization group flows in N =3 Chern-Simons-Matter theory from N =3 4D gauged supergravity

    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.

  2. Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene

    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.

  3. Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

    NASA Astrophysics Data System (ADS)

    Saptsov, R. B.; Wegewijs, M. R.

    2012-12-01

    We study electron quantum transport through a strongly interacting Anderson quantum dot at finite bias voltage and magnetic field at zero temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic (generalized master) equation for the reduced density operator. To this end, we further develop the general, finite-temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville Fock space strongly simplifies the construction of operators and superoperators that transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule of quantum mechanics for the total system of quantum dot plus reservoirs. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator kernel becomes explicit. Using the constraints of the causal structure, we construct a parametrization of the exact effective time-evolution kernel for which we analytically find the eigenvectors and eigenvalues in terms of a minimal set of only 30 independent coefficients. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Contreras-Pulido , Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling Γ. Furthermore, in the wide-band limit, the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. The remaining diagrams can be identified simply by their topology and are manifestly independent of the energy cutoff term by term. By an exact reformulation of this series, we integrate out all infinite-temperature effects, obtaining an expansion targeting only the nontrivial, finite-temperature corrections, and

  4. Full density-matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

    NASA Astrophysics Data System (ADS)

    Merker, L.; Weichselbaum, A.; Costi, T. A.

    2012-08-01

    Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models [see A. Weichselbaum and J. von Delft, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.076402 99, 076402 (2007)] by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller [F. B. Anders and A. Schiller, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. While these developments prove particularly useful in the calculation of transient response and finite-temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.

  5. Renormalization-group improved inflationary scalar electrodynamics and SU(5) scenarios confronted with Planck 2013 and BICEP2 results

    NASA Astrophysics Data System (ADS)

    Elizalde, E.; Odintsov, S. D.; Pozdeeva, E. O.; Vernov, S. Yu.

    2014-10-01

    The possibility to construct inflationary models for the renormalization-group (RG) improved potentials corresponding to scalar electrodynamics and to SU(2) and SU(5) models is investigated. In all cases, the tree-level potential, which corresponds to the cosmological constant in the Einstein frame, is seen to be nonsuitable for inflation. Rather than adding the Hilbert-Einstein term to the action, quantum corrections to the potential, coming from the RG equation, are included. The inflationary scenario is analyzed with unstable de Sitter solutions that correspond to positive values of the coupling function, only. We show that, for the finite SU(2) model and SU(2) gauge model, there are no de Sitter solutions suitable for inflation, unless exit from it occurs according to some weird, nonstandard scenarios. Inflation is realized both for scalar electrodynamics and for SU(5) RG-improved potentials, and the corresponding values of the coupling function are seen to be positive. It is shown that, for quite reasonable values of the parameters, the inflationary models obtained both from scalar electrodynamics and from the SU(5) RG-improved potentials are in good agreement with the most recent observational data coming from the Planck 2013 and BICEP2 collaborations.

  6. Radiative corrections to e/sup +/e/sup -/ reactions to all orders in. cap alpha. using the renormalization group

    SciTech Connect

    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/.

  7. Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections

    NASA Astrophysics Data System (ADS)

    Tazai, Rina; Yamakawa, Youichi; Tsuchiizu, Masahisa; Kontani, Hiroshi

    2016-09-01

    In various multiorbital systems, the emergence of the orbital fluctuations and their role on the pairing mechanism attract increasing attention. To achieve deep understanding on these issues, we perform a functional renormalization group (fRG) study for the two-orbital Hubbard model. The vertex corrections for the electron-boson coupling (U -VC), which are dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG equation. We reveal that the dressed electron-boson coupling for the charge channel Ûeffc becomes much larger than the bare Coulomb interaction Û 0 due to the U -VC in the presence of moderate spin fluctuations. For this reason, the attractive pairing interaction due to the charge or orbital fluctuations is enlarged by the factor (Ûeffc/Û0) 2≫1 . In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel U -VC, because of the relation Ûeffs≪Û 0 . The present study demonstrates that the orbital or charge fluctuation pairing mechanism can be realized in various multiorbital systems thanks to the U -VC, such as in Fe-based superconductors.

  8. 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

  9. Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

    SciTech Connect

    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.

  10. Multi-scale renormalization

    NASA Astrophysics Data System (ADS)

    Ford, C.; Wiesendanger, C.

    1997-02-01

    The standard MS renormalization prescription is inadequate for dealing with multi-scale problems. To illustrate this we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that it is natural to employ a two-scale renormalization group. We give a modified version of a two-scale scheme introduced by Einhorn and Jones. In such schemes the beta functions necessarily contain potentially large logarithms of the RG scale ratios. For credible perturbation theory one must implement a large logarithms resummation on the beta functions themselves. We show how the integrability condition for the two RG equations allows one to perform this resummation.

  11. Magnetic transition from the paramagnetic to long-period structure in RMn2O5 multiferroics: Renormalization group analysis of critical behavior

    NASA Astrophysics Data System (ADS)

    Men'shenin, V. V.

    2013-06-01

    A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn2O5 multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.

  12. Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors

    SciTech Connect

    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.

  13. Generation of SFR few-group constants using the Monte Carlo code Serpent

    SciTech Connect

    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)

  14. 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.

  15. Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene

    NASA Astrophysics Data System (ADS)

    Shirakawa, Tomonori; Yunoki, Seiji

    2014-11-01

    We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multiorbital Anderson impurity model where not only inter- and intraorbital Coulomb interactions but also Hund's coupling and pair hopping interactions are included. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene with a structural defect and with a single hydrogen or fluorine absorbed, where a single Anderson impurity is coupled to conduction electrons in the honeycomb lattice. These models include (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis of the local dynamical magnetic susceptibility and the local density of states at the impurity site reveals that, for the particle-hole symmetric case at half-filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening, while the ground state of the other two models forms a spin-singlet state where the impurity moment is screened by the conduction electrons. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence or absence of unscreened

  16. Functional renormalization-group study of the pairing symmetry and pairing mechanism of the FeAs-based high-temperature superconductor.

    PubMed

    Wang, Fa; Zhai, Hui; Ran, Ying; Vishwanath, Ashvin; Lee, Dung-Hai

    2009-01-30

    We apply the fermion functional renormalization-group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended s wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter-Fermi-surface Josephson scattering generated by the antiferromagnetic correlation.

  17. Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.

    PubMed

    Evenbly, G; Vidal, G

    2015-11-13

    We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

  18. 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.

  19. Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s =3 /2 Ising model from renormalization-group theory

    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.

  20. Cumulant Approximated Second-Order Perturbation Theory Based on the Density Matrix Renormalization Group for Transition Metal Complexes: A Benchmark Study.

    PubMed

    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

  1. Toward Reliable Prediction of Hyperfine Coupling Constants Using Ab Initio Density Matrix Renormalization Group Method: Diatomic (2)Σ and Vinyl Radicals as Test Cases.

    PubMed

    Lan, Tran Nguyen; Kurashige, Yuki; Yanai, Takeshi

    2014-05-13

    The density matrix renormalization group (DMRG) method is used in conjunction with the complete active space (CAS) procedure, the CAS configuration interaction (CASCI), and the CAS self-consistent field (CASSCF) to evaluate hyperfine coupling constants (HFCCs) for a series of diatomic (2)Σ radicals (BO, CO(+), CN, and AlO) and vinyl (C2H3) radical. The electron correlation effects on the computed HFCC values were systematically investigated using various levels of active space, which were increasingly extended from single valence space to large-size model space entailing double valence and at least single polarization shells. In addition, the core correlation was treated by including the core orbitals in active space. Reasonably accurate results were obtained by the DMRG-CASSCF method involving orbital optimization, while DMRG-CASCI calculations with Hartree-Fock orbitals provided poor agreement of the HFCCs with the experimental values. To achieve further insights into the accuracy of HFCC calculations, the orbital contributions to the total spin density were analyzed at a given nucleus, which is directly related to the FC term and is numerically sensitive to the level of correlation treatment and basis sets. The convergence of calculated HFCCs with an increasing number of renormalized states was also assessed. This work serves as the first study on the performance of the ab initio DMRG method for HFCC prediction.

  2. A multi-group Monte Carlo core analysis method and its application in SCWR design

    SciTech Connect

    Zhang, P.; Wang, K.; Yu, G.

    2012-07-01

    Complex geometry and spectrum have been the characteristics of many newly developed nuclear energy systems, so the suitability and precision of the traditional deterministic codes are doubtable while being applied to simulate these systems. On the contrary, the Monte Carlo method has the inherent advantages of dealing with complex geometry and spectrum. The main disadvantage of Monte Carlo method is that it takes long time to get reliable results, so the efficiency is too low for the ordinary core designs. A new Monte Carlo core analysis scheme is developed, aimed to increase the calculation efficiency. It is finished in two steps: Firstly, the assembly level simulation is performed by continuous energy Monte Carlo method, which is suitable for any geometry and spectrum configuration, and the assembly multi-group constants are tallied at the same time; Secondly, the core level calculation is performed by multi-group Monte Carlo method, using the assembly group constants generated in the first step. Compared with the heterogeneous Monte Carlo calculations of the whole core, this two-step scheme is more efficient, and the precision is acceptable for the preliminary analysis of novel nuclear systems. Using this core analysis scheme, a SCWR core was designed based on a new SCWR assembly design. The core output is about 1,100 MWe, and a cycle length of about 550 EFPDs can be achieved with 3-batch refueling pattern. The average and maximum discharge burn-up are about 53.5 and 60.9 MWD/kgU respectively. (authors)

  3. Phase-separated ferromagnetism in a spin-imbalanced system of Fermi atoms loaded in an optical ladder: A density-matrix renormalization-group study

    SciTech Connect

    Okumura, M.; Yamada, S.; Machida, M.; Aoki, H.

    2011-03-15

    We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction U and spin imbalance p in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough U and p. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.

  4. Solutions of the renormalization-group equations for minimal supergravity SU(5) grand unified theory and strong constraints on its parameters

    SciTech Connect

    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.

  5. Renormalization of dimension 6 gluon operators

    NASA Astrophysics Data System (ADS)

    Kim, HyungJoo; Lee, Su Houng

    2015-09-01

    We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.

  6. Kenneth Wilson — Renormalization and QCD

    NASA Astrophysics Data System (ADS)

    Wegner, Franz J.

    2014-07-01

    Kenneth Wilson had an enormous impact on field theory, in particular on the renormalization group and critical phenomena, and on QCD. I had the great pleasure to work in three fields to which he contributed essentially: Critical phenomena, gauge-invariance in duality and QCD, and flow equations and similarity renormalization.

  7. Renormalized action improvements

    SciTech Connect

    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.

  8. 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

  9. Renormalization group analysis of the 2000-2002 anti-bubble in the US S&P500 index: explanation of the hierarchy of five crashes and prediction

    NASA Astrophysics Data System (ADS)

    Zhou, Wei-Xing; Sornette, Didier

    2003-12-01

    We propose a straightforward extension of our previously proposed log-periodic power-law model of the “anti-bubble” regime of the USA stock market since the summer of 2000, in terms of the renormalization group framework to model critical points. Using a previous work by Gluzman and Sornette (Phys. Rev. E 65 (2003) 036142) on the classification of the class of Weierstrass-like functions, we show that the five crashes that occurred since August 2000 can be accurately modeled by this approach, in a fully consistent way with no additional parameters. Our theory suggests an overall consistent organization of the investors forming a collective network which interact to form the pessimistic bearish “anti-bubble” regime with intermittent acceleration of the positive feedbacks of pessimistic sentiment leading to these crashes. We develop retrospective predictions, that confirm the existence of significant arbitrage opportunities for a trader using our model. Finally, we offer a prediction for the unknown future of the US S&P500 index extending over 2003 and 2004, that refines the previous prediction of Sornette and Zhou (Quant. Finance 2 (2002) 468).

  10. p -orbital density wave with d symmetry in high-Tc cuprate superconductors predicted by renormalization-group + constrained RPA theory

    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.

  11. Conformation space renormalization of polymers. I. Single chain equilibrium properties using Wilson-type renormalization

    NASA Astrophysics Data System (ADS)

    Oono, Y.; Freed, Karl F.

    1981-07-01

    A conformation space renormalization group is developed to describe polymer excluded volume in single polymer chains. The theory proceeds in ordinary space in terms of position variables and the contour variable along the chain, and it considers polymers of fixed chain length. The theory is motivated along two lines. The first presents the renormalization group transformation as the means for extracting the macroscopic long wavelength quantities from the theory. An alternative viewpoint shows how the renormalization group transformation follows as a natural consequence of an attempt to correctly treat the presence of a cut-off length scale. It is demonstrated that the current configuration space renormalization method has a one-to-one correspondence with the Wilson-Fisher field theory formulation, so our method is valid to all orders in ɛ = 4-d where d is the spatial dimensionality. This stands in contrast to previous attempts at a configuration space renormalization approach which are limited to first order in ɛ because they arbitrarily assign monomers to renormalized ''blobs.'' In the current theory the real space chain conformations dictate the coarse graining transformation. The calculations are presented to lowest order in ɛ to enable the development of techniques necessary for the treatment of dynamics in Part II. The theory is presented both in terms of the simple delta function interaction as well as using realistic-type interaction potentials. This illustrates the renormalization of the interactions, the emergence of renormalized many-body interactions, and the complexity of the theta point.

  12. Nonnegative Anisotropic Group Cross Sections: A Hybrid Monte Carlo-Discrete Elements-Discrete Ordinates Approach

    SciTech Connect

    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.

  13. Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2015-10-30

    We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.

  14. Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

    SciTech Connect

    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.

  15. CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry

    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.

  16. Renormalization in Periodically Driven Quantum Dots.

    PubMed

    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

  17. Renormalization Group Approach to the X-Ray Absorption Problem and Application to the Vigman-Finkelshtein Model for Magnetic Impurities in Metals.

    NASA Astrophysics Data System (ADS)

    Nunes de Oliveira, Luiz

    The renormalization group techniques developed by Wilson for the Kondo problem are applied to three related problems: the absorption of x-rays by metals, the absorption of x-rays by impurities in metals, and the specific heat of dilute magnetic alloys. In the first problem considered, the x-ray absorption problem, the metal is represented by a half-filled conduction band and a deep level representing a core state. The absorption of an x-ray photon excites an electron from this core level to the conduction band creating a core hole whose positive charge interacts with the conduction electrons. The absorption spectrum is, for the first time, calculated in the energy range 10('-10)D < (omega)-(omega)(,T) < D, where (omega) and (omega)(,T) are the x-ray and threshold frequencies, respectively, and D is the conduction bandwidth. For (omega)-(omega)(,T) < 10('-9)D, the absorption spectrum (mu)((omega)) is described by a power law (mu)(,o) {((omega) -(omega)(,T))/D}('-(alpha)) whose exponent (alpha) agrees with that of the Nozieres-De Dominicis asymptotic (i.e., valid in the limit (omega) (--->) (omega)(,T)) expression to seven decimal places; the prefactor (mu)(,o) is calculated for the first time. For (omega)-(omega)(,T) (TURNEQ) D, remarkably small deviations (e.g., deviations of 15% for (omega)-(omega)(,T) = .3D) from the Nozieres-De Dominicis power law are found. As a second application of the renormalization group techniques, the x-ray absorption spectrum for the resonant level model for impurities in metals is calculated. In this model, the metal is represented by a half-filled conduction band and the impurity by two levels: a core level from which an electron is excited to the conduction band by the absorption of an x-ray photon, and a resonant level, coupled to the conduction electrons, whose energy is lowered by the interaction with the core hole created by the absorption of the x-ray. In the x-ray absorption process, the resonant level is thus shifted to lower

  18. Magnetic properties and pairing tendencies of the iron-based superconducting ladder BaFe2S3: Combined ab initio and density matrix renormalization group study

    DOE PAGES

    Patel, Niravkumar D.; Nocera, Alberto; Alvarez, Gonzalo; Arita, Ryotaro; Moreo, Adriana; Dagotto, Elbio

    2016-08-10

    The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe2S3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015)] 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 withmore » 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 oneWannier orbital receiving the hole carriers while the other remains half-filled. Lastly, 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.« less

  19. Magnetic properties and pairing tendencies of the iron-based superconducting ladder BaFe2S3 : Combined ab initio and density matrix renormalization group study

    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.

  20. Density matrix renormalization group study in energy space for a single-impurity Anderson model and an impurity quantum phase transition

    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.

  1. Monte Carlo reference data sets for imaging research: Executive summary of the report of AAPM Research Committee Task Group 195.

    PubMed

    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

  2. Monte Carlo reference data sets for imaging research: Executive summary of the report of AAPM Research Committee Task Group 195.

    PubMed

    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

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

    PubMed

    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

  4. Renormalization from Classical to Quantum Physics

    NASA Astrophysics Data System (ADS)

    Kar, Arnab

    The concept of renormalization was first introduced by Dirac to investigate the infinite self energy of an electron classically. This radical theory was probably the first time when an infinity occurring in a physical system was systematically investigated. This thesis presents a new perspective of renormalization by introducing methods from metric geometry to control divergences. We start by extending Dirac's work and analyzing how the radiation reaction due to the precision of the electron's magnetic moment affects its motion. This is followed by modeling scalar field theory on lattices of various kinds. Scale invariance, which plays a major role in the very few renormalizable theories in nature, is inbuilt in our formalism. We also use Wilson's ideas of effective theory and finite element methods to study continuum systems. Renormalization group transformations form the central theme in this picture. By incorporating finite element methods, an idea borrowed from mechanical engineering, we study scalar fields on triangular lattices in a hierarchal manner. In our case, the cotangent formula turns out to be a fixed point of the renormalization group transformations. We end our thesis by introducing a new metric for space-time which emerges from the scalar field itself. The standard techniques used in the theory of renormalization so far attempt to redefine coupling constants of the theory to remove divergences at short distance scales. In our formalism, we deduce the distance scale itself. In our notion of distance, built from correlation functions of the fields, the divergences disappear.

  5. Renormalization of Extended QCD2

    NASA Astrophysics Data System (ADS)

    Fukaya, Hidenori; Yamamura, Ryo

    2015-10-01

    Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N_c, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region.

  6. Particle ID numbers, decay tables, and other possible contributions of the Particle Data Group to Monte Carlo standards

    SciTech Connect

    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.

  7. Boundary quantum critical phenomena with entanglement renormalization

    SciTech Connect

    Evenbly, G.; Pfeifer, R. N. C.; Tagliacozzo, L.; McCulloch, I. P.; Vidal, G.; Pico, V.; Iblisdir, S.

    2010-10-15

    We propose the use of entanglement renormalization techniques to study boundary critical phenomena on a lattice system. The multiscale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the MERA, an accurate approximation to the ground state of a semi-infinite critical chain with an open boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales. We present benchmark results for the quantum Ising and quantum XX models with free and fixed boundary conditions.

  8. 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.

  9. Lectures on renormalization and asymptotic safety

    SciTech Connect

    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.

  10. Renormalizing Entanglement Distillation.

    PubMed

    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.

  11. 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.

  12. Renormalization and power counting of chiral nuclear forces

    SciTech Connect

    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.

  13. N-Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly(p-Phenylenevinylene).

    PubMed

    Guo, Sheng; Watson, Mark A; Hu, Weifeng; Sun, Qiming; Chan, Garnet Kin-Lic

    2016-04-12

    The strongly contracted variant of second-order N-electron valence state perturbation theory (NEVPT2) is an efficient perturbative method to treat dynamic correlation without the problems of intruder states or level shifts, while the density matrix renormalization group (DMRG) provides the capability to address static correlation in large active spaces. We present a combination of the DMRG and strongly contracted NEVPT2 (DMRG-SC-NEVPT2) that uses an efficient algorithm to compute high-order reduced-density matrices from DMRG wave functions. The capabilities of DMRG-SC-NEVPT2 are demonstrated on calculations of the chromium dimer potential energy curve at the basis set limit, and the excitation energies of a trimer model of poly(p-phenylenevinylene) (PPV(n = 3)). PMID:26914415

  14. Implementation of hybrid variance reduction methods in a multi group Monte Carlo code for deep shielding problems

    SciTech Connect

    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)

  15. Renormalization scheme dependence in a QCD cross section

    NASA Astrophysics Data System (ADS)

    Chishtie, Farrukh; McKeon, D. G. C.; Sherry, T. N.

    2016-09-01

    The zero to four loop contribution to the cross section Re+e- for e+e-→ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log, next-to-leading-log, …, next-to-next-to-next-to-leading-log perturbative contributions. It is shown how all logarithmic contributions to Re+e- can be summed and that Re+e- can be expressed in terms of the log-independent contributions, and once this is done, the running coupling a is evaluated at a point independent of the renormalization scale μ . All explicit dependence of Re+e- on μ cancels against its implicit dependence on μ through the running coupling a so that the ambiguity associated with the value of μ is shown to disappear. The renormalization scheme dependency of the "summed" cross section Re+e- is examined in three distinct renormalization schemes. In the first two schemes, Re+e- is expressible in terms of renormalization scheme-independent parameters τi and is explicitly and implicitly independent of the renormalization scale μ . Two of the forms are then compared graphically both with each other and with the purely perturbative results and the renormalization group-summed next-to-next-to-next-to-leading-log results.

  16. Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion.

    PubMed

    Růžička, Štěpán; Allen, Michael P

    2015-08-11

    Experiments done on polydisperse particles of cadmium selenide have recently shown that the particles form spherical isolated clusters with low polydispersity of cluster size. The computer simulation model of Xia et al. ( Nat. Nanotechnol. 2011 , 6 , 580 ) explaining this behavior used a short-range van der Waals attraction combined with a variable long-range screened electrostatic repulsion, depending linearly on the volume of the clusters. In this work, we term this dependence "linear renormalization" of the repulsive term, and we use advanced Monte Carlo simulations to investigate the kinetically slowed down phase separation in a similar but simpler model. We show that amorphous drops do not dissolve and crystallinity evolves very slowly under linear renormalization, and we confirm that low polydispersity of cluster size can also be achieved using this model. The results indicate that the linear renormalization generally leads to monodisperse clusters.

  17. 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.

  18. Reductive renormalization of the phase-field crystal equation.

    PubMed

    Oono, Y; Shiwa, Y

    2012-12-01

    It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods. Reductive renormalization was proposed to make this unification practically accessible; actually, this reductive perturbation is far simpler than most reduction methods, such as the rather standard scaling expansion. However, a rather cryptic exposition of the method seems to have been the cause of some trouble. Here, an explicit demonstration of the consistency of the reductive renormalization-group procedure is given for partial differentiation equations (of a certain type, including time-evolution semigroup type equations). Then, the procedure is applied to the reduction of a phase-field crystal equation to illustrate the streamlined reduction method. We conjecture that if the original system is structurally stable, the reductive renormalization-group result and that of the original equation are diffeomorphic.

  19. Nonperturbative renormalization of scalar quantum electrodynamics in d=3

    SciTech Connect

    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.

  20. Renormalization on noncommutative torus

    NASA Astrophysics Data System (ADS)

    D'Ascanio, D.; Pisani, P.; Vassilevich, D. V.

    2016-04-01

    We study a self-interacting scalar \\varphi ^4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.

  1. Nucleon-nucleon scattering within a multiple subtractive renormalization approach

    SciTech Connect

    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.

  2. Quantum gravity and renormalization

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano

    2015-01-01

    The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

  3. Renormalized Lie perturbation theory

    SciTech Connect

    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.

  4. A Monte Carlo Investigation of the Contrasting Groups Standard Setting Method.

    ERIC Educational Resources Information Center

    Cizek, Gregory J.; Husband, Timothy H.

    The contrasting groups method is one of many possible methods for setting passing scores. The most commonly used method is probably that developed by W. H. Angoff (1971), but it has been suggested that the Angoff method may not be appropriate for many standard setting applications in education. The contrasting groups method is explored as an…

  5. Multidimensional stochastic approximation Monte Carlo.

    PubMed

    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

  6. 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) .

  7. 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.

  8. 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.

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

    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!!!

  10. Scalar relativistic calculations of hyperfine coupling constants using ab initio density matrix renormalization group method in combination with third-order Douglas-Kroll-Hess transformation: case studies on 4d transition metals.

    PubMed

    Nguyen Lan, Tran; Kurashige, Yuki; Yanai, Takeshi

    2015-01-13

    We have developed a new computational scheme for high-accuracy prediction of the isotropic hyperfine coupling constant (HFCC) of heavy molecules, accounting for the high-level electron correlation effects, as well as the scalar-relativistic effects. For electron correlation, we employed the ab initio density matrix renormalization group (DMRG) method in conjunction with a complete active space model. The orbital-optimization procedure was employed to obtain the optimized orbitals required for accurately determining the isotropic HFCC. For the scalar-relativistic effects, we initially derived and implemented the Douglas-Kroll-Hess (DKH) hyperfine coupling operators up to the third order (DKH3) by using the direct transformation scheme. A set of 4d transition-metal radicals consisting of Ag atom, PdH, and RhH2 were chosen as test cases. Good agreement between the isotropic HFCC values obtained from DMRG/DKH3 and experiment was archived. Because there are no available gas-phase values for PdH and RhH2 radicals in the literature, the results from the present high-level theory may serve as benchmark data.

  11. From dynamical systems to renormalization

    SciTech Connect

    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.

  12. From dynamical systems to renormalization

    NASA Astrophysics Data System (ADS)

    Menous, Frédéric

    2013-09-01

    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.

  13. Quasiparticle weight and renormalized Fermi velocity of graphene with long-range Coulomb interactions

    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.

  14. 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.

  15. Renormalization flows in complex networks.

    PubMed

    Radicchi, Filippo; Barrat, Alain; Fortunato, Santo; Ramasco, José J

    2009-02-01

    Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social, and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

  16. Renormalization in Coulomb gauge QCD

    SciTech Connect

    Andrasi, A.; Taylor, John C.

    2011-04-15

    Research Highlights: > The Hamiltonian in the Coulomb gauge of QCD contains a non-linear Christ-Lee term. > We investigate the UV divergences from higher order graphs. > We find that they cannot be absorbed by renormalization of the Christ-Lee term. - Abstract: 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.

  17. Dimensional renormalization: Ladders and rainbows

    SciTech Connect

    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.}

  18. Renormalization for insulating states of matter

    NASA Astrophysics Data System (ADS)

    Hong, Seungmin

    In this thesis, we study three cases of insulating states of matter in terms of the renormalization procedure where the conventional renormalization group scheme is not simply applicable. The first subject is the spectral weight structure of hole-doped Mott insulators. As the mixing between two separate Hubbard bands is dynamically generated, additional charge degrees of freedom is required to give a proper description to the relevant low-energy physics. On this account, we first discuss how the low-energy Hubbard band should be partitioned to account for the extra degrees of freedom. Following the exact integration procedure of the upper Hubbard band, we explicitly demonstrate that the conserved charge cannot be exhausted by counting quasiparticles. In addition, we argue that it is the existence of dynamically generated charge degrees of freedom that gives rise to the coexistence of poles and zeroes in the single-particle Green function. In comparison to the Fermi arc structure, which is intrinsic to cuperate phenomenology, we suggest that the suppression of the spectral weight at the back side of the arc is a consequence of composite excitations, arising from dynamical mixing. The second topic we study is the nature of the transition between two insulating states of matter in a weakly disordered bosonic system. In particular, we investigate the instabilities of the Mott-insulating phase within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. To this end, we identify a new order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to another insulating state with finite compressibility, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. From its distinctive behavior on each phase, we find that the divergence of the relative variance in

  19. Monte Carlo methods in lattice gauge theories

    SciTech Connect

    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.

  20. Renormalization group running of neutrino parameters.

    PubMed

    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

  1. Renormalization group running of neutrino parameters.

    PubMed

    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.

  2. Wilson's Renormalization Group: A Paradigmatic Shift

    NASA Astrophysics Data System (ADS)

    Brézin, E.

    2014-03-01

    A personal and subjective recollection, concerning mainly Wilson's lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on November 16, 2013 at the occasion of the memorial Kenneth G. Wilson conference).

  3. 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.

  4. 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.

  5. 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.

  6. Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

    SciTech Connect

    Decanini, Yves; Folacci, Antoine

    2008-08-15

    We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

  7. Renormalization in general theories with intergeneration mixing

    NASA Astrophysics Data System (ADS)

    Kniehl, Bernd A.; Sirlin, Alberto

    2012-02-01

    We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with intergeneration mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of intergeneration mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from matrix algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties.

  8. RENORM predictions of diffraction at LHC confirmed

    SciTech Connect

    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.

  9. Averaging and renormalization for the Korteveg–deVries–Burgers equation

    PubMed Central

    Chorin, Alexandre J.

    2003-01-01

    We consider traveling wave solutions of the Korteveg–deVries–Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an “eddy” (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out. PMID:12913126

  10. Renormalization of high-energy Lorentz-violating four-fermion models

    SciTech Connect

    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.

  11. Universal Dynamics and Renormalization in Many-Body-Localized Systems

    NASA Astrophysics Data System (ADS)

    Altman, Ehud; Vosk, Ronen

    2015-03-01

    We survey the recent progress made in understanding nonequilibrium dynamics in closed random systems. The emphasis is on the important role played by concepts from quantum information theory and on the application of systematic renormalization group methods to capture universal aspects of the dynamics. Finally, we outline some outstanding open questions, which include the description of the many-body-localization phase transition and the identification of physical systems that allow systematic experimental study of these phenomena.

  12. Cohesive energy and structural parameters of binary oxides of groups IIA and IIIB from diffusion quantum Monte Carlo

    DOE PAGES

    Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.; Reboredo, Fernando A.

    2016-05-03

    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 and semi-local 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 and semi-local DFT approximations themore » deviation is 3.06 and 0.94 eV, respectively. For lattice constants, the mean absolute deviation in DMC, local and semi-local DFT approximations, are 0.017(1), 0.07 and 0.05 , respectively. In conclusion, DMC is highly accurate method, outperforming the local and semi-local DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.« less

  13. 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.

  14. Signal inference with unknown response: calibration-uncertainty renormalized estimator.

    PubMed

    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.

  15. Renormalization effects on the MSSM from a calculable model of a strongly coupled hidden sector

    SciTech Connect

    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.

  16. Renormalization and universality of blowup in hydrodynamic flows.

    PubMed

    Mailybaev, Alexei A

    2012-06-01

    We consider self-similar solutions describing intermittent bursts in shell models of turbulence and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to self-similar solution for the Fourier transformed inviscid Burgers equation corresponding to shock formation from smooth initial data. Then, the result is generalized to hyperbolic conservation laws in one space dimension describing compressible flows. It is shown that the renormalized wave profile tends to a universal function, which is independent both of initial conditions and of a specific form of the conservation law. This phenomenon can be viewed as a new manifestation of the renormalization group theory. Finally, we discuss possibilities for application of the developed theory for detecting and describing a blowup in incompressible flows.

  17. E-cigarette Marketing and Older Smokers: Road to Renormalization

    PubMed Central

    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

  18. 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.

  19. Supervised classification in the presence of misclassified training data: a Monte Carlo simulation study in the three group case.

    PubMed

    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.

  20. Supervised classification in the presence of misclassified training data: a Monte Carlo simulation study in the three group case

    PubMed Central

    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

  1. 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

  2. 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.

  3. 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

  4. Lattice simulations of phase morphology on lipid bilayers: Renormalization, membrane shape, and electrostatic dipole interactions

    PubMed Central

    Amazon, Jonathan J.; Feigenson, Gerald W.

    2015-01-01

    When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant. PMID:25353504

  5. Lattice simulations of phase morphology on lipid bilayers: renormalization, membrane shape, and electrostatic dipole interactions.

    PubMed

    Amazon, Jonathan J; Feigenson, Gerald W

    2014-02-01

    When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant. PMID:25353504

  6. Lattice simulations of phase morphology on lipid bilayers: Renormalization, membrane shape, and electrostatic dipole interactions

    NASA Astrophysics Data System (ADS)

    Amazon, Jonathan J.; Feigenson, Gerald W.

    2014-02-01

    When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant.

  7. 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.

  8. Euclidean Epstein-Glaser renormalization

    SciTech Connect

    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.

  9. 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.

  10. Nonlocal scaling operators with entanglement renormalization

    SciTech Connect

    Evenbly, G.; Corboz, P.; Vidal, G.

    2010-10-01

    The multiscale entanglement renormalization ansatz (MERA) can be used, in its scale invariant version, to describe the ground state of a lattice system at a quantum-critical point. From the scale invariant MERA one can determine the local scaling operators of the model. Here we show that, in the presence of a global symmetry G, it is also possible to determine a class of nonlocal scaling operators. Each operator consists, for a given group element g is an element of G, of a semi-infinite string {Gamma}{sub g} with a local operator {phi} attached to its open end. In the case of the quantum Ising model, G=Z{sub 2}, they correspond to the disorder operator {mu}, the fermionic operators {psi} and {psi}, and all their descendants. Together with the local scaling operators identity I, spin {sigma}, and energy {epsilon}, the fermionic and disorder scaling operators {psi}, {psi}, and {mu} are the complete list of primary fields of the Ising CFT. Therefore the scale invariant MERA allows us to characterize all the conformal towers of this CFT.

  11. Renormalization in charged colloids: non-monotonic behaviour with the surface charge.

    PubMed

    Haro-Pérez, C; Quesada-Pérez, M; Callejas-Fernández, J; Schurtenberger, P; Hidalgo-Álvarez, R

    2006-07-19

    The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges.

  12. Inverse Mellin Transformation of Continuous Singular Value Decomposition: A Route to Holographic Renormalization

    NASA Astrophysics Data System (ADS)

    Matsueda, Hiroaki

    2016-11-01

    We examine holographic renormalization by singular value decomposition (SVD) of matrix data generated by a Monte Carlo snapshot of the two-dimensional (2D) classical Ising model at criticality. Taking the continuous limit of the SVD enables us to find the mathematical form of each SVD component by the inverse Mellin transformation as well as the power-law behavior of the SVD spectrum. We find that each SVD component is characterized by the two-point spin correlator with a finite correlation length. Then, the continuous limit of the decomposition index in the SVD corresponds to the inverse of the correlation length. These features strongly indicate that the SVD contains the same mathematical structure as the holographic renormalization.

  13. Novel formulations of CKM matrix renormalization

    SciTech Connect

    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.

  14. Error estimates and specification parameters for functional renormalization

    SciTech Connect

    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.

  15. Renormalization In Quantum Gauge Theory Using Zeta-Function Method

    SciTech Connect

    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.

  16. Comparison of a 3-D multi-group SN particle transport code with Monte Carlo for intracavitary brachytherapy of the cervix uteri.

    PubMed

    Gifford, Kent A; Wareing, Todd A; Failla, Gregory; Horton, John L; Eifel, Patricia J; Mourtada, Firas

    2009-12-03

    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.

  17. Finite volume renormalization scheme for fermionic operators

    SciTech Connect

    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.

  18. Hopf-algebraic renormalization of QED in the linear covariant gauge

    NASA Astrophysics Data System (ADS)

    Kißler, Henry

    2016-09-01

    In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green's functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

  19. Renormalization of transport equations in Fokker-Planck models

    NASA Astrophysics Data System (ADS)

    Grabert, Hermann; Weidlich, Wolfgang

    1980-06-01

    This paper is concerned with the derivation of nonlinear fluctuation-renormalized transport equations of a fluctuating thermodynamic system, on the assumption that the macroscopic variables defining a state undergo a Fokker-Planck process. It is shown that the renormalization effect may consist of two parts: a renormalization of the thermodynamic forces and a renormalization of the transport coefficients. Closed analytical expressions for the renormalized quantities in terms of the bare quantities appearing in the Fokker-Planck equation are derived. A scheme for the approximate evaluation of these expressions is given.

  20. Bose gases near resonance: Renormalized interactions in a condensate

    SciTech Connect

    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.

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

    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!!!

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

    SciTech Connect

    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.

  3. Poissonian renormalizations, exponentials, and power laws

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  4. Poissonian renormalizations, exponentials, and power laws.

    PubMed

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  5. Renormalized Resonance Quartets in Dispersive Wave Turbulence

    SciTech Connect

    Lee, Wonjung; Kovacic, Gregor; Cai, David

    2009-07-10

    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.

  6. 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.

  7. Holographic renormalization and the electroweak precision parameters

    SciTech Connect

    Round, Mark

    2010-09-01

    We study the effects of holographic renormalization on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS{sub 5} geometry containing a bulk scalar and SU(2)xSU(2) gauge fields. The scalar field obtains a vacuum expectation value (VEV) which represents a condensate that triggers electroweak symmetry breaking. Fermion fields are constrained to live on the UV brane and do not propagate in the bulk. The two-point functions are holographically renormalized through the addition of boundary counterterms. Measurable quantities are then expressed in terms of well-defined physical parameters, free from any spurious dependence on the UV cutoff. A complete study of the precision parameters is carried out and bounds on physical quantities derived. The large-N scaling of results is discussed.

  8. 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.

  9. Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality

    SciTech Connect

    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

  10. Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix

    SciTech Connect

    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.

  11. Renormalization of a two-loop neutrino mass model

    SciTech Connect

    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.

  12. 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.

  13. Renormalized Newtonian cosmic evolution with primordial non-Gaussianity

    SciTech Connect

    Izumi, Keisuke; Soda, Jiro

    2007-10-15

    We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affects the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wave number. On the other hand, the negative skewness gives the opposite result.

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

    NASA Astrophysics Data System (ADS)

    Turcati, Rodrigo; Neves, Mario Junior

    2016-08-01

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

  15. Renormalization schemes: Where do we stand

    SciTech Connect

    Ward, B.F.L.

    1989-07-01

    We consider the status of the current approaches to the application of the renormalization program to the standard SU/sub 2L/ /times/ U/sub 1/ theory from the standpoint of the interplay of the scheme chosen for such an application and the attendant high-precision tests of the respective loop effects. We thus review the available schemes and discuss their theoretical relationships. We also show how such schemes stand in numerical relation to one another in the context of high-precision Z/sup 0/ physics, as an illustration. 15 refs., 2 figs., 2 tabs.

  16. Renormalization group equation for f (R ) gravity on hyperbolic spaces

    NASA Astrophysics Data System (ADS)

    Falls, Kevin; Ohta, Nobuyoshi

    2016-10-01

    We derive the flow equation for the gravitational effective average action in an f (R ) truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to evaluate traces exactly using the optimized cutoff. This reveals in particular that all modes can be integrated out for a finite value of the cutoff due to a gap in the spectrum of the Laplacian, leading to the effective action. Studying polynomial solutions, we find poorer convergence than has been found on compact spacetimes even though at small curvature the equations only differ in the treatment of certain modes. In the vicinity of an asymptotically free fixed point, we find the universal beta function for the R2 coupling and compute the corresponding effective action which involves an R2log (R2) quantum correction.

  17. 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.

  18. The δN formula is the dynamical renormalization group

    SciTech Connect

    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.

  19. A Renormalization Group Like Model for a Democratic Dictatorship

    NASA Astrophysics Data System (ADS)

    Galam, Serge

    2015-03-01

    We review a model of sociophysics which deals with democratic voting in bottom up hierarchical systems. The connection to the original physical model and technics are outlined underlining both the similarities and the differences. Emphasis is put on the numerous novel and counterintuitive results obtained with respect to the associated social and political framework. Using this model a real political event was successfully predicted with the victory of the French extreme right party in the 2000 first round of French presidential elections. The perspectives and the challenges to make sociophysics a predictive solid field of science are discussed.

  20. Monte Carlo investigation of critical properties of the Landau point of a biaxial liquid-crystal system.

    PubMed

    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.

  1. Phase diagram of self-assembled rigid rods on two-dimensional lattices: theory and Monte Carlo simulations.

    PubMed

    López, L G; Linares, D H; Ramirez-Pastor, A J; Cannas, S A

    2010-10-01

    Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.

  2. Structure of the Broken Phase of the Sine-Gordon Model Using Functional Renormalization

    NASA Astrophysics Data System (ADS)

    Pangon, V.

    We study in this paper the sine-Gordon model using functional renormalization group at local potential approximation using different renormalization group (RG) schemes. In d = 2, using Wegner-Houghton RG we demonstrate that the location of the phase boundary is entirely driven by the relative position to the Coleman fixed point even for strongly coupled bare theories. We show the existence of a set of IR fixed points in the broken phase that are reached independently of the bare coupling. The bad convergence of the Fourier series in the broken phase is discussed and we demonstrate that these fixed points can be found only using a global resolution of the effective potential. We then introduce the methodology for the use of average action method where the regulator breaks periodicity and show that it provides the same conclusions for various regulators. The behavior of the model is then discussed in d≠2 and the absence of the previous fixed points is interpreted.

  3. Renormalization of the BCS-BEC crossover by order-parameter fluctuations

    SciTech Connect

    Bartosch, Lorenz; Kopietz, Peter; Ferraz, Alvaro

    2009-09-01

    We use the functional renormalization group approach with partial bosonization in the particle-particle channel to study the effect of order parameter fluctuations on the BCS-Bose-Einstein condensate (BEC) crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single-particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.

  4. 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

  5. Importance of proper renormalization scale-setting for QCD testing at colliders

    SciTech Connect

    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 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

  6. Importance of proper renormalization scale-setting for QCD testing at colliders

    DOE PAGES

    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

  7. Validation of the Monte Carlo criticality program KENO IV and the Hansen-Roach sixteen-energy-group-cross sections for high-assay uranium systems. [KENO IV criticality code

    SciTech Connect

    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.

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

    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.

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

    SciTech Connect

    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 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 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 groupi}-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.

  10. Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

    NASA Astrophysics Data System (ADS)

    Volpez, Yanick; Scherer, Daniel D.; Scherer, Michael M.

    2016-10-01

    Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group, and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor, and second-nearest-neighbor repulsion. To this end, we employ the multipatch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.

  11. 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.

  12. 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.

  13. Semihard processes with BLM renormalization scale setting

    SciTech Connect

    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.

  14. Monte Carlo Benchmark

    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.

  15. Sleep and Synaptic Renormalization: A Computational Study

    PubMed Central

    Olcese, Umberto; Esser, Steve K.

    2010-01-01

    Recent evidence indicates that net synaptic strength in cortical and other networks increases during wakefulness and returns to a baseline level during sleep. These homeostatic changes in synaptic strength are accompanied by corresponding changes in sleep slow wave activity (SWA) and in neuronal firing rates and synchrony. Other evidence indicates that sleep is associated with an initial reactivation of learned firing patterns that decreases over time. Finally, sleep can enhance performance of learned tasks, aid memory consolidation, and desaturate the ability to learn. Using a large-scale model of the corticothalamic system equipped with a spike-timing dependent learning rule, in agreement with experimental results, we demonstrate a net increase in synaptic strength in the waking mode associated with an increase in neuronal firing rates and synchrony. In the sleep mode, net synaptic strength decreases accompanied by a decline in SWA. We show that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength. Moreover, when the model “learns” a sequence of activation during waking, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time. Finally, sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios, increased resistance to interference, and desaturation of learning capabilities. Although the specific mechanisms implemented in the model cannot capture the variety and complexity of biological substrates, and will need modifications in line with future evidence, the present simulations provide a unified, parsimonious account for diverse experimental findings coming from molecular, electrophysiological, and behavioral approaches. PMID:20926617

  16. Magnetic Kronig-Penney-type graphene superlattices: finite energy Dirac points with anisotropic velocity renormalization.

    PubMed

    Qui Le, V; Huy Pham, C; Lien Nguyen, V

    2012-08-29

    We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic.

  17. On the renormalization of the electroweak chiral Lagrangian with a Higgs

    NASA Astrophysics Data System (ADS)

    Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; Saa, S.

    2015-03-01

    We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle. For a leading order Lagrangian, the complete one-loop off-shell renormalization procedure is performed, including the effects of a finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. A novel general parametrization of the Goldstone boson matrix is proposed, which reduces to the various usual ones for specific values of its parameter. Furthermore, new counterterms involving the Higgs field which are apparently chiral non-invariant are identified in the perturbative analysis. A redefinition of the Goldstone boson fields which absorbs all chiral non-invariant counterterms is then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies.

  18. Renormalization-scheme-invariant perturbation theory: Miracle or mirage

    SciTech Connect

    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.

  19. 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.

  20. Renormalization of the Brazilian chiral nucleon-nucleon potential

    SciTech Connect

    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.

  1. Renormalization of the Brazilian chiral nucleon-nucleon potential

    NASA Astrophysics Data System (ADS)

    Da Rocha, Carlos A.; Timóteo, Varese S.

    2013-03-01

    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.

  2. Screening of heterogeneous surfaces: charge renormalization of Janus particles.

    PubMed

    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.

  3. Aspects of renormalization in finite-density field theory

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

  4. Non-perturbative Renormalization with Staggered Fermions

    NASA Astrophysics Data System (ADS)

    Lytle, Andrew

    Lattice studies of Standard Model phenomenology frequently require knowledge of matching factors, or "Z-factors," that convert lattice operators defined at the lattice scale to operators in a continuum scheme at a scale mu. We make the first non-perturbative determinations of Z-factors for improved, fully dynamical staggered fermions. We compute the mass renormalization factor Zm for the Asqtad action, which is the action used by the MILC collaboration[1]. We find the strange quark mass to be mMSs (2 GeV) = 103(3) MeV; significantly larger than the result obtained using the perturbative Z-factor[2]. We compute all 256 bilinear Z-factors for the HYP-smeared action, which provides a laboratory for comparison to the results of one-loop perturbation theory[3]. Our results indicate broad agreement for ratios of Z-factors, at the few percent level, while the Z-factors themselves differ at around the ten percent level. The bilinear calculations are a stepping stone towards computation of the four-Fermi Z-factors relevant for an ongoing precision calculation of BK[4, 5, 6, 7], the knowledge of which is used to constrain the CKM matrix. Uncertainty in the required matching factors constitutes the dominant source of error.

  5. Nonlinear dynamics in combinatorial games: Renormalizing Chomp

    NASA Astrophysics Data System (ADS)

    Friedman, Eric J.; Landsberg, Adam Scott

    2007-06-01

    We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to transform a combinatorial game like Chomp into a type of dynamical system. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play in Chomp and an answer to a longstanding question about the nature of the winning opening move), but more generally, it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory.

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

    PubMed

    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.

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

    PubMed

    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

  8. Monte Carlo Example Programs

    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.

  9. Early management of type 2 diabetes based on a SMBG strategy: the way to diabetes regression--the St Carlos study : a 3-year, prospective, randomized, clinic-based, interventional study with parallel groups.

    PubMed

    García de la Torre, Nuria; Durán, Alejandra; Del Valle, Laura; Fuentes, Manuel; Barca, Idoya; Martín, Patricia; Montañez, Carmen; Perez-Ferre, Natalia; Abad, Rosario; Sanz, Fuencisla; Galindo, Mercedes; Rubio, Miguel A; Calle-Pascual, Alfonso L

    2013-08-01

    The aims are to define the regression rate in newly diagnosed type 2 diabetes after lifestyle intervention and pharmacological therapy based on a SMBG (self-monitoring of blood glucose) strategy in routine practice as compared to standard HbA1c-based treatment and to assess whether a supervised exercise program has additional effects. St Carlos study is a 3-year, prospective, randomized, clinic-based, interventional study with three parallel groups. Hundred and ninety-five patients were randomized to the SMBG intervention group [I group; n = 130; Ia: SMBG (n = 65) and Ib: SMBG + supervised exercise (n = 65)] and to the HbA1c control group (C group) (n = 65). The primary outcome was to estimate the regression rate of type 2 diabetes (HbA1c <6 % on metformin treatment). After 3 years of follow-up, diabetes regression was achieved by 56 patients, 6 (9.2 %) from the C group, 21 (32.3 %) from the Ia group and 29 (44.6 %) from the Ib group. RR (95 % CI) for diabetes regression in the intervention group (Ia + Ib) was 4.5 (2.1-9); p < 0.001 and remained after stratification by gender, age and BMI. This difference was associated with healthier changes in lifestyle and greater weight loss. RR for a weight loss >4 kg was 3.6 (1.8-7); p < 0.001. This study shows that the use of SMBG in an educational program effectively increases the regression rate in newly diagnosed type 2 diabetic patients after 3 years of follow-up. These data suggest that SMBG-based programs should be extended to primary care settings where diabetic patients are usually attended.

  10. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

    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.

  11. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations.

    PubMed

    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.

  12. 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.

  13. Tensor hypercontraction. II. Least-squares renormalization.

    PubMed

    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

  14. 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.

  15. 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.

  16. Quantum Monte Carlo for atoms and molecules

    SciTech Connect

    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.

  17. 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.

  18. Renormalized dissipation in the nonconservatively forced Burgers equation

    SciTech Connect

    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.

  19. Screening of heterogeneous surfaces: charge renormalization of Janus particles.

    PubMed

    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

  20. Renormalized time scale for anticipating and lagging synchronization.

    PubMed

    Hayashi, Yoshikatsu; Nasuto, Slawomir J; Eberle, Henry

    2016-05-01

    Anticipating synchronization has been recently proposed as a mechanism of interaction in dynamical systems which are able to bring about predictions of future states of a driver system. We suggest that an interesting insight into anticipating synchronization can be obtained by the renormalization of the time scale in the driven system. Our approach directly links the feedback delay of the driven system with the renormalized time scale of the driven system, identifying the main component in the anticipating synchronization paradigm and suggesting an alternative method to generate anticipating and lagging synchronization. PMID:27300902

  1. λφ 4 q-Renormalization program

    NASA Astrophysics Data System (ADS)

    Rodriguez-Romo, Suemi

    1994-03-01

    A regularization scheme for quantum field theories given in a q-mutator algebra for the internal momentum space in a loop integration is constructed. We show Feynman integrals that are finite for q≠ 1but diverse as q → 1. Using this regularization scheme, we propose a renormalization program in q-mutator space ( q-renormalization program) for the λf 4 theory as an example, up to some one-loop diagrams. This work paves the way to obtaining physically measurable quantities from quantum field theories over spaces that neither commute nor anticommute.

  2. [lambda][phi][sup 4] q-renormalization program

    SciTech Connect

    Rodriguez-Romo, S. )

    1994-03-01

    A regularization scheme for quantum field theories given in q-mutator algebra for the internal momentum space in a loop integration is constructed. The author shows Feynman integrals that are finite for q [ne] 1 but diverse as q [yields] 1. Using this regularization scheme, the author proposes a renormalization program in q-mutator space (q-renormalization program) for the [lambda][phi][sup 4] theory as an example, up to some one-loop diagrams. This work paves the way to obtaining physically measureable quantities from quantum field theories over spaces that neither commute nor anticommute.

  3. 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.

  4. Two loop divergences studied with one loop constrained differential renormalization

    SciTech Connect

    Seijas, Cesar . E-mail: cesar@fpaxp1.usc.es

    2007-08-15

    In the context of differential renormalization, using constrained differential renormalization rules at one-loop, we show how to obtain concrete results in two-loop calculations without making use of Ward identities. In order to do that, we obtain a list of integrals with overlapping divergences compatible with CDR that can be applied to various two-loop background field calculations. As an example, we obtain the two-loop coefficient of the beta function of QED, SuperQED and Yang-Mills theory.

  5. Peripheral NN scattering from subtractive renormalization of chiral interactions

    SciTech Connect

    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}.

  6. Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence.

    PubMed

    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

  7. Monte Carlo fundamentals

    SciTech Connect

    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.

  8. 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.

  9. Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Bardenet, Rémi

    2013-07-01

    Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chain (MCMC) methods. We give intuition on the theoretical justification of the algorithms as well as practical advice, trying to relate both. We discuss the application of Monte Carlo in experimental physics, and point to landmarks in the literature for the curious reader.

  10. Band-Renormalization Effects and Predominant Antiferromagnetic Order in Two-Dimensional Hubbard Model

    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.

  11. Monte Carlo field-theoretic simulations of a homopolymer blend

    NASA Astrophysics Data System (ADS)

    Spencer, Russell; Matsen, Mark

    Fluctuation corrections to the macrophase segregation transition (MST) in a symmetric homopolymer blend are examined using Monte Carlo field-theoretic simulations (MC-FTS). This technique involves treating interactions between unlike monomers using standard Monte-Carlo techniques, while enforcing incompressibility as is done in mean-field theory. When using MC-FTS, we need to account for a UV divergence. This is done by renormalizing the Flory-Huggins interaction parameter to incorporate the divergent part of the Hamiltonian. We compare different ways of calculating this effective interaction parameter. Near the MST, the length scale of compositional fluctuations becomes large, however, the high computational requirements of MC-FTS restrict us to small system sizes. We account for these finite size effects using the method of Binder cumulants, allowing us to locate the MST with high precision. We examine fluctuation corrections to the mean field MST, χN = 2 , as they vary with the invariant degree of polymerization, N =ρ2a6 N . These results are compared with particle-based simulations as well as analytical calculations using the renormalized one loop theory. This research was funded by the Center for Sustainable Polymers.

  12. Nonperturbative renormalization of QED in light-cone quantization

    SciTech Connect

    Hiller, J.R.; Brodsky, S.J.

    1996-08-01

    As a precursor to work on QCD, we study the dressed electron in QED non-perturbatively. The calculational scheme uses an invariant mass cutoff, discretized light cone quantization, a Tamm-Dancoff truncation of the Fock space, and a small photon mass. Nonperturbative renormalization of the coupling and electron mass is developed.

  13. Systematic renormalization of the effective theory of Large Scale Structure

    NASA Astrophysics Data System (ADS)

    Akbar Abolhasani, Ali; Mirbabayi, Mehrdad; Pajer, Enrico

    2016-05-01

    A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

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

    SciTech Connect

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

    2007-06-14

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

  15. SAN CARLOS APACHE PAPERS.

    ERIC Educational Resources Information Center

    ROESSEL, ROBERT A., JR.

    THE FIRST SECTION OF THIS BOOK COVERS THE HISTORICAL AND CULTURAL BACKGROUND OF THE SAN CARLOS APACHE INDIANS, AS WELL AS AN HISTORICAL SKETCH OF THE DEVELOPMENT OF THEIR FORMAL EDUCATIONAL SYSTEM. THE SECOND SECTION IS DEVOTED TO THE PROBLEMS OF TEACHERS OF THE INDIAN CHILDREN IN GLOBE AND SAN CARLOS, ARIZONA. IT IS DIVIDED INTO THREE PARTS--(1)…

  16. Analytic and Monte Carlo studies of jets with heavy mesons and quarkonia

    NASA Astrophysics Data System (ADS)

    Bain, Reggie; Dai, Lin; Hornig, Andrew; Leibovich, Adam K.; Makris, Yiannis; Mehen, Thomas

    2016-06-01

    We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified hadron in a jet with angularity, τ a . The FJFs are convolutions of fragmentation functions (FFs), evolved to the jet energy scale, with perturbatively calculable matching coefficients. Renormalization group equations are used to provide resummed calculations with next-to-leading logarithm prime (NLL') accuracy. We apply this formalism to two-jet events in e + e - collisions with B mesons in the jets, and three-jet events in which a J/ψ is produced in the gluon jet. In the case of B mesons, we use a phenomenological FF extracted from e + e - collisions at the Z 0 pole evaluated at the scale μ = m b . For events with J/ψ, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix elements at the scale μ = 2 m c . The z and τ a distributions from our NLL' calculations are compared with predictions from monte carlo event generators. While we find consistency between the predictions for B mesons and the J/ψ distributions in τ a , we find the z distributions for J/ψ differ significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs that gives good agreement with NLL' calculations of the z distributions.

  17. Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network.

    PubMed

    Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji

    2012-09-01

    We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.

  18. MORSE Monte Carlo code

    SciTech Connect

    Cramer, S.N.

    1984-01-01

    The MORSE code is a large general-use multigroup Monte Carlo code system. Although no claims can be made regarding its superiority in either theoretical details or Monte Carlo techniques, MORSE has been, since its inception at ORNL in the late 1960s, the most widely used Monte Carlo radiation transport code. The principal reason for this popularity is that MORSE is relatively easy to use, independent of any installation or distribution center, and it can be easily customized to fit almost any specific need. Features of the MORSE code are described.

  19. Symbolic implicit Monte Carlo

    SciTech Connect

    Brooks, E.D. III )

    1989-08-01

    We introduce a new implicit Monte Carlo technique for solving time dependent radiation transport problems involving spontaneous emission. In the usual implicit Monte Carlo procedure an effective scattering term in dictated by the requirement of self-consistency between the transport and implicitly differenced atomic populations equations. The effective scattering term, a source of inefficiency for optically thick problems, becomes an impasse for problems with gain where its sign is negative. In our new technique the effective scattering term does not occur and the excecution time for the Monte Carlo portion of the algorithm is independent of opacity. We compare the performance and accuracy of the new symbolic implicit Monte Carlo technique to the usual effective scattering technique for the time dependent description of a two-level system in slab geometry. We also examine the possibility of effectively exploiting multiprocessors on the algorithm, obtaining supercomputer performance using shared memory multiprocessors based on cheap commodity microprocessor technology. {copyright} 1989 Academic Press, Inc.

  20. Ising Models, Universality and the Non Renormalization of the Quantum Anomalies

    NASA Astrophysics Data System (ADS)

    Mastropietro, Vieri

    2010-03-01

    A number of universal relations (proposed by Kadanoff, Luther, Peschel and Haldane) are believed to be true in a wide class of systems with continuously varying indices, among which are interacting planar Ising models, vertex or Ashkin-Teller models, quantum spin chains and 1D Fermi systems; by such relations one can predict several quantities in terms of a few measurable parameters without relying on the specific microscopic details. The validity of such relations can be checked in special solvable models but, despite several attempts, the proof of their general validity was up to now an open problem. A rigorous derivation of several of such relations (for solvable and not solvable models and without any use of exact solutions) has been recently obtained in [8] and [11] through Renormalization Group methods. The proof is based on the representation in terms of Grassmann integrals and the validity of the Adler-Bardeen property of the non renormalization of the quantum anomalies in the asymptotic Ward identities. Gauge invariance is exact only in the scaling limit but the lattice corrections can be rigorously taken into account.

  1. The renormalization scale problem and novel perspectives for QCD

    NASA Astrophysics Data System (ADS)

    Brodsky, Stanley J.

    2015-11-01

    I discuss a number of novel tests of QCD, measurements which can illuminate fundamental features of hadron physics. These include the origin of the “ridge” in proton-proton collisions; the production of the Higgs at high xF; the role of digluon-initiated processes for quarkonium production; flavor-dependent anti-shadowing; the effect of nuclear shadowing on QCD sum rules; direct production of hadrons at high transverse momentum; and leading-twist lensing corrections; and the breakdown of perturbative QCD factorization. I also review the “Principle of Maximum Conformalit” (PMC) which systematically sets the renormalization scale order-by-order in pQCD, independent of the choice of renormalization scheme, thus eliminating an unnecessary theoretical uncertainty.

  2. On the renormalization of non-commutative field theories

    NASA Astrophysics Data System (ADS)

    Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael

    2013-01-01

    This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.

  3. Dimension-5 CP -odd operators: QCD mixing and renormalization

    DOE PAGES

    Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; Mereghetti, Emanuele; Yoon, Boram

    2015-12-23

    Here, 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. Furthermore, we present the renormalization matrix to one loop in themore » $$\\bar{MS}$$ 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 $$\\bar{MS}$$ scheme to one loop in perturbation theory, using both the naïve dimensional regularization and ’t Hooft–Veltman prescriptions for γ5.« less

  4. Renormalization and Induced Gauge Action on a Noncommutative Space

    NASA Astrophysics Data System (ADS)

    Grosse, H.; Wohlgenannt, M.

    Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R.~Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to φ^3 models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θ-deformed space and derive noncommutative gauge actions.

  5. Renormalized transport equations for the bistable potential model

    NASA Astrophysics Data System (ADS)

    Weidlich, Wolfgang; Grabert, Hermann

    1980-09-01

    Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value < x> t can be evaluated in both domains < D>∈ x ± and < x>∈ D 0 outside and between the potential minima, leading to drastic differences of the dynamics prevailing in D ± and D 0, respectively.

  6. A renormalization approach to the universality of scaling in phyllotaxis

    NASA Astrophysics Data System (ADS)

    Reick, Christian H.

    2015-04-01

    Phyllotaxis, i.e. the arrangement of plant organs like leaves, florets, scales, bracts etc. around a shoot, stem, or cone, is often highly regular. Across the plant kingdom phyllotaxis shows not only qualitatively, but also quantitatively identical features, like the occurrence of divergence angles close to noble irrationals. In a previous study (Reick, 2012) a mechanism has been identified that explains the selection of these particular divergence angles on the basis of self-similarity and scaling, numerically found in the bifurcation diagrams of simple dynamical models of phyllataxis. In the present paper, by constructing a renormalization theory, the universality of this scaling is proved for a whole class of models, prototypically represented by Thornley's model of phyllotaxis (Thornley, 1975). The renormalization is constructed from another self-similarity found numerically for the Fourier transform of the abstract potential governing the mutual inhibition of primordia. Surprisingly, the resulting renormalization transformation is already known from the treatment of the quasiperiodic transition to chaos but operates here on a different function space. It turns out that the fixed points of the renormalization transformation are characterized by divergences of the form Θ (κ) = 1 /τ (κ), where, written as continued fraction, τ (κ) = [ κ ; κ , κ , … ] , κ ∈N+. To show the universality of the scaling, it is demonstrated that the fixed points are unstable and that the associated scaling factors α (κ) = -(τ (κ)) 2 and β (κ) =τ (κ) are exactly those that were numerically found in (Reick, 2012) to rule the selfsimilarity of the bifurcation structure. Thereby, the present paper puts forward an explanation for the universal appearance of certain phyllotactic patterns that is independent of physiological detail of plant growth.

  7. Derivative expansions of renormaliztion group effective potentials for {phi}{sup 4} field theories

    SciTech Connect

    Shepard, J.R.; McNeil, J.A.

    1995-10-01

    We approximate an exact Renormalization Group (RG) equation for the flow of the effective action of {phi}{sup 4} field theories by including next-to-leading order (NLO) terms in a derivative expansion. This level of approximation allows us to treat effects of wavefunction renormalization which are beyond the scope of the leading order (LO) formulation. We compare calculations based on a {open_quote}latticized {close_quotes} version of our RG equation in 3 Euclidean dimensions directly with Monte Carlo (MC) results and find excellent overall agreement as well as substantial improvement over LO calculations. We solve the continuum form of our equation to find the Wilson fixed point and determine the critical exponent {eta} (0.046). We also find the critical exponents {nu} (0.666) and {omega} (0.735). These latter two are in much improved agreement with {open_quote}world`s best{close_quotes} values com- pared to those obtained at LO (where no prediction for {eta} is possible). We also find that the {open_quote}universal potential{close_quote} determined via MC methods by Tsypin can be understood quantitatively using our NLO RG equations. Careful analysis shows that ambiguities which plague {open_quote}smooth cutoff{close_quotes} formulations do not arise with our RG equations.

  8. Renormalizing a viscous fluid model for large scale structure formation

    NASA Astrophysics Data System (ADS)

    Führer, Florian; Rigopoulos, Gerasimos

    2016-02-01

    Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.

  9. Nonperturbative renormalization for 2PI effective action techniques

    SciTech Connect

    Berges, J. . E-mail: j.berges@thphys.uni-heidelberg.de; Borsanyi, Sz. . E-mail: borsanyi@thphys.uni-heidelberg.de; Reinosa, U. . E-mail: julien.serreau@th.u-psud.fr

    2005-12-15

    Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their renormalizability, since these approximations involve selective summations to infinite perturbative orders. In this paper, we show how to renormalize all n-point functions of the theory, which are given by derivatives of the 2PI-resummed effective action {gamma} [{phi}] for scalar fields {phi}. This provides a complete description in terms of the generating functional for renormalized proper vertices, which extends previous prescriptions in the literature on the renormalization for 2PI effective actions. The importance of the 2PI-resummed generating functional for proper vertices stems from the fact that the latter respect all symmetry properties of the theory and, in particular, Goldstone's theorem in the phase with spontaneous symmetry breaking. This is important in view of the application of these techniques to gauge theories, where Ward identities play a crucial role.

  10. Charge renormalization of bilayer elastic properties.

    PubMed

    Sknepnek, Rastko; Vernizzi, Graziano; Olvera de la Cruz, Monica

    2012-09-14

    By combining molecular dynamics simulations and analytical arguments, we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity κ and the two-dimensional bulk modulus λ and Young's modulus Y are found to depend on the values of the charges assigned to the lipid head groups. To extract κ and λ, we fit the molecular dynamics data to a standard elastic model for lipid bilayers. Moreover, we analytically obtain the dependence of the Young modulus Y on the relative strengths of electrostatic and van der Waals interactions in the zero temperature limit.

  11. Renormalization plasma shielding effects on scattering entanglement fidelity in dense plasmas

    SciTech Connect

    Lee, Gyeong Won; Shim, Jaewon; Jung, Young-Dae

    2014-10-15

    The influence of renormalization plasma screening on the entanglement fidelity for the elastic electron-atom scattering is investigated in partially ionized dense hydrogen plasmas. The partial wave analysis and effective interaction potential are employed to obtain the scattering entanglement fidelity in dense hydrogen plasmas as functions of the collision energy, the Debye length, and the renormalization parameter. It is found that the renormalization plasma shielding enhances the scattering entanglement fidelity. Hence, we show that the transmission of the quantum information can be increased about 10% due to the renormalization shielding effect in dense hydrogen plasmas. It is also found that the renormalization shielding effect on the entanglement fidelity for the electron-atom collision increases with an increase of the collision energy. In addition, the renormalization shielding function increases with increasing collision energy and saturates to the unity with an increase of the Debye length.

  12. Influence of renormalization shielding on the electron-impact ionization process in dense partially ionized plasmas

    SciTech Connect

    Song, Mi-Young; Yoon, Jung-Sik; Jung, Young-Dae

    2015-04-15

    The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it is found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.

  13. Vectorized Monte Carlo

    SciTech Connect

    Brown, F.B.

    1981-01-01

    Examination of the global algorithms and local kernels of conventional general-purpose Monte Carlo codes shows that multigroup Monte Carlo methods have sufficient structure to permit efficient vectorization. A structured multigroup Monte Carlo algorithm for vector computers is developed in which many particle events are treated at once on a cell-by-cell basis. Vectorization of kernels for tracking and variance reduction is described, and a new method for discrete sampling is developed to facilitate the vectorization of collision analysis. To demonstrate the potential of the new method, a vectorized Monte Carlo code for multigroup radiation transport analysis was developed. This code incorporates many features of conventional general-purpose production codes, including general geometry, splitting and Russian roulette, survival biasing, variance estimation via batching, a number of cutoffs, and generalized tallies of collision, tracklength, and surface crossing estimators with response functions. Predictions of vectorized performance characteristics for the CYBER-205 were made using emulated coding and a dynamic model of vector instruction timing. Computation rates were examined for a variety of test problems to determine sensitivities to batch size and vector lengths. Significant speedups are predicted for even a few hundred particles per batch, and asymptotic speedups by about 40 over equivalent Amdahl 470V/8 scalar codes arepredicted for a few thousand particles per batch. The principal conclusion is that vectorization of a general-purpose multigroup Monte Carlo code is well worth the significant effort required for stylized coding and major algorithmic changes.

  14. Renormalization shielding effect on the Wannier-ridge mode for double-electron continua in partially ionized dense hydrogen plasmas

    NASA Astrophysics Data System (ADS)

    Lee, Myoung-Jae; Jung, Young-Dae

    2016-01-01

    The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.

  15. Carlos Chagas: biographical sketch.

    PubMed

    Moncayo, Alvaro

    2010-01-01

    Carlos Chagas was born on 9 July 1878 in the farm "Bon Retiro" located close to the City of Oliveira in the interior of the State of Minas Gerais, Brazil. He started his medical studies in 1897 at the School of Medicine of Rio de Janeiro. In the late XIX century, the works by Louis Pasteur and Robert Koch induced a change in the medical paradigm with emphasis in experimental demonstrations of the causal link between microbes and disease. During the same years in Germany appeared the pathological concept of disease, linking organic lesions with symptoms. All these innovations were adopted by the reforms of the medical schools in Brazil and influenced the scientific formation of Chagas. Chagas completed his medical studies between 1897 and 1903 and his examinations during these years were always ranked with high grades. Oswaldo Cruz accepted Chagas as a doctoral candidate and directed his thesis on "Hematological studies of Malaria" which was received with honors by the examiners. In 1903 the director appointed Chagas as research assistant at the Institute. In those years, the Institute of Manguinhos, under the direction of Oswaldo Cruz, initiated a process of institutional growth and gathered a distinguished group of Brazilian and foreign scientists. In 1907, he was requested to investigate and control a malaria outbreak in Lassance, Minas Gerais. In this moment Chagas could not have imagined that this field research was the beginning of one of the most notable medical discoveries. Chagas was, at the age of 28, a Research Assistant at the Institute of Manguinhos and was studying a new flagellate parasite isolated from triatomine insects captured in the State of Minas Gerais. Chagas made his discoveries in this order: first the causal agent, then the vector and finally the human cases. These notable discoveries were carried out by Chagas in twenty months. At the age of 33 Chagas had completed his discoveries and published the scientific articles that gave him world

  16. Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model

    NASA Astrophysics Data System (ADS)

    Qin, Meng; Ren, Zhong-Zhou; Zhang, Xin

    2016-01-01

    In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.

  17. Exact Renormalization of Super-Diffusion on the Tower-of-Hanoi Network

    NASA Astrophysics Data System (ADS)

    Boettcher, Stefan; Goncalves, Bruno

    2008-03-01

    We propose the Tower-of-Hanoi network as a hierarchical, small-world network possessing both, geometric and long-range links. Modeling diffusion via a random walk on this network provides a mean-square displacement with an exact, anomalous exponent dw=2-(φ)/(2)=1.30576. Here, φ=(1+√5)/2 is the ``golden ratio'' that is intimately related to Fibonacci sequences. This may be the first solvable model with super-diffusion for any fractal structure. This appears to be also the first known instance of any physical exponent containing φ. It originates from an unusual renormalization group fixed point with a subtle boundary layer. The connection between network geometry and the emergence of φ in this context is still elusive.

  18. The metric on field space, functional renormalization, and metric-torsion quantum gravity

    NASA Astrophysics Data System (ADS)

    Reuter, Martin; Schollmeyer, Gregor M.

    2016-04-01

    Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric-torsion system considered.

  19. Monte Carlo simulations of lattice gauge theories

    SciTech Connect

    Rebbi, C

    1980-02-01

    Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)

  20. Renormalized dynamics of the Dean-Kawasaki model

    NASA Astrophysics Data System (ADS)

    Bidhoodi, Neeta; Das, Shankar P.

    2015-07-01

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

  1. Diagrammatic Monte Carlo Method for Many-Polaron Problems

    NASA Astrophysics Data System (ADS)

    Mishchenko, Andrey S.; Nagaosa, Naoto; Prokof'ev, Nikolay

    2014-10-01

    We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at a finite electron density nonperturbatively, i.e., by including vertex corrections to high orders. Using the Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from a renormalized Fermi liquid to a single polaron, across the nonadiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections, the accuracy of the theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for the electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the electron density at constant electron-phonon coupling strength.

  2. Monte Carlo neutrino oscillations

    SciTech Connect

    Kneller, James P.; McLaughlin, Gail C.

    2006-03-01

    We demonstrate that the effects of matter upon neutrino propagation may be recast as the scattering of the initial neutrino wave function. Exchanging the differential, Schrodinger equation for an integral equation for the scattering matrix S permits a Monte Carlo method for the computation of S that removes many of the numerical difficulties associated with direct integration techniques.

  3. Baseball Monte Carlo Style.

    ERIC Educational Resources Information Center

    Houser, Larry L.

    1981-01-01

    Monte Carlo methods are used to simulate activities in baseball such as a team's "hot streak" and a hitter's "batting slump." Student participation in such simulations is viewed as a useful method of giving pupils a better understanding of the probability concepts involved. (MP)

  4. Current-induced phonon renormalization in molecular junctions

    NASA Astrophysics Data System (ADS)

    Bai, Meilin; Cucinotta, Clotilde S.; Jiang, Zhuoling; Wang, Hao; Wang, Yongfeng; Rungger, Ivan; Sanvito, Stefano; Hou, Shimin

    2016-07-01

    We explain how the electrical current flow in a molecular junction can modify the vibrational spectrum of the molecule by renormalizing its normal modes of oscillations. This is demonstrated with first-principles self-consistent transport theory, where the current-induced forces are evaluated from the expectation value of the ionic momentum operator. We explore here the case of H2 sandwiched between two Au electrodes and show that the current produces stiffening of the transverse translational and rotational modes and softening of the stretching modes along the current direction. Such behavior is understood in terms of charge redistribution, potential drop, and elasticity changes as a function of the current.

  5. Lagrangian constraints and renormalization of 4D gravity

    NASA Astrophysics Data System (ADS)

    Park, I. Y.

    2015-04-01

    It has been proposed in [21] that 4D Einstein gravity becomes effectively reduced to 3D after solving the Lagrangian analogues of the Hamiltonian and momentum constraints of the Hamiltonian quantization. The analysis in [21] was carried out at the classical/operator level. We review the proposal and make a transition to the path integral account. We then set the stage for explicitly carrying out the two-loop renormalization procedure of the resulting 3D action. We also address a potentially subtle issue in the gravity context concerning whether renormalizability does not depend on the background around which the original action is expanded.

  6. Renormalized anisotropic exchange for representing heat assisted magnetic recording media

    SciTech Connect

    Jiao, Yipeng; Liu, Zengyuan; Victora, R. H.

    2015-05-07

    Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation.

  7. Renormalization of high-energy Lorentz-violating QED

    SciTech Connect

    Anselmi, Damiano; Taiuti, Martina

    2010-04-15

    We study a QED extension that is unitary, CPT invariant, and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyze the relation between them. It emerges that the powerlike divergences of the low-energy theory are multiplied by arbitrary constants, inherited by the high-energy theory, and therefore can be set to zero at no cost, bypassing the hierarchy problem.

  8. Monte Carlo Shielding Analysis Capabilities with MAVRIC

    SciTech Connect

    Peplow, Douglas E.

    2011-01-01

    Monte Carlo shielding analysis capabilities in SCALE 6 are centered on the CADIS methodology Consistent Adjoint Driven Importance Sampling. CADIS is used to create an importance map for space/energy weight windows as well as a biased source distribution. New to SCALE 6 are the Monaco functional module, a multi-group fixed-source Monte Carlo transport code, and the MAVRIC sequence (Monaco with Automated Variance Reduction Using Importance Calculations). MAVRIC uses the Denovo code (also new to SCALE 6) to compute coarse-mesh discrete ordinates solutions which are used by CADIS to form an importance map and biased source distribution for the Monaco Monte Carlo code. MAVRIC allows the user to optimize the Monaco calculation for a specify tally using the CADIS method with little extra input compared to a standard Monte Carlo calculation. When computing several tallies at once or a mesh tally over a large volume of space, an extension of the CADIS method called FW-CADIS can be used to help the Monte Carlo simulation spread particles over phase space to get more uniform relative uncertainties.

  9. Lattice gauge theory and Monte Carlo methods

    SciTech Connect

    Creutz, M.

    1988-11-01

    Lattice gauge theory is now the primary non-perturbative technique for quantum field theory. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. Numerical simulation has become the approach to calculating hadronic properties. The basic algorithms for obtaining appropriately weighted gauge field configurations are discussed. Algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations, are also discussed. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. 39 refs.

  10. Communication: Random phase approximation renormalized many-body perturbation theory

    SciTech Connect

    Bates, Jefferson E.; Furche, Filipp

    2013-11-07

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

  11. Measuring the aspect ratio renormalization of anisotropic-lattice gluons

    SciTech Connect

    Alford, M.; Drummond, I. T.; Horgan, R. R.; Shanahan, H.; Peardon, M.

    2001-04-01

    Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios {chi}{sub 0}=4,6,10 and inverse lattice spacing in the range a{sub s}{sup -1}=660--840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in the Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size L, while in the former, parameters showed only a weak dependence on L easily extrapolated to L={infinity}. The renormalized anisotropy {chi}{sub R} was measured using both the torelon dispersion relation and the sideways potential method. There is general agreement between these approaches, but there are discrepancies which are evidence for the presence of lattice artifact contributions. For the torelon these are estimated to be O({alpha}{sub S}a{sub s}{sup 2}/R{sup 2}), where R is the flux-tube radius. We also present some new data that suggest that rotational invariance is established more accurately for the mean-link action than the plaquette action.

  12. Electron hamiltonian renormalized by optical phonons in a two-orbital model of mixed valence

    NASA Astrophysics Data System (ADS)

    Spał, J.; Chao, K. A.

    1985-02-01

    We use a poor man's scaling argument along the line developed by Hewson in order to obtain an effective electronic model of mixed valence, with its interaction parameters renormalized by virtual optical phonon excitations. The atomic (f) electrons acquire a finite bandwidth, in addition to the renormalization of the hybridization.

  13. An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization

    SciTech Connect

    Fried, H.M.; Tsang, P.H.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.

    2015-08-15

    A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.

  14. Remarks on the Renormalization Properties of Lorentz- and CPT-Violating Quantum Electrodynamics

    NASA Astrophysics Data System (ADS)

    Santos, Tiago R. S.; Sobreiro, Rodrigo F.

    2016-08-01

    In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz- and CPT-violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz-violating sector can be renormalized by 19 independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize and is not radiatively generated. One-loop computations are also presented and compared with the existing literature.

  15. Background field method and the cohomology of renormalization

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano

    2016-03-01

    Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.

  16. Space and time renormalization in phase transition dynamics

    DOE PAGES

    Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; Zurek, Wojciech H.

    2016-02-18

    Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigatingmore » an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.« less

  17. Autonomous renormalization of Φ4 in finite geometry

    NASA Astrophysics Data System (ADS)

    Ritschel, U.

    1993-12-01

    The autonomous renormalization of the O (N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system of finite size, where all non-constant modes can be integrated out perturbatively and the constant mode is treated by a saddle-point approximation in the thermodynamic limit. Our calculation provides a better understanding of the properties of the effective action and corroborates earlier findings concerning a heavy Higgs particle at about 2 TeV [M. Consoli, Phys. Lett. B 305 (1993) 93; R. Iban~ez-Meier and P.M. Stevenson, Phys. Lett. B 297 (1992) 144; R. Iban~ez-Meier, I. Stancu and P.M. Stevenson, Gaussian Effective Potential for U(1) Higgs Model, Rice University preprint DOE/ER/05096-51].

  18. Quasiparticle scattering interference in the renormalized Hubbard model

    NASA Astrophysics Data System (ADS)

    Wang, Shu-Hua; Zhao, Huai-Song; Yuan, Feng

    2015-02-01

    In this paper, we study the quasiparticle scattering interference phenomenon in the presence of a single impurity within the renormalized Hubbard model. By calculating the energy and momentum dependence of the Fourier-transformed local density of states in the full Brillouin zone, we can qualitatively describe the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors using a single point-like impurity. In particular, we show that with increasing energy, the position of the peak along the nodal ([0, 0] → [ π, π]) direction moves steadily to a large momentum region, while the position of the peak along the antinodal ([0, 0] → [ π, 0]) direction moves toward the center of the Brillouin zone.

  19. Anomalous contagion and renormalization in networks with nodal mobility

    NASA Astrophysics Data System (ADS)

    Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.

    2016-07-01

    A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.

  20. Local Scale Transformations on the Lattice with Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2016-01-29

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.

  1. Local Scale Transformations on the Lattice with Tensor Network Renormalization

    NASA Astrophysics Data System (ADS)

    Evenbly, G.; Vidal, G.

    2016-01-01

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.

  2. Gauge mediation scenario with hidden sector renormalization in MSSM

    SciTech Connect

    Arai, Masato; Okada, Nobuchika

    2010-02-01

    We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5 minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

  3. Percolation, renormalization, and quantum computing with nondeterministic gates.

    PubMed

    Kieling, K; Rudolph, T; Eisert, J

    2007-09-28

    We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.

  4. Renormalized strong-coupling quenched QED in four dimensions

    SciTech Connect

    Hawes, F.T.; Sizer, T.; Williams, A.G. |

    1997-03-01

    We study renormalized quenched strong-coupling QED in four dimensions in an arbitrary covariant gauge. Above the critical coupling leading to dynamical chiral symmetry breaking, we show that there is no finite chiral limit. This behavior is found to be independent of the detailed choice of photon-fermion proper vertex in the Dyson-Schwinger equation formalism, provided that the vertex is consistent with the Ward-Takahashi identity and multiplicative renormalizability. We show that the finite solutions previously reported lie in an unphysical regime of the theory with multiple solutions and ultraviolet oscillations in the mass functions. This study is consistent with the assertion that in four dimensions strong coupling QED does not have a continuum limit in the conventional sense. {copyright} {ital 1997} {ital The American Physical Society}

  5. Fermion Mass Renormalization Using Time-dependent Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Kutnink, Timothy; Santrach, Amelia; Hocket, Sarah; Barcus, Scott; Petridis, Athanasios

    2015-10-01

    The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm with refcecting boundary conditions. The stability region of the method versus the interaction strength and the spatial-grid size over time-step ratio is established. The expectation values of several dynamic operators are then evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass, as the self-interacting spinors are no longer mass-eigenfunctions. There is a characteristic, non-exponential, oscillatory dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated in detail. Statistical regularization is proposed to remove the grid-size dependence.

  6. Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N.

    2016-08-01

    By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-1 /2 Heisenberg model with the first-neighbor (J1), second-neighbor (J2), and additional scalar chiral interaction JχSi.(Sj×Sk) on the triangular lattice. In the nonmagnetic phase of the J1-J2 triangular model with 0.08 ≲J2/J1≲0.16 , recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015), 10.1103/PhysRevB.92.041105 and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015), 10.1103/PhysRevB.92.140403] find a possible gapped spin liquid with the signal of a competition between a chiral and a Z2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction JχSi.(Sj×Sk) as a perturbation for this nonmagnetic phase. We find that with growing Jχ, the gapless U(1) Dirac spin liquid, which has the best variational energy for Jχ=0 , exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number C =1 /2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the J1-J2 triangular model.

  7. Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains.

    PubMed

    Gershgorin, Boris; Lvov, Yuri V; Cai, David

    2007-04-01

    The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in thermal equilibrium are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in thermal equilibrium can be effectively described by a system of weakly interacting renormalized nonlinear waves that possess (i) the Rayleigh-Jeans distribution and (ii) zero correlations between waves, just as noninteracting free waves would. This renormalization is achieved through a set of canonical transformations. The renormalized linear dispersion of these renormalized waves is obtained and shown to be in excellent agreement with numerical experiments. Moreover, a dynamical interpretation of the renormalization of the dispersion relation is provided via a self-consistency, mean-field argument. It turns out that this renormalization arises mainly from the trivial resonant wave interactions, i.e., interactions with no momentum exchange. Furthermore, using a multiple time-scale, statistical averaging method, we show that the interactions of near-resonant waves give rise to the broadening of the resonance peaks in the frequency spectrum of renormalized modes. The theoretical prediction for the resonance width for the thermalized beta -FPU chain is found to be in very good agreement with its numerically measured value.

  8. Setting the renormalization scale in perturbative QCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

    A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the "Principle of Maximum Conformality" (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the "sequential extended BLM" (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0 -expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. We then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio Re+e- at four-loop order in pQCD.

  9. Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

    SciTech Connect

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

    2015-05-26

    A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R

  10. Monte Carlo fluorescence microtomography

    NASA Astrophysics Data System (ADS)

    Cong, Alexander X.; Hofmann, Matthias C.; Cong, Wenxiang; Xu, Yong; Wang, Ge

    2011-07-01

    Fluorescence microscopy allows real-time monitoring of optical molecular probes for disease characterization, drug development, and tissue regeneration. However, when a biological sample is thicker than 1 mm, intense scattering of light would significantly degrade the spatial resolution of fluorescence microscopy. In this paper, we develop a fluorescence microtomography technique that utilizes the Monte Carlo method to image fluorescence reporters in thick biological samples. This approach is based on an l0-regularized tomography model and provides an excellent solution. Our studies on biomimetic tissue scaffolds have demonstrated that the proposed approach is capable of localizing and quantifying the distribution of optical molecular probe accurately and reliably.

  11. Revisiting on-shell renormalization conditions in theories with flavor mixing

    NASA Astrophysics Data System (ADS)

    Grimus, W.; Löschner, M.

    2016-08-01

    In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in 𝜀 = p2 - m n2, where p is the external four-momentum and mn is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.

  12. Random sequential renormalization and agglomerative percolation in networks: Application to Erdös-Rényi and scale-free graphs

    NASA Astrophysics Data System (ADS)

    Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

    2011-12-01

    We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song , Nature (London)NATUAS0028-083610.1038/nature03248 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N0→0 in the limit of large systems (where N0 is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N0 in sparse ER graphs and in the annealed model, while it happens for N/N0→1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.148701 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering “supernodes” as clusters) are much easier to study using the fast Newman-Ziff algorithm for

  13. Monte Carlo variance reduction approaches for non-Boltzmann tallies

    SciTech Connect

    Booth, T.E.

    1992-12-01

    Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed.

  14. Comment on the charge-renormalization effects of quartic scalar self-interactions

    SciTech Connect

    Jones, D.R.T.

    1980-12-15

    The charge-renormalization effects of quartic scalar interactions are calculated in a general gauge theory at the three-loop level using the Gegenbauer series expansion technique. The result agrees with a previous calculation by Curtright.

  15. Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

    NASA Astrophysics Data System (ADS)

    Connes, Alain; Kreimer, Dirk

    This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

  16. Grand canonical finite size numerical approaches in one and two dimensions: Real space energy renormalization and edge state generation

    NASA Astrophysics Data System (ADS)

    Hotta, Chisa; Nishimoto, Satoshi; Shibata, Naokazu

    2013-03-01

    The grand canonical numerical analysis recently developed for quantum many-body systems on a finite cluster [C. Hotta and N. Shibata, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.86.041108 86, 041108(R) (2012)] is the technique to efficiently obtain the physical quantities in an applied field. There, the observables are the continuous and real functions of fields, mimicking their thermodynamic limit, even when a small cluster is adopted. We develop a theory to explain the mechanism of this analysis based on the deformation of the Hamiltonian. The deformation spatially scales down the energy unit from the system center toward zero at the open edge sites, which introduces the renormalization of the energy levels in a way reminiscent of Wilson's numerical renormalization group. However, compared to Wilson's case, our deformation generates a number of far well-localized edge states near the chemical potential level, which are connected via a very small quantum fluctuation in k space with the “bulk” states which spread at the center of the system. As a response to the applied field, the particles on the cluster are self-organized to tune the particle number of the bulk states to their thermodynamic limit by using the “edges” as a buffer. We demonstrate the present analysis in two-dimensional quantum spin systems on square and triangular lattices, and determine the smooth magnetization curve with a clear (1)/(3) plateau structure in the latter.

  17. Many-body localization: construction of the emergent local conserved operators via block real-space renormalization

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2016-03-01

    A fully many-body localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via block real-space renormalization. The principle is that each renormalization group step diagonalizes the smallest remaining blocks and produces a conserved operator for each block. The final output for a chain of N spins is a hierarchical organization of the N conserved operators with ≤ft(\\frac{\\ln N}{\\ln 2}\\right) layers. The system size nature of the conserved operators of the top layers is necessary to describe the possible long-range order of the excited eigenstates and the possible critical points between different FMBL phases. We discuss the similarities and the differences with the strong disorder RSRG-X method that generates the whole set of the 2 N eigenstates via a binary tree of N layers. The approach is applied to the long-range quantum spin-glass Ising model, where the constructed excited eigenstates are found to be exactly like ground states in another disorder realization, so that they can be either in the paramagnetic phase, in the spin-glass phase or critical.

  18. Material and Doping Dependence of the Nodal and Antinodal Dispersion Renormalizations in Single- and Multilayer Cuprates

    DOE PAGES

    Johnston, S.; Lee, W. S.; Chen, Y.; Nowadnick, E. A.; Moritz, B.; Shen, Z. -X.; Devereaux, T. P.

    2010-01-01

    We presenmore » t a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of Cu O 2 layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.« less

  19. Persistence-length renormalization of polymers in a crowded environment of hard disks.

    PubMed

    Schöbl, S; Sturm, S; Janke, W; Kroy, K

    2014-12-01

    The most conspicuous property of a semiflexible polymer is its persistence length, defined as the decay length of tangent correlations along its contour. Using an efficient stochastic growth algorithm to sample polymers embedded in a quenched hard-disk fluid, we find apparent wormlike chain statistics with a renormalized persistence length. We identify a universal form of the disorder renormalization that suggests itself as a quantitative measure of molecular crowding. PMID:25526167

  20. MCMini: Monte Carlo on GPGPU

    SciTech Connect

    Marcus, Ryan C.

    2012-07-25

    MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.