Science.gov

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. Conformal or walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

    SciTech Connect

    Hasenfratz, Anna

    2010-07-01

    Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N{sub f}=8 flavor system, thus verifying its QCD-like nature. With N{sub f}=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free-field value.

  3. Monte-Carlo renormalization group study of gauged RP2 spin models in two dimensions

    NASA Astrophysics Data System (ADS)

    Catterall, S. M.; Hasenbusch, M.; Horgan, R. R.; Renken, R.

    1998-04-01

    The 2D RP2 gauge model is studied using the Monte-Carlo Renormalization Group (MCRG). We confirm the first-order transition reported in [1] ending in a critical point associated with vorticity. We find evidence for a new renormalized trajectory (RT) which is responsible for a cross-over from the vortex dominated regime to the O(3)_ regime as the coupling is reduced. Near to the cross-over region a good signal for scaling will be observed in RP2 but this is illusory and is due to the proximity of the RT. We suggest that this is the origin of the 'pseudo'-scaling observed in [2]. We find that the continuum limit of RP2 is controlled by the O(3) fixed point.

  4. Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model

    NASA Technical Reports Server (NTRS)

    Heller, Urs M.

    1988-01-01

    An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

  5. 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).

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. Gutzwiller renormalization group

    DOE PAGES

    Lanatà, Nicola; Yao, Yong -Xin; Deng, Xiaoyu; ...

    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

  11. Gutzwiller renormalization group

    SciTech Connect

    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 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.

  12. 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.

  13. Renormalization group approach to satisfiability

    NASA Astrophysics Data System (ADS)

    Coppersmith, S. N.

    2007-02-01

    Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical ORs of these variables is true. Here, a renormalization group transformation is constructed and used to relate the properties of satisfiability problems with different numbers of variables in each clause. The transformation yields new insight into phase transitions delineating "hard" and "easy" satisfiability problems.

  14. Renormalization group analysis of turbulence

    NASA Technical Reports Server (NTRS)

    Smith, Leslie M.

    1989-01-01

    The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.

  15. Improved system identification with Renormalization Group.

    PubMed

    Wang, Qing-Guo; Yu, Chao; Zhang, Yong

    2014-09-01

    This paper proposes an improved system identification method with Renormalization Group. Renormalization Group is applied to a fine data set to obtain a coarse data set. The least squares algorithm is performed on the coarse data set. The theoretical analysis under certain conditions shows that the parameter estimation error could be reduced. The proposed method is illustrated with examples.

  16. 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.

  17. Renormalization-group improved inflationary scenarios

    NASA Astrophysics Data System (ADS)

    Pozdeeva, E. O.; Vernov, S. Yu.

    2017-03-01

    The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.

  18. Functional renormalization group in Floquet space

    NASA Astrophysics Data System (ADS)

    Eissing, Anna Katharina; Meden, Volker; Kennes, Dante Marvin

    2016-12-01

    We present an extension of the functional renormalization group to Floquet space, which enables us to treat the long time behavior of interacting time periodically driven quantum dots. It is one of its strength that the method is neither bound to small driving amplitudes nor to small driving frequencies, i.e., very general time periodic signals can be considered. It is applied to the interacting resonant level model, a prototype model of a spinless, fermionic quantum dot. The renormalization in several setups with different combinations of time periodic parameters is studied, where the numerical results are complemented by analytic expressions for the renormalization in the limit of small driving amplitude. We show how the driving frequency acts as an infrared cutoff of the underlying renormalization group flow which manifests in novel power laws. We utilize the tunability of the effective reservoir distribution function in a periodically driven onsite energy setup to show how its shape is directly reflected in the renormalization group flow. This allows us to flexibly tune the power-law renormalization generically encountered in quantum dot structures. Finally, an in-phase quantum pump as well as a single parameter pump are investigated in the whole regime of driving frequency, demonstrating that the new power law in the driving frequency is reflected in the mean current of the latter.

  19. 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.

  20. 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.

  1. Renormalization group equations for the CKM matrix

    SciTech Connect

    Kielanowski, P.; Juarez W, S. R.; Montes de Oca Y, J. H.

    2008-12-01

    We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the standard model, its two Higgs extension, and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle {phi}{sub 2} of the unitarity triangle. For the special case of the standard model and its extensions with v{sub 1}{approx_equal}v{sub 2} we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters {rho} and {eta} are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix might have a simple, special form at asymptotic energies.

  2. Renormalization-Group Analysis of Turbulence

    NASA Astrophysics Data System (ADS)

    Smith, Leslie M.

    The renormalization-group (RG) analysis of turbulence, based primarily on KG Wilson's coarse-graining procedure, leads to suggestive results for turbulence coefficients and models. Application of the method to turbulence evolved from the contributions of many authors and received widespread attention following the 1986 work of V Yakhot and SA Orszag. The Yakhot-Orszag method involves the basic renormalization-group scale-removal procedure, as well as additional hypotheses and approximations; their analysis is reviewed here with an attempt to clarify those approximations. Discussion of some related and subsequent literature is also included. Following the work of M Avellaneda and AJ Majda, a simpler version of the method is appplied to a model passive scalar problem wherein it is seen that, in certain cases, the RG method can recover exact results.

  3. Renormalization group for non-relativistic fermions.

    PubMed

    Shankar, R

    2011-07-13

    A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.

  4. Noncommutativity from exact renormalization group dualities

    NASA Astrophysics Data System (ADS)

    Gangopadhyay, Sunandan; Scholtz, Frederik G.

    2014-08-01

    Here we demonstrate, first, the construction of dualities using the exact renormalization group approach and, second, that spatial noncommutativity can emerge as such a duality. This is done in a simple quantum mechanical setting that establishes an exact duality between the commutative and noncommutative quantum Hall systems with harmonic interactions. It is also demonstrated that this link can be understood as a blocking (coarse graining) transformation in time that relates commutative and noncommutative degrees of freedom.

  5. 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.

  6. Renormalization Group in the Standard Model

    SciTech Connect

    Kielanowski, P.; Juarez W, S. R.

    2007-11-27

    We discuss two applications of the renormalization group method in the Standard Model. In the first one we present some theorems about the running of the Cabibbo-Kobayashi-Maskawa matrix and show that the evolution depends on one function of energy only. In the second one we discuss the properties of the running of the Higgs potential and derive the limits for the Higgs mass.

  7. Renormalization group and perfect operators for stochastic differential equations.

    PubMed

    Hou, Q; Goldenfeld, N; McKane, A

    2001-03-01

    We develop renormalization group (RG) methods for solving partial and stochastic differential equations on coarse meshes. RG transformations are used to calculate the precise effect of small-scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.

  8. Renormalization group flow of the Holst action

    NASA Astrophysics Data System (ADS)

    Daum, J.-E.; Reuter, M.

    2012-03-01

    The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under spacetime diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three-parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way.

  9. Generalized geometry, T-duality, and renormalization group flow

    NASA Astrophysics Data System (ADS)

    Streets, Jeffrey

    2017-04-01

    We interpret the physical B-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural ;Ricci flow; for generalized geometry. Next we show that the B-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the B-field renormalization group flow.

  10. Nonlinear relativistic plasma resonance: Renormalization group approach

    NASA Astrophysics Data System (ADS)

    Metelskii, I. I.; Kovalev, V. F.; Bychenkov, V. Yu.

    2017-02-01

    An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

  11. Development of renormalization group analysis of turbulence

    NASA Technical Reports Server (NTRS)

    Smith, L. M.

    1990-01-01

    The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

  12. 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.

  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. General covariance from the quantum renormalization group

    NASA Astrophysics Data System (ADS)

    Shyam, Vasudev

    2017-03-01

    The quantum renormalization group (QRG) is a realization of holography through a coarse-graining prescription that maps the beta functions of a quantum field theory thought to live on the "boundary" of some space to holographic actions in the "bulk" of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the D +1 dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the D dimensional boundary. This will be a particular form of the Wess-Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of the gradient form.

  15. 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.

  16. Solving renormalization group equations with the Lambert W function

    NASA Astrophysics Data System (ADS)

    Sonoda, H.

    2013-04-01

    It has been known for some time that 2-loop renormalization group equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed point to construct renormalization group invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.

  17. 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.

  18. 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.

  19. Renormalization group invariant of lepton Yukawa couplings

    NASA Astrophysics Data System (ADS)

    Tsuyuki, Takanao

    2015-04-01

    By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them, Iq, is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant Il for Dirac and Majorana neutrino cases and find that Il can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality Iq=Il can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.

  20. Renormalization group flow for noncommutative Fermi liquids

    SciTech Connect

    Estrada-Jimenez, Sendic; Garcia-Compean, Hugo; Wu Yongshi

    2011-06-15

    Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding B-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS' and BCS are discussed in detail. It is shown that while the Gaussian fixed-point remains unchanged, the BCS instability is modified due to the space noncommutativity.

  1. 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.

  2. Renormalization Group Reduction of Non Integrable Hamiltonian Systems

    SciTech Connect

    Stephan I. Tzenov

    2002-05-09

    Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.

  3. 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.

  4. 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

  5. Holographic torus entanglement and its renormalization group flow

    NASA Astrophysics Data System (ADS)

    Bueno, Pablo; Witczak-Krempa, William

    2017-03-01

    We study the universal contributions to the entanglement entropy (EE) of 2 +1 -dimensional and 3 +1 -dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2 +1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 γ . This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of γ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in 2 +1 dimensions and 3 +1 dimensions.

  6. Unifying renormalization group and the continuous wavelet transform

    NASA Astrophysics Data System (ADS)

    Altaisky, M. V.

    2016-05-01

    It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e., those depending on both the position x and the resolution a . Such a theory, earlier described in [1,2], is finite by construction. The space of scale-dependent functions {ϕa(x )} is more relevant to a physical reality than the space of square-integrable functions L2(Rd); because of the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than a point. The effective action Γ(A ) of our theory turns out to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet—an "aperture function" of a measuring device used to produce the snapshot of a field ϕ at the point x with the resolution a . The standard renormalization group results for ϕ4 model are reproduced.

  7. Renormalization-group study of the four-body problem

    SciTech Connect

    Schmidt, Richard; Moroz, Sergej

    2010-05-15

    We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.

  8. 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.

  9. 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.

  10. Topologically twisted renormalization group flow and its holographic dual

    NASA Astrophysics Data System (ADS)

    Nakayama, Yu

    2017-03-01

    Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (also known as topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a nontrivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS /CFT . We argue that the nontrivial fixed points require fine-tuning of the bulk theory, in general, but remarkably we find that the O (3 ) Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean anti-de Sitter metric.

  11. Solvable model in renormalization group analysis for effective eddy viscosity.

    PubMed

    Chang, Chien C; Lin, Bin-Shei; Wang, Chi-Tzung

    2003-04-01

    This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).

  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. 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}.

  14. Subtractive Renormalization Group Invariance: Pionless EFT at NLO

    NASA Astrophysics Data System (ADS)

    Timóteo, Varese S.; Szpigel, Sérgio; Durães, Francisco O.

    2010-11-01

    We show some results concerning the renormalization group (RG) invariance of the nucleon-nucleon (NN) interaction in pionless effective field theory at next-to-leading order (NLO), using a non-relativistic Callan-Symanzik equation (NRCS) for the driving term of the Lippmann-Schwinger (LS) equation with three recursive subtractions. The phase-shifts obtained for the RG evolved potential are same as those for the original potential, apart from relative differences of order 10-15.

  15. Philosophical Implications of Kadanoff's Work on the Renormalization Group

    NASA Astrophysics Data System (ADS)

    Batterman, Robert W.

    2016-11-01

    This paper investigates the consequences for our understanding of physical theories as a result of the development of the renormalization group. Kadanoff's assessment of these consequences is discussed. What he called the "extended singularity theorem" (that phase transitons only can occur in infinite systems) poses serious difficulties for philosophical interpretation of theories. Several responses are discussed. The resolution demands a philosophical rethinking of the role of mathematics in physical theorizing.

  16. Keldysh functional renormalization group for electronic properties of graphene

    NASA Astrophysics Data System (ADS)

    Fräßdorf, Christian; Mosig, Johannes E. M.

    2017-03-01

    We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible nonzero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer et al., Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409.

  17. 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.

  18. Renormalization group analysis of the gluon mass equation

    NASA Astrophysics Data System (ADS)

    Aguilar, A. C.; Binosi, D.; Papavassiliou, J.

    2014-04-01

    We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.

  19. Universal short-time dynamics: Boundary functional renormalization group for a temperature quench

    NASA Astrophysics Data System (ADS)

    Chiocchetta, Alessio; Gambassi, Andrea; Diehl, Sebastian; Marino, Jamir

    2016-11-01

    We present a method to calculate short-time nonequilibrium universal exponents within the functional-renormalization-group scheme. As an example, we consider the classical critical dynamics of the relaxational model A after a quench of the temperature of the system and calculate the initial-slip exponent which characterizes the nonequilibrium universal short-time behavior of both the order parameter and correlation functions. The value of this exponent is found to be consistent with the result of a perturbative dimensional expansion and of Monte Carlo simulations in three spatial dimensions.

  20. Nonperturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action

    SciTech Connect

    Ide, K.; Aoki, S.; Kanaya, K.; Taniguchi, Y.; Burkhalter, R.; Ishikawa, K.-I.; Ishizuka, N.; Iwasaki, Y.; Ukawa, A.; Yoshie, T.; Fukugita, M.; Hashimoto, S.; Kaneko, T.; Kuramashi, Y.; Ishikawa, T.; Lesk, V.; Umeda, T.; Okawa, M.

    2004-10-01

    Renormalization constants (Z-factors ) of vector and axial-vector currents are determined nonperturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole-improved clover quark action using the Schroedinger functional method. Nonperturbative values of Z-factors turn out to be smaller than 1-loop perturbative values by O(15%) at a lattice spacing of a{sup -1}{approx_equal} 1 GeV. The pseudoscalar and vector meson decay constants calculated with the nonperturbative Z-factors show a much better scaling behavior compared to previous results obtained with tadpole-improved one-loop Z-factors. In particular, the nonperturbative Z-factors normalized at infinite physical volume show that the scaling violations of the decay constants are within about 10% up to the lattice spacing a{sup -1}{approx}1 GeV. The continuum estimates obtained from data in the range a{sup -1}{approx} 1-2 GeV agree with those determined from finer lattices (a{sup -1}{approx}2-4 GeV) with the standard action.

  1. Renormalization group analysis of turbulence. I - Basic theory

    NASA Astrophysics Data System (ADS)

    Yakhot, Victor; Orszag, Steven A.

    The dynamic renormalization group (RNG) method is developed for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, permits the evaluation of transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrum = 1.617; turbulent Prandtl number for high-Reynolds-number heat transfer = 0.7179; Batchelor constant = 1.161; and skewness factor = 0.4878. A differential transport model, is derived which is particularly useful near walls.

  2. Broken current anomalous dimensions, conformal manifolds, and renormalization group flows

    NASA Astrophysics Data System (ADS)

    Bashmakov, Vladimir; Bertolini, Matteo; Raj, Himanshu

    2017-03-01

    We consider deformations of a conformal field theory that explicitly break some global symmetries of the theory. If the deformed theory is still a conformal field theory, one can exploit the constraints put by conformal symmetry to compute broken currents anomalous dimensions. We consider several instances of this scenario, using field theory techniques and also holographic ones, where necessary. Field theoretical methods suffice to discuss examples of symmetry-breaking deformations of the O (N ) model in d =4 -ɛ dimensions. Holography is instrumental, instead, for computing current anomalous dimensions in β -deformed superconformal field theories and in a class of supersymmetric renormalization group flows at large N .

  3. 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.

  4. Functional renormalization group study of nuclear and neutron matter

    SciTech Connect

    Drews, Matthias; Weise, Wolfram

    2016-01-22

    A chiral model based on nucleons interacting via boson exchange is investigated. Fluctuation effects are included consistently beyond the mean-field approximation in the framework of the functional renormalization group. The liquid-gas phase transition of symmetric nuclear matter is studied in detail. No sign of a chiral restoration transition is found up to temperatures of about 100 MeV and densities of at least three times the density of normal nuclear matter. Moreover, the model is extended to asymmetric nuclear matter and the constraints from neutron star observations are discussed.

  5. Applying tensor renormalization group methods to frustrated and glassy systems: advantages, limitations, and applications

    NASA Astrophysics Data System (ADS)

    Zhu, Zheng; Katzgraber, Helmut G.

    2014-03-01

    We study the thermodynamic properties of the two-dimensional Edwards-Anderson Ising spin-glass model on a square lattice using the tensor renormalization group method based on a higher-order singular-value decomposition. Our estimates of the internal energy per spin agree very well with high-precision parallel tempering Monte Carlo studies, thus illustrating that the method can, in principle, be applied to frustrated magnetic systems. In particular, we discuss the necessary tuning of parameters for convergence, memory requirements, efficiency for different types of disorder, as well as advantages and limitations in comparison to conventional multicanonical and Monte Carlo methods. Extensions to higher space dimensions, as well as applications to spin glasses in a field are explored.

  6. 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.

  7. 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.

  8. Numerical renormalization group study of a dissipative quantum dot

    NASA Astrophysics Data System (ADS)

    Glossop, M. T.; Ingersent, K.

    2007-03-01

    We study the quantum phase transition (QPT) induced by dissipation in a quantum dot device at the degeneracy point. We employ a Bose-Fermi numerical renormalization group approach [1] to study the simplest case of a spinless resonant-level model that couples the charge density on the dot to a dissipative bosonic bath with density of states B(φ)ŝ. In anticipation of future experiments [2] and to assess further the validity of theoretical techniques in this rapidly developing area, we take the conduction-electron leads to have a pseudogap density of states: ρ(φ) |φ|^r, as considered in a very recent perturbative renormalization group study [3]. We establish the conditions on r and s such that a QPT arises with increasing dissipation strength --- from a delocalized phase, where resonant tunneling leads to large charge fluctuations on the dot, to a localized phase where such fluctuations are frozen. We present results for the single-particle spectrum and the response of the system to a local electric field, extracting critical exponents that depend in general on r and s and obey hyperscaling relations. We make full comparison with results of [3] where appropriate. Supported by NSF Grant DMR-0312939. [1] M. T. Glossop and K. Ingersent, PRL 95, 067202 (2005); PRB (2006). [2] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, PRL 97, 096603 (2006). [3] C.-H. Chung, M. Kir'can, L. Fritz, and M. Vojta (2006).

  9. 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.

  10. 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)

  11. 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}.

  12. Exploration of Similarity Renormalization Group Generators in 1-Dimensional Potentials

    NASA Astrophysics Data System (ADS)

    Heinz, Matthias

    2016-09-01

    The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. The user input into the SRG evolution is a matrix called the generator, which determines to what form the Hamiltonian is transformed. As it is currently used, the SRG evolves Hamiltonian into a band diagonal form. However, due to many-body forces induced by the evolution, the SRG introduces errors when used to renormalize many-body potentials. This makes it unfit for calculations with nuclei larger than a certain size. A recent paper suggests that alternate generators may induce smaller many-body forces. Smaller many-body force induction would allow SRG use to be extended to larger nuclei. I use 1-dimensional systems of two, three, and four bosons to further study the SRG evolution and how alternate generators affect many-body forces induced.

  13. Magnus expansion and in-medium similarity renormalization group

    NASA Astrophysics Data System (ADS)

    Morris, T. D.; Parzuchowski, N. M.; Bogner, S. K.

    2015-09-01

    We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-Hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and 16O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.

  14. 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.

  15. Renormalization group invariants in the MSSM and its extensions

    NASA Astrophysics Data System (ADS)

    Demir, Durmus A.

    2005-11-01

    We derive one-loop renormalization group (RG) invariant observables and analyze their phenomenological implications in the MSSM and its μ problem solving extensions, U(1)' model and NMSSM. We show that there exist several RG invariants in the gauge, Yukawa and soft-breaking sectors of each model. In general, RG invariants are highly useful for projecting experimental data to messenger scale, for revealing correlations among the model parameters, and for probing the mechanism that breaks supersymmetry. The Yukawa couplings and trilinear soft terms in U(1)' model and NMSSM do not form RG invariants though there exist approximate invariants in low tan β domain. In the NMSSM, there are no invariants that contain the Higgs mass-squareds. We provide a comparative analysis of RG invariants in all three models and analyze their model-building and phenomenological implications by a number of case studies.

  16. Aperiodic quantum XXZ chains: Renormalization-group results

    NASA Astrophysics Data System (ADS)

    Vieira, André P.

    2005-04-01

    We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.

  17. 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

  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 flow equations for chiral nuclear models

    NASA Astrophysics Data System (ADS)

    Johnson, Andrew Sheriden

    1997-10-01

    The renormalization group (RG) is a tool for the qualitative and quantitative nonperturbative understanding of physical systems. There are many examples of physical systems that defy any perturbative approach, e.g. strongly correlated statistical systems and strongly coupled quantum field theories. The currently accepted theory of the strong interactions, Quantum Chromodynamics (QCD), is an example of the latter. Unlike the case of its gauge theory counterpart, Quantum Electrodynamics (QED), many consequences of QCD cannot be computed using perturbation theory. Instead, closed form perturbative solutions of QCD are possible only for a limited subset of phenomena such as high momentum-transfer scattering processes. These solutions afford little insight into the most ubiquitous and experimentally accessible consequences of QCD: the bound states of the theory, e.g. nucleons and nuclei. In this thesis we present a nonperturbative solution of the σ-model which was originally proposed in the late 50s as a phenomenological description of the dynamics of nucleons and mesons. In our version of the model the fermions are interpreted as quarks which interact via the sigma and pi mesons. The model exhibits an approximate SU(2) × SU(2) chiral symmetry which is understood as a low energy consequence of QCD. We use the Renormalization Group to study the behavior of the model as we evolve from a high to a low momentum scale and as chiral symmetry is both spontaneously and explicitly broken. The results show a marked improvement over the perturbative calculation and are consistent with experiment and other nonperturbative calculations such as chiral perturbation theory and lattice gauge theory. We next review the Renormalization Group idea first with a heuristic example drawing from the contrast between the hydrodynamic and the statistical continuum limit. For physical systems in which the microscopic behavior does not sufficiently decouple from the macroscopic behavior, the de

  20. Generalized approach to global renormalization-group theory for fluids

    NASA Astrophysics Data System (ADS)

    Ramana, A. Sai Venkata; Menon, S. V. G.

    2012-04-01

    The global renormalization-group theory (GRGT) for fluids is derived starting with the square-gradient approximation for the Helmholtz free energy functional such that any mean-field free energy density and direct correlation function can be employed. The new derivation uses Wilson's functions for representing density fluctuations, thereby relaxing the assumption of cosine variation of density fluctuations used in earlier approaches. The generality of the present approach is shown by deriving the relationships to the earlier developments. A qualitative way to infer the free parameters in the present form of GRGT is also suggested. The new theory is applied to square-well fluids of ranges 1.5 and 3.0 (in units of hard-sphere diameter) and Lennard-Jones fluids. It is shown that the present theory produces a flat isotherm in the two-phase region. Thus the theory accounts for fluctuations at all length scales and avoids the use of Maxwell's construction. An analysis of the liquid-vapor phase diagrams and the critical constants obtained for different potentials shows that, with a mean-field free energy density that is accurate away from the critical region and an appropriate coarse graining length for the mean-field theory, GRGT can provide results in good agreement with the simulation and experimental results.

  1. High-performance functional Renormalization Group calculations for interacting fermions

    NASA Astrophysics Data System (ADS)

    Lichtenstein, J.; Sánchez de la Peña, D.; Rohe, D.; Di Napoli, E.; Honerkamp, C.; Maier, S. A.

    2017-04-01

    We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the t ,t‧ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.

  2. Functional renormalization group studies of nuclear and neutron matter

    NASA Astrophysics Data System (ADS)

    Drews, Matthias; Weise, Wolfram

    2017-03-01

    Functional renormalization group (FRG) methods applied to calculations of isospin-symmetric and asymmetric nuclear matter as well as neutron matter are reviewed. The approach is based on a chiral Lagrangian expressed in terms of nucleon and meson degrees of freedom as appropriate for the hadronic phase of QCD with spontaneously broken chiral symmetry. Fluctuations beyond mean-field approximation are treated solving Wetterich's FRG flow equations. Nuclear thermodynamics and the nuclear liquid-gas phase transition are investigated in detail, both in symmetric matter and as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of symmetric nuclear matter and pure neutron matter are found to be in good agreement with advanced ab-initio many-body computations. Contacts with perturbative many-body approaches (in-medium chiral perturbation theory) are discussed. As an interesting test case, the density dependence of the pion mass in the medium is investigated. The question of chiral symmetry restoration in nuclear and neutron matter is addressed. A stabilization of the phase with spontaneously broken chiral symmetry is found to persist up to high baryon densities once fluctuations beyond mean-field are included. Neutron star matter including beta equilibrium is discussed under the aspect of the constraints imposed by the existence of two-solar-mass neutron stars.

  3. The impact of renormalization group theory on magnetism

    NASA Astrophysics Data System (ADS)

    Köbler, U.; Hoser, A.

    2007-11-01

    The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ɛ that is independent of spin structure and lattice symmetry. Normally the Tɛ function holds up to ~0.85Tc where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the Tɛ function are demonstrated for the spontaneous magnetization and for the heat capacity.

  4. Renormalization group evolution of the universal theories EFT

    NASA Astrophysics Data System (ADS)

    Wells, James D.; Zhang, Zhengkang

    2016-06-01

    The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.

  5. Critical asymmetry in renormalization group theory for fluids.

    PubMed

    Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun

    2013-06-21

    The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

  6. Improved renormalization group theory for critical asymmetry of fluids.

    PubMed

    Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun

    2013-09-28

    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.

  7. 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.

  8. Renormalization group evolution of the universal theories EFT

    SciTech Connect

    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, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. 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.

  9. 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

  10. Automatic calculation of supersymmetric renormalization group equations and loop corrections

    NASA Astrophysics Data System (ADS)

    Staub, Florian

    2011-03-01

    SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_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.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose

  11. Functional renormalization group for the U (1 )-T56 tensorial group field theory with closure constraint

    NASA Astrophysics Data System (ADS)

    Lahoche, Vincent; Ousmane Samary, Dine

    2017-02-01

    This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

  12. From Asymptotic Freedom Toward Heavy Quarkonia Within the Renormalization-Group Procedure for Effective Particles

    NASA Astrophysics Data System (ADS)

    Gómez-Rocha, María

    2017-03-01

    The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling constant with the renormalization-group scale and we summarize the basic elements needed in the formulation of the bound-state problem.

  13. Efficient perturbation theory to improve the density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej

    2017-02-01

    The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.

  14. 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.

  15. 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.

  16. Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings

    NASA Astrophysics Data System (ADS)

    Gaite, José

    2004-10-01

    The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them stochastic Langevin equations. Furthermore, if the renormalization group is a gradient flow, the space of couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas. The formulation of the renormalization group as supersymmetric quantum mechanics is useful for analysing the topology of the space of couplings by means of Morse theory. We present simple examples with one or two couplings.

  17. Cluster-algorithm renormalization-group study of universal fluctuations in the two-dimensional Ising model.

    PubMed

    Palma, G; Zambrano, D

    2008-12-01

    In this paper we propose a method to study critical systems numerically, which combines collective-mode algorithms and renormalization group on the lattice. This method is an improved version of the Monte Carlo renormalization group in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature T(L) . "Universal fluctuations" were first proposed in the work of Bramwell, Holdsworth, and Pinton [Nature (London) 396, 552 (1998)] and stated that the probability density function of a global quantity for very dissimilar systems, such as a confined turbulent flow and a two-dimensional (2D) magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution," originally obtained for magnetization in the 2D XY model in the low-temperature region. The results for the critical exponents and the renormalization-group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.

  18. Generalization of the tensor renormalization group approach to 3-D or higher dimensions

    NASA Astrophysics Data System (ADS)

    Teng, Peiyuan

    2017-04-01

    In this paper, a way of generalizing the tensor renormalization group (TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered. A theoretical contraction framework is therefore proposed. Furthermore, the canonical polyadic decomposition is introduced to tensor network theory. A numerical verification of this method on the 3-D Ising model is carried out.

  19. Renormalization-group study of the ferromagnetic Ising model on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Unger, Chris

    1984-08-01

    The dynamic real-space renormalization group of Mazenko and Valls is applied to the zero-field ferromagnetic Ising model on the triangular lattice. Renormalization equations valid for all temperatures above the critical temperature Tc are derived for the susceptibility, specific heat, structure factor, and correlation length. The magnetization is found for Trenormalization-group results is good to excellent, and shows that this renormalization-group method can accurately calculate nonuniversal, as well as universal, quantities on different lattices. The computed dynamic structure factor, however, exhibits nonmonotonic behavior as a function of temperature. This nonmonotonic behavior is conjectured to be due to approximations in determining the expansion parameters.

  20. Renormalization-group theory for the eddy viscosity in subgrid modeling

    NASA Technical Reports Server (NTRS)

    Zhou, YE; Vahala, George; Hossain, Murshed

    1988-01-01

    Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

  1. 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.

  2. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

    NASA Astrophysics Data System (ADS)

    José, Jorge V.

    2013-06-01

    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  3. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

    NASA Astrophysics Data System (ADS)

    José, Jorge V.

    2017-03-01

    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  4. 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

  5. Nonequilibrium functional renormalization group for interacting quantum systems.

    PubMed

    Jakobs, Severin G; Meden, Volker; Schoeller, Herbert

    2007-10-12

    We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.

  6. 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.

  7. Closed-form irreducible differential formulations of the Wilson renormalization group

    NASA Astrophysics Data System (ADS)

    Vvedensky, D. D.; Chang, T. S.; Nicoll, J. F.

    1983-06-01

    We present a detailed derivation of the one-particle-irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order ɛ2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and η to order ɛ2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator.

  8. a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.

    NASA Astrophysics Data System (ADS)

    Cowan, Mark Timothy

    The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.

  9. 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

    2016-07-07

    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.

  10. 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.

  11. 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.

  12. Subgrid modeling of convective turbulence in weakly ionized collisional plasma by renormalization group analysis

    SciTech Connect

    Hamza, A.M.; Sudan, R.N.

    1995-03-01

    The equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the ExB or gradient-drift instability were derived by Sudan and Keskinen for addressing the electrostatic turbulence in the E and F regions of the Earth`s ionosphere. The authors have developed a subgrid model suitable for the numerical simulation of these equations which is closely related to renormalized diffusion caused by small-scale fluctuation spectrum. {open_quotes}Dynamical Renormalization Group{close_quotes} (RNG) methods are employed to obtain the renormalized diffusion. This procedure computes the long-wavelength, long-time behavior of density correlations generated by the evolution equation for the plasma stirred by a Gaussian random force characterized by a correlation function {proportional_to} k{sup m} where k is the wavenumber of the forcing function. The effect of small scales on the large-scale dynamics in the limit k{yields}0 and infinite Reynolds number can be expressed in the form of renormalized coefficients; in this case, renormalized diffusion. If one assumes the power spectra to be given by the Kolmogorov argument of cascading of energy through k space then one can derive a subgrid model based on the results of RNG. 27 refs.

  13. Turbulent transport of a passive-scalar field by using a renormalization-group method

    NASA Technical Reports Server (NTRS)

    Hossain, Murshed

    1992-01-01

    A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

  14. Action Ward Identity and the Stückelberg-Petermann Renormalization Group

    NASA Astrophysics Data System (ADS)

    Dütsch, Michael; Fredenhagen, Klaus

    A fresh look at the renormalization group (in the sense of Stückelberg-Petermann) from the point of view of algebraic quantum field theory is given, and it is shown that a consistent definition of local algebras of observables and of interacting fields in renormalized perturbative quantum field theory can be given in terms of retarded products. The dependence on the Lagrangian enters this construction only through the classical action. This amounts to the commutativity of retarded products with derivatives, a property named Action Ward Identity by Stora.

  15. Loop expansion of the average effective action in the functional renormalization group approach

    NASA Astrophysics Data System (ADS)

    Lavrov, Peter M.; Merzlikin, Boris S.

    2015-10-01

    We formulate a perturbation expansion for the effective action in a new approach to the functional renormalization group method based on the concept of composite fields for regulator functions being their most essential ingredients. We demonstrate explicitly the principal difference between the properties of effective actions in these two approaches existing already on the one-loop level in a simple gauge model.

  16. New method of the functional renormalization group approach for Yang-Mills fields

    NASA Astrophysics Data System (ADS)

    Lavrov, P. M.; Shapiro, I. L.

    2014-12-01

    We propose a new formulation of the functional renormalization group (FRG) approach, based on the use of regulator functions as composite operators. In this case one can provide (in contrast with standard approach) on-shell gauge-invariance for the effective average action.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2010-01-01

    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 [Cu2O2]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 [Cu2O2]2+.

  3. Multi-regulator functional renormalization group for many-fermion systems

    NASA Astrophysics Data System (ADS)

    Tanizaki, Yuya; Hatsuda, Tetsuo

    We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen-Cooper-Schrieffer (BCS) phase and the Bose-Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières-Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS-BEC crossover, can be derived from MR-FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

  4. Application of renormalization group theory to the large-eddy simulation of transitional boundary layers

    NASA Technical Reports Server (NTRS)

    Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.

    1990-01-01

    An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

  5. Renormalization group equations and matching in a general quantum field theory with kinetic mixing

    NASA Astrophysics Data System (ADS)

    Fonseca, Renato M.; Malinský, Michal; Staub, Florian

    2013-11-01

    We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.

  6. Finite-scale singularity in the renormalization group flow of a reaction-diffusion system.

    PubMed

    Gredat, Damien; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan

    2014-01-01

    We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a different (conjugated) universality class.

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

    NASA Astrophysics Data System (ADS)

    Morris, T. D.; Bogner, S. K.

    2014-10-01

    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.

  8. 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.

  9. 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.

  10. Evolution of the Robertson-Walker metric under 2-loop renormalization group flow

    NASA Astrophysics Data System (ADS)

    Hesamifard, F.; Rezaii, M. M.

    Here, we study the evolution of a Robertson-Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.

  11. Harmonic expansion of the effective potential in a functional renormalization group at finite chemical potential

    NASA Astrophysics Data System (ADS)

    Barnaföldi, G. G.; Jakovác, A.; Pósfay, P.

    2017-01-01

    In this paper we propose a method to study the functional renormalization group (FRG) at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with zero boundary conditions. To solve this equation we use an expansion of the potential in a harmonic basis. With this method we determined the phase diagram of a simple Yukawa-type model; as expected, the bosonic fluctuations decrease the strength of the transition.

  12. 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.

  13. Conformal invariance and renormalization group in quantum gravity near two dimensions

    NASA Astrophysics Data System (ADS)

    Aida, Toshiaki; Kitazawa, Yoshihisa; Kawai, Hikaru; Ninomiya, Masao

    1994-09-01

    We study quantum gravity in 2 + ɛ dimensions in such a way as to preserve the volume-preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to the Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for a matter central charge 0 < c < 25. We show that the spacetime singularity at the big bang is resolved by the renormalization effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.

  14. Ordered phase of the O(N) model within the nonperturbative renormalization group.

    PubMed

    Peláez, Marcela; Wschebor, Nicolás

    2016-10-01

    We analyze nonperturbative renormalization group flow equations for the ordered phase of Z_{2} and O(N) invariant scalar models. This is done within the well-known derivative expansion scheme. For its leading order [local potential approximation (LPA)], we show that not every regulator yields a smooth flow with a convex free energy and discuss for which regulators the flow becomes singular. Then we generalize the known exact solutions of smooth flows in the "internal" region of the potential and exploit these solutions to implement an improved numerical algorithm, which is much more stable than previous ones for N>1. After that, we study the flow equations at second order of the derivative expansion and analyze how and when the LPA results change. We also discuss the evolution of the field renormalization factors.

  15. Scaling in landscape erosion: Renormalization group analysis of a model with infinitely many couplings

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

    Applying the standard field theory renormalization group to the model of landscape erosion introduced by Pastor-Satorras and Rothman yields unexpected results: the model is multiplicatively renormalizable only if it involves infinitely many coupling constants (i.e., the corresponding renormalization group equations involve infinitely many β-functions). We show that the one-loop counterterm can nevertheless be expressed in terms of a known function V (h) in the original stochastic equation and its derivatives with respect to the height field h. Its Taylor expansion yields the full infinite set of the one-loop renormalization constants, β-functions, and anomalous dimensions. Instead of a set of fixed points, there arises a two-dimensional surface of fixed points that quite probably contains infrared attractive regions. If that is the case, then the model exhibits scaling behavior in the infrared range. The corresponding critical exponents turn out to be nonuniversal because they depend on the coordinates of the fixed point on the surface, but they satisfy certain universal exact relations.

  16. Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2004-08-01

    Ground state properties of the S=1/2 antiferromagnetic XXZ chain with Fibonacci exchange modulation are studied using the real space renormalization group method for strong modulation. The quantum dynamical critical behavior with a new universality class is predicted in the isotropic case. Combining our results with the weak coupling renormalization group results by Vidal et al., the ground state phase diagram is obtained.

  17. Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model

    NASA Astrophysics Data System (ADS)

    Meloni, Davide; Ohlsson, Tommy; Riad, Stella

    2017-03-01

    We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10 H, 120 H, and 126 H representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M I. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10 H and 126 H representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.

  18. Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

    NASA Astrophysics Data System (ADS)

    Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

    2010-01-01

    We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter η in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with η , but when η approaches zero, they drop abruptly.

  19. On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

    NASA Technical Reports Server (NTRS)

    Smith, L. M.; Reynolds, W. C.

    1992-01-01

    An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

  20. Scalar mass stability bound in a simple Yukawa-theory from renormalization group equations

    NASA Astrophysics Data System (ADS)

    Jakovác, A.; Kaposvári, I.; Patkós, A.

    2017-01-01

    Functional renormalization group (FRG) equations are constructed for a simple Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. The evolution of the effective potential of the model, generically depending on two invariants, is explored with the help of power series expansions. Systematic investigation of the effect of a class of irrelevant operators on the lower (stability) bound allows a non-perturbative extension of the maximal cutoff value consistent with any given mass of the scalar field.

  1. Real-space renormalization group for spectral properties of hierarchical networks

    NASA Astrophysics Data System (ADS)

    Boettcher, Stefan; Li, Shanshan

    2015-10-01

    We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees generally proliferate with increasing average degree, the results show that modifications within the basic patterns of design of these hierarchical networks can lead to significant variations in their complexity. To this end, we develop renormalization group methods to obtain recursion equations from which many spectral properties can be obtained. This provides the basis for future applications to explore the physics of several dynamic processes.

  2. A renormalization group analysis of the Hill model and its HEIDI extension

    NASA Astrophysics Data System (ADS)

    Basso, L.; Fischer, O.; van der Bij, J. J.

    2014-03-01

    The parameter space of the simplest extension of the standard model is studied in the light of the 125 GeV Higgs boson discovery. The Hill model extends the scalar sector of the standard model with a real singlet, that mixes with the standard model Higgs boson only via cubic interactions. The two-loop standard model renormalization group equations are completed with the one-loop Hill equations. Stability up to the Planck scale is possible without tension with the other parameters. An extension with more singlet fields, in particular a higher-dimensional (HEIDI) field, is presented.

  3. Replica field theory and renormalization group for the Ising spin glass in an external magnetic field.

    PubMed

    Temesvári, T; De Dominicis, C

    2002-08-26

    We use the generic replica symmetric cubic field theory to study the transition of short-range Ising spin glasses in a magnetic field around the upper critical dimension. A novel fixed point is found from the application of the renormalization group. In the spin-glass limit, this fixed point governs the critical behavior of a class of systems characterized by a single cubic parameter. For this universality class, the spin-glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, however, behaves unusually. The physical consequences of this unusual behavior are discussed, and a comparison with the conventional de Almeida-Thouless scenario is presented.

  4. Functional renormalization group study of an eight-band model for the iron arsenides

    NASA Astrophysics Data System (ADS)

    Lichtenstein, J.; Maier, S. A.; Honerkamp, C.; Platt, C.; Thomale, R.; Andersen, O. K.; Boeri, L.

    2014-06-01

    We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.

  5. Functional renormalization group study of an 8-band model for the iron arsenides

    NASA Astrophysics Data System (ADS)

    Honerkamp, Carsten; Lichtenstein, Julian; Maier, Stefan A.; Platt, Christian; Thomale, Ronny; Andersen, Ole Krogh; Boeri, Lilia

    2014-03-01

    We investigate the superconducting pairing instabilities of eight-band models for 1111 iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.

  6. 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.

  7. On the functional renormalization group approach for Yang-Mills fields

    NASA Astrophysics Data System (ADS)

    Lavrov, Peter M.; Shapiro, Ilya L.

    2013-06-01

    We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of S-matrix.

  8. An Application of Functional Renormalization Group Method for Superdense Nuclear Matter

    NASA Astrophysics Data System (ADS)

    Barnaföldi, G. G.; Jakovác, A.; Pósfay, P.

    2017-01-01

    We proposed a method, using the expansion of the effective potential in a base of harmonic functions, to study the Functional Renormalization Group (FRG) method at finite chemical potential. Within this theoretical framework we determined the equation of state and the phase diagram of a simple model of massless fermions coupled to scalars through Yukawa-couling at the zero-temperature limit. Here, we use our FRG-based equation of state to describe the superdense nuclear matter inside compact astrophysical objects. We calculated the mass-radius relation for a compact star using the TOV equation, which was compared to other results.

  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

    2016-09-01

    The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully to the ground state of closed shell finite nuclei. Recent work has extended its ability to target excited states of these closed shell systems via equation of motion methods, and also complete spectra of the whole SD shell via effective shell model interactions. A recent alternative method for solving of the IM-SRG equations, based on the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

  11. 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.

  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. Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

    NASA Astrophysics Data System (ADS)

    Benhamou, M.; Chahid, M.

    2008-09-01

    We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t , before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t) , which is a function of the wave vector q , temperature T , time t , and reticulation dose D . To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, ζ . First, by averaging over ζ , we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t) , in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q-1, a time length scale R(t) thicksim t1/z , and the mesh size ξ* . The scale R(t) is interpreted as the size of growing microdomains at time t . When R(t) becomes of the order of ξ* , the dynamics is stopped. The final time, t * , then scales as t * thicksim ξ{ast z} , with the dynamic exponent z = 6 - η . Here, η is the usual Ising critical exponent. Since the final size of microdomains ξ* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.

  14. Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

    2017-03-01

    The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d = 4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d = 3, at d = 4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d = 3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and ɛ = 4 - d. All calculations are performed in the leading one-loop approximation.

  15. Interaction-induced local moments in parallel quantum dots within the functional renormalization group approach

    NASA Astrophysics Data System (ADS)

    Protsenko, V. S.; Katanin, A. A.

    2016-11-01

    We propose a version of the functional renormalization-group (fRG) approach, which is, due to including Litim-type cutoff and switching off (or reducing) the magnetic field during fRG flow, capable of describing a singular Fermi-liquid (SFL) phase, formed due to the presence of local moments in quantum dot structures. The proposed scheme allows one to describe the first-order quantum phase transition from the "singular" to the "regular" paramagnetic phase with applied gate voltage to parallel quantum dots, symmetrically coupled to leads, and shows sizable spin splitting of electronic states in the SFL phase in the limit of vanishing magnetic field H →0 ; the calculated conductance shows good agreement with the results of the numerical renormalization group. Using the proposed fRG approach with the counterterm, we also show that for asymmetric coupling of the leads to the dots the SFL behavior similar to that for the symmetric case persists, but with occupation numbers, effective energy levels, and conductance changing continuously through the quantum phase transition into the SFL phase.

  16. 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

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

    PubMed

    Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic

    2014-01-14

    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.

  18. Nonperturbative renormalization group for scalar fields in de Sitter space: Beyond the local potential approximation

    NASA Astrophysics Data System (ADS)

    Guilleux, Maxime; Serreau, Julien

    2017-02-01

    Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O (N ) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induced dimensional reduction pointed out in previous studies. We show that, as a consequence, the effective potential at the end of the flow is unchanged as compared to the local potential approximation, the main effect of the running anomalous dimension being merely to slow down the flow. We discuss some consequences of these findings.

  19. 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.

  20. Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

    NASA Astrophysics Data System (ADS)

    Mukhopadhyay, S.; Ramasesha, S.

    2009-08-01

    We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting π electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

  1. Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method.

    PubMed

    Mukhopadhyay, S; Ramasesha, S

    2009-08-21

    We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

  2. A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

    NASA Astrophysics Data System (ADS)

    Sharma, Sandeep

    2015-01-01

    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 C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh 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 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg 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 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

  3. 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.

  4. The bending of light within gravity with large scale renormalization group effects

    NASA Astrophysics Data System (ADS)

    Rodrigues, Davi C.; Koch, Benjamin; Piattella, Oliver F.; Shapiro, Ilya L.

    2015-03-01

    We briefly present the theoretical basis for evaluating the bending of light in a theory of gravity with a Renormalization Group (RG) correction to the gravitational coupling G, which induces a correction to the cosmological constant χ. In particular, spherically symmetric solutions are evaluated in detail. We have shown in previous publications that the effect of such a correction may be significant to the dynamics of astrophysical systems, and may in particular mimic at least a significant part of the kinematical effects of dark matter in galaxies in great precision. Here we show that these RG effects can also influence the bending of light, but in a form different from standard dark matter. To better evaluate the amount of dark matter needed in this approach, considering data from galaxy-galaxy lensing, more detailed cosmological evaluation of the model is still in need.

  5. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

    NASA Astrophysics Data System (ADS)

    Nocera, A.; Alvarez, G.

    2016-11-01

    Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.

  6. Orbital nematic instability in the two-orbital Hubbard model: renormalization-group + constrained RPA analysis.

    PubMed

    Tsuchiizu, Masahisa; Ohno, Yusuke; Onari, Seiichiro; Kontani, Hiroshi

    2013-08-02

    Motivated by the nematic electronic fluid phase in Sr(3)Ru(2)O(7), we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the (d(xz), d(yz))-orbital Hubbard model with high accuracy. It is confirmed that the present model exhibits a ferro-orbital instability near the magnetic or superconducting quantum criticality, due to the Aslamazov-Larkin-type vertex corrections. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr(3)Ru(2)O(7), and is expected to be realized in various multiorbital systems, such as Fe-based superconductors.

  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. Comparison of renormalization group schemes for sine-Gordon-type models

    SciTech Connect

    Nandori, I.; Nagy, S.; Sailer, K.; Trombettoni, A.

    2009-07-15

    The scheme dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoretic models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising-type phase transition of the massive sine-Gordon model. For the latter case, the Maxwell construction represents a strong constraint on the RG flow, which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.

  9. Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group

    PubMed Central

    2017-01-01

    We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex. PMID:28094988

  10. 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.

  11. Accessing topological superconductivity via a combined STM and renormalization group analysis.

    PubMed

    Elster, Lars; Platt, Christian; Thomale, Ronny; Hanke, Werner; Hankiewicz, Ewelina M

    2015-09-08

    The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.

  12. Exact Renormalization Group Analysis of Turbulent Transport by the Shear Flow

    NASA Astrophysics Data System (ADS)

    E, Weinan; Shen, Hao

    2013-11-01

    The exact renormalization group (RG) method initiated by Wilson and further developed by Polchinski is used to study the shear flow model proposed by Avellaneda and Majda as a simplified model for the diffusive transport of a passive scalar by a turbulent velocity field. It is shown that this exact RG method is capable of recovering all the scaling regimes as the spectral parameters of velocity statistics vary, found by Avellaneda and Majda in their rigorous study of this model. This gives further confidence that the RG method, if implemented in the right way instead of using drastic truncations as in the Yakhot-Orszag’s approximate RG scheme, does give the correct prediction for the large scale behaviors of solutions of stochastic partial differential equations (PDE). We also derive the analog of the “large eddy simulation” models when a finite amount of small scales are eliminated from the problem.

  13. Benchmarking Density Functional Theory with Density Matrix Renormalization Group and Lessons For Higher Dimensions

    NASA Astrophysics Data System (ADS)

    Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron

    2014-03-01

    Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).

  14. N-leg spin-S Heisenberg ladders: A density-matrix renormalization group study

    NASA Astrophysics Data System (ADS)

    Ramos, F. B.; Xavier, J. C.

    2014-03-01

    We investigate the N-leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap Δs and of the ground-state energy per site e∞N in the thermodynamic limit for ladders with widths up to six legs and spin S≤5/2. We also estimate the ground-state energy per site e∞2D for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.

  15. Nonperturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation.

    PubMed

    Benitez, F; Blaizot, J-P; Chaté, H; Delamotte, B; Méndez-Galain, R; Wschebor, N

    2012-02-01

    We present the implementation of the Blaizot-Méndez-Wschebor approximation scheme of the nonperturbative renormalization group we present in detail, which allows for the computation of the full-momentum dependence of correlation functions. We discuss its significance and its relation with other schemes, in particular, the derivative expansion. Quantitative results are presented for the test ground of scalar O(N) theories. Besides critical exponents, which are zero-momentum quantities, we compute the two-point function at criticality in the whole momentum range in three dimensions and, in the high-temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.

  16. From asymmetric nuclear matter to neutron stars: A functional renormalization group study

    NASA Astrophysics Data System (ADS)

    Drews, Matthias; Weise, Wolfram

    2015-03-01

    A previous study of nuclear matter in a chiral nucleon-meson model is extended to isospin-asymmetric matter. Fluctuations beyond mean-field approximation are treated in the framework of the functional renormalization group. The nuclear liquid-gas phase transition is investigated in detail as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of both symmetric nuclear matter and pure neutron matter are found to be in good agreement with realistic many-body computations. We also study the density dependence of the pion mass in the medium. The question of chiral symmetry restoration in neutron matter is addressed; we find a stabilization of the phase with spontaneously broken chiral symmetry once fluctuations are included. Finally, neutron-star matter including β equilibrium is discussed. The model satisfies the constraints imposed by the existence of two-solar mass neutron stars.

  17. Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling

    NASA Technical Reports Server (NTRS)

    Longcope, D. W.; Sudan, R. N.

    1991-01-01

    The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.

  18. Adaptive broadening to improve spectral resolution in the numerical renormalization group

    NASA Astrophysics Data System (ADS)

    Lee, Seung-Sup B.; Weichselbaum, Andreas

    2016-12-01

    We propose an adaptive scheme of broadening the discrete spectral data from numerical renormalization group (NRG) calculations to improve the resolution of dynamical properties at finite energies. While the conventional scheme overbroadens narrow features at large frequency by broadening discrete weights with constant width in log-frequency, our scheme broadens each discrete contribution individually based on its sensitivity to a z -shift in the logarithmic discretization intervals. We demonstrate that the adaptive broadening better resolves various features in noninteracting and interacting models at comparable computational cost. The resolution enhancement is more significant for coarser discretization as typically required in multiband calculations. At low frequency below the energy scale of temperature, the discrete NRG data necessarily needs to be broadened on a linear scale. Here we provide a method that minimizes transition artifacts in between these broadening kernels.

  19. Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group.

    PubMed

    Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus

    2017-02-14

    We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.

  20. Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene

    NASA Astrophysics Data System (ADS)

    Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi; Chan, Garnet Kin-Lic

    2008-04-01

    In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.

  1. Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic

    2006-10-01

    We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10μEh precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.

  2. Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes.

    PubMed

    Hu, Weifeng; Chan, Garnet Kin-Lic

    2015-07-14

    We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection.

  3. The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

    NASA Astrophysics Data System (ADS)

    Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter

    2014-06-01

    In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.

  4. Ab initio characterization of the quantum linear-zigzag transition using density matrix renormalization group calculations

    NASA Astrophysics Data System (ADS)

    Silvi, Pietro; Calarco, Tommaso; Morigi, Giovanna; Montangero, Simone

    2014-03-01

    Ions of the same charge inside confining potentials can form crystalline structures which can be controlled by means of the ion density and of the external trap parameters. In particular, a linear chain of trapped ions exhibits a transition to a zigzag equilibrium configuration, which is controlled by the strength of the transverse confinement. Studying this phase transition in the quantum regime is a challenging problem, even when employing numerical methods to simulate microscopically quantum many-body systems. Here we present a compact analytical treatment to map the original long-range problem into a short-range quantum field theory on a lattice. We provide a complete numerical architecture, based on the density matrix renormalization group, to address the effective quantum ϕ4 model. This technique is instrumental in giving a complete characterization of the phase diagram, as well as pinpointing the universality class of the criticality.

  5. 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

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

    SciTech Connect

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

  7. Quantum transport through a molecular level: a scattering states numerical renormalization group study

    NASA Astrophysics Data System (ADS)

    Jovchev, Andre; Anders, Frithjof B.

    2015-10-01

    We use the scattering states numerical renormalization group (SNRG) approach to calculate the current I(V) through a single molecular level coupled to a local molecular phonon. The suppression of I for asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed. We compare the SNRG currents with recently published data obtained by an iterative summation of path integrals approach (ISPI). Our results excellently agree with the ISPI currents for small and intermediate voltages. In the linear response regime I(V) approaches the current calculated from the equilibrium spectral function. We also present the temperature and voltage evolution of the non-equilibrium spectral functions for a particle-hole asymmetric junction with symmetric coupling to the lead.

  8. 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.

  9. Density matrix renormalization group approach to two-fluid open many-fermion systems

    NASA Astrophysics Data System (ADS)

    Rotureau, J.; Michel, N.; Nazarewicz, W.; Płoszajczak, M.; Dukelsky, J.

    2009-01-01

    We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

  10. Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time

    NASA Astrophysics Data System (ADS)

    Kamikado, Kazuhiko; Kanazawa, Takuya; Uchino, Shun

    2017-01-01

    Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground-state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polaron and the effective mass and quasiparticle weight of attractive and repulsive polarons, and clarify how they are affected by mass imbalances.

  11. Differential renormalization-group generators for static and dynamic critical phenomena

    NASA Astrophysics Data System (ADS)

    Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

    1992-09-01

    The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

  12. Effects of turbulent mixing on critical behaviour: renormalization-group analysis of the Potts model

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Malyshev, A. V.

    2012-06-01

    The critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field-theoretic renormalization group. Specifically, the relaxational stochastic dynamics of a non-conserved multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken to be Gaussian, white in time, with a correlation function of the form ∝δ(t - t‧)/|k⊥|d - 1 + ξ, where k⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble was introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381) within the context of passive scalar advection. This model can describe a rich class of physical situations. It is shown that, depending on the values of the parameters that define the self-interaction of the order parameter and the relation between the exponent ξ and the space dimension d, the system exhibits various types of large-scale scaling behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. In addition to known asymptotic regimes (critical dynamics of the Potts model and passively advected field without self-interaction), the existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the leading order of the double expansion in ξ and ɛ = 6 - d (one-loop approximation). The scaling appears to be strongly anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.

  13. Multi-step Monte Carlo calculations applied to nuclear reactor instrumentation - source definition and renormalization to physical values

    SciTech Connect

    Radulovic, Vladimir; Barbot, Loic; Fourmentel, Damien; Villard, Jean-Francois; Snoj, Luka; Zerovnik, Gasper; Trkov, Andrej

    2015-07-01

    Significant efforts have been made over the last few years in the French Alternative Energies and Atomic Energy Commission (CEA) to adopt multi-step Monte Carlo calculation schemes in the investigation and interpretation of the response of nuclear reactor instrumentation detectors (e.g. miniature ionization chambers - MICs and self-powered neutron or gamma detectors - SPNDs and SPGDs). The first step consists of the calculation of the primary data, i.e. evaluation of the neutron and gamma flux levels and spectra in the environment where the detector is located, using a computational model of the complete nuclear reactor core and its surroundings. These data are subsequently used to define sources for the following calculation steps, in which only a model of the detector under investigation is used. This approach enables calculations with satisfactory statistical uncertainties (of the order of a few %) within regions which are very small in size (the typical volume of which is of the order of 1 mm{sup 3}). The main drawback of a calculation scheme as described above is that perturbation effects on the radiation conditions caused by the detectors themselves are not taken into account. Depending on the detector, the nuclear reactor and the irradiation position, the perturbation in the neutron flux as primary data may reach 10 to 20%. A further issue is whether the model used in the second step calculations yields physically representative results. This is generally not the case, as significant deviations may arise, depending on the source definition. In particular, as presented in the paper, the injudicious use of special options aimed at increasing the computation efficiency (e.g. reflective boundary conditions) may introduce unphysical bias in the calculated flux levels and distortions in the spectral shapes. This paper presents examples of the issues described above related to a case study on the interpretation of the signal from different types of SPNDs, which

  14. The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

    NASA Astrophysics Data System (ADS)

    Menezes, Natália; Alves, Van Sérgio; Smith, Cristiane Morais

    2016-12-01

    The experimental observation of the renormalization of the Fermi velocity v F as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field B, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in B, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.

  15. Functional renormalization group approach for inhomogeneous one-dimensional Fermi systems with finite-ranged interactions

    NASA Astrophysics Data System (ADS)

    Weidinger, Lukas; Bauer, Florian; von Delft, Jan

    2017-01-01

    We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance

  16. Application of renormalization group corrected coupling parameter expansion method to square well fluids

    NASA Astrophysics Data System (ADS)

    Sai Venkata Ramana, A.

    2016-01-01

    In this paper, we have applied the seventh order version of coupling parameter expansion (CPE) method combined with global renormalization group theory (GRGT) to square well fluids of various ranges and have performed the following studies. Firstly, the convergence of the GRGT iteration scheme has been studied. It is observed that the point-wise convergence is non-uniform and slow in the coexistence region away from the critical point. However, the point-wise convergence improved as the critical temperature is approached. Secondly, we have obtained the liquid-vapor phase diagrams (LVPDs) for the square well fluids. The LVPDs obtained using GRGT corrected seventh order CPE are significantly accurate over those obtained from GRGT corrected 1-order thermodynamic perturbation theory (TPT). Also, excessive flatness of LVPDs close to the critical region as observed in GRGT corrected 1-order TPT has not been seen in the LVPDs of present method. Thirdly, the critical exponents have been obtained using present method. The exponents are seen to be of Ising universality class and follow the Rushbrooke and Griffiths equalities qualitatively. Finally, a study of Yang-Yang anomaly has been done using our method. It has been observed that the method predicts the existence of the anomaly but the predictions of the strength of anomaly differed from those of simulations. The reasons for the differences are analyzed.

  17. Renormalization group study of the minimal Majoronic dark radiation and dark matter model

    SciTech Connect

    Chang, We-Fu; Ng, John N.

    2016-07-18

    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 △N{sub eff}∼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 bb-bar and/or ωω. A sensitive search will come from rare Z decays via the chain Z→S+ff-bar, 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 Sρρ-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at M{sub ρ} could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.

  18. 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.

  19. Density matrix renormalization group study of the Anyon-Hubbard model

    NASA Astrophysics Data System (ADS)

    Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.

    2016-02-01

    Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.

  20. Renormalization-group theory for cooling first-order phase transitions in Potts models

    NASA Astrophysics Data System (ADS)

    Liang, Ning; Zhong, Fan

    2017-03-01

    We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q -state Potts model for q >10 /3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.

  1. Systematic improvements of ab-initio in-medium similarity renormalization group calculations

    NASA Astrophysics Data System (ADS)

    Morris, Titus Dan

    The In-Medium Similarity Renormalization Group (IM-SRG) is an ab initio many-body method that has enjoyed increasing prominence in nuclear theory, due to its soft polynomial scaling with system size, and the flexibility to target ground and excited states of both closed- and open-shell systems. Despite many successful applications of the IM-SRG to microscopic calculations of medium-mass nuclei in recent years, the conventional formulation of the method suffers a number of limitations. Key amongst these are i) large memory demands that limit calculations in heavier systems and render the calculation of observables besides energy spectra extremely difficult, and ii) the lack of a computationally feasible sequence of improved approximations that converge to the exact solution in the appropriate limit, thereby verifying that the IM-SRG is systematically improvable. In this thesis, I present a novel formulation of the IM-SRG based on the Magnus expansion. I will show that this improved formulation, guided by intuition gleaned from a diagrammatic analysis of the perturbative content of different truncations and parallels with coupled-cluster theory, allows one to bypass the computational limitations of traditional implementations, and provides computationally viable approximations that go beyond the truncations used to date. The effectiveness of the new Magnus formulation is illustrated for several many-nucleon and many-electron systems.

  2. Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass

    NASA Astrophysics Data System (ADS)

    Oh, Jae-Hyuk

    2016-11-01

    We explore the mathematical relation between stochastic quantization (SQ) and the holographic Wilsonian renormalization group (HWRG) of a massive scalar field defined in asymptotically anti-de Sitter space. We compute the stochastic two-point correlation function by quantizing the boundary on-shell action (it is identified with the Euclidean action in our stochastic frame) of the scalar field, requiring the initial value of the stochastic field Dirichlet boundary condition, and study its relationship with the double-trace deformation in HWRG computation. It turns out that the stochastic two-point function precisely corresponds to the double-trace deformation through the relation proposed in [J. High Energy Phys. 11 (2012) 144] even in the case that the scalar field mass is arbitrary. In our stochastic framework, the Euclidean action constituting the Langevin equation is not the same as that in the original stochastic theory; in fact, it contains the stochastic time "t -dependent" kernel in it. A justification for the exotic Euclidean action is provided by proving that it transforms to the usual form of the Euclidean action in a new stochastic frame by an appropriate rescaling of both the stochastic fields and time. We also apply the Neumann boundary condition to the stochastic fields to study the relation between SQ and the HWRG when alternative quantization is allowed. It turns out that the application of the Neumann boundary condition to the stochastic fields generates the radial evolution of the single-trace operator as well as the double-trace term.

  3. Functional renormalization group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice

    NASA Astrophysics Data System (ADS)

    Hering, Max; Reuther, Johannes

    2017-02-01

    We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated J1-J2 kagome-Heisenberg model using the pseudofermion functional renormalization group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of noncollinear magnetic orders of the J1-J2 Heisenberg model (q =0 , √{3 }×√{3 } , and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral herbertsmithite which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicate that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for herbertsmithite, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.

  4. Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group

    NASA Astrophysics Data System (ADS)

    Vian, F.

    1999-05-01

    The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.

  5. 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.

  6. Renormalization-group approach to an Abelian sandpile model on planar lattices

    NASA Astrophysics Data System (ADS)

    Lin, Chai-Yu; Hu, Chin-Kun

    2002-08-01

    One important step in the renormalization-group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in the RG approach to the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 59, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. 72, 1690 (1994)], and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. 76, 3368 (1996)]. Using this algorithm, we are able to carry out RG transformations more quickly with large cell size, e.g., 3×3 cell for the square (SQ) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E 51, 1711 (1995)]. For SQ and plane triangular (PT) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent τ and the dynamical exponent z. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.

  7. Renormalization Group Analysis of Yukawa Parameters with One and Two Higgs Doublets, and Flavor Gauge Theory

    NASA Astrophysics Data System (ADS)

    Cvetič, G.; Kim, C. S.

    We assume that the standard model (SM) breaks down around some energy Λ and is replaced there by a new (Higgsless) flavor gauge theory (FGT) with fewer input parameters in the interactions corresponding to the Yukawa sector of SM. This would imply more symmetry for the values of the Yukawa (running) parameters of SM at E Λ, possibly by a (approximate) flavor democracy (for the quark mass sector). We investigate this possibility by studying the renormalization group equations (RGE's) for the quark Yukawa couplings of SM with one and two Higgs doublets, by running them from the known physical values at low energies (E 1 GeV) to Λ (> 1 TeV) and comparing the resulting quark masses mq (E Λ) for various mt and υU/υD. Unlike previous investigations of these RGE's, we do not implement the requirement mt(Λpole) = ∞. We found that SM with two Higgs doublets (type 2) is most likely to experience a gradual transition to FGT. Our results also shed more light on the adequacy and deficiencies of the usual RGE approaches within TMSM and related models. We also found that, independent of the assumption of a transition mechanism to FGT, mt phy< ˜ 200 GeV for Λpole≪ ΛPlanck in most cases of SM with two Higgs doublets.

  8. Many-body localization in one dimension as a dynamical renormalization group fixed point.

    PubMed

    Vosk, Ronen; Altman, Ehud

    2013-02-08

    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 loglogt 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.

  9. Renormalization group study of excitonic and superconducting order in doped honeycomb bilayer

    NASA Astrophysics Data System (ADS)

    Murray, James; Vafek, Oskar

    2014-03-01

    We explore the competition between spin-charge order and unconventional superconductivity in the context of the AB stacked bilayer honeycomb lattice, realized experimentally as bilayer graphene, which features approximately parabolically touching electron bands. Using a weak-coupling renormalization group theory, we show that unconventional superconductivity arises generically for repulsively interacting fermions as excitonic order is suppressed by adding charge carriers to the system. We investigate the effects of finite temperature and further-neighbor hopping, the latter of which leads to so-called ``trigonal warping'' and destroys the perfect circular symmetry of the Fermi surfaces. We show that superconductivity survives for a finite range of trigonal warping, and that the nature of the superconducting phase may change as a function of further neighbor hopping. Depending on the range of interactions and the degree of trigonal warping, we find that the most likely superconducting instabilities are to f-wave, chiral d-wave, and pair density wave phases. It is shown that unconventional superconductivity is significantly enhanced by fluctuations in particle-hole channels, with the critical temperature reaching a maximum near the excitonic phase. Supported by the NSF CAREER award under Grant No. DMR-0955561, NSF Cooperative Agreement No. DMR-0654118, and the State of Florida, as well as by ICAM-I2CAM (NSF grant DMR-0844115) and by DoE, Office of Basic Energy Sciences (Award DE-FG02-08ER46544).

  10. Renormalization group-induced phenomena of top pairs from four-quark effective operators

    NASA Astrophysics Data System (ADS)

    Jung, Sunghoon; Ko, P.; Yoon, Yeo Woong; Yu, Chaehyun

    2014-08-01

    We study the renormalization group(RG) evolution of four-quark operators that contribute to the top pair production. In particular, we focus on the cases in which certain observables are first induced from the one-loop RG while being absent at tree-level. From the operator mixing pattern, we classify all such RG-induced phenomena and underlying models that can induce them. We then calculate the full one-loop QCD RG evolution as the leading estimator of the effects and address the question of which RG-induced phenomena have largest and observable effects. The answer is related to the color structure of QCD. The studied topics include the RG-induction of top asymmetries, polarizations and polarization mixings as well as issues arising at this order. The RG-induction of top asymmetries is further compared with the generation of asymmetries from QCD and QED at one-loop order. We finally discuss the validity of using the RG as the proxy of one-loop effects on the top pair production. As an aside, we clarify the often-studied relations between top pair observables.

  11. 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.

  12. Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Ehlers, G.; White, S. R.; Noack, R. M.

    2017-03-01

    The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

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

    PubMed

    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 C2 and F2. 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.

  14. Renormalization-group flow of the effective action of cosmological large-scale structures

    NASA Astrophysics Data System (ADS)

    Floerchinger, Stefan; Garny, Mathias; Tetradis, Nikolaos; Wiedemann, Urs Achim

    2017-01-01

    Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.

  15. 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.

  16. Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

    NASA Astrophysics Data System (ADS)

    Zhou, Shun

    2017-04-01

    In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle {θ }12\\to {θ }12-π /2 and the exchange of first two neutrino masses {m}1≤ftrightarrow {m}2, if the standard parametrization of lepton flavor mixing matrix is adopted. To maintain this symmetry in perturbative calculations, we present a symmetric formulation of the effective Hamiltonian by introducing an η-gauge neutrino mass-squared difference {{{Δ }}}* \\equiv η {{{Δ }}}31+(1-η ){{{Δ }}}32 for 0≤slant η ≤slant 1, where {{{Δ }}}{ji}\\equiv {m}j2-{m}i2 for {ji}=21,31,32, and show that only η =1/2, η ={\\cos }2{θ }12 or η ={\\sin }2{θ }12 is allowed. Furthermore, we prove that η ={\\cos }2{θ }12 is the best choice to derive more accurate and compact neutrino oscillation probabilities, by implementing the approach of renromalization-group equations. The validity of this approach becomes transparent when an analogy is made between the parameter η herein and the renormalization scale μ in relativistic quantum field theories.

  17. 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.

  18. 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.

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

    SciTech Connect

    Carena, M.; Draper, P.; Shah, N. R.; Wagner, C. E. M.

    2011-02-18

    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.

  20. In-medium similarity renormalization group for closed and open-shell nuclei

    NASA Astrophysics Data System (ADS)

    Hergert, H.

    2017-02-01

    We present a pedagogical introduction to the in-medium similarity renormalization group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: the first is the multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of non-empirical valence-space interactions that can be used as input for nuclear shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+shell model approach provides immediate access to excitation spectra, transitions, etc, but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IMSRG and IMSRG+shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.

  1. Functional renormalization group and bosonization as a solver for 2D fermionic Hubbard models

    NASA Astrophysics Data System (ADS)

    Schuetz, Florian; Marston, Brad

    2007-03-01

    The functional renormalization group (fRG) provides an unbiased framework to analyze competing instabilities in two-dimensional electron systems and has been used extensively over the past decade [1]. In order to obtain an equally unbiased tool to interprete the flow, we investigate the combination of a many-patch, one-loop calculation with higher dimensional bosonization [2] of the resulting low-energy action. Subsequently a semi-classical approximation [3] can be used to describe the resulting phases. The spinless Hubbard model on a square lattice with nearest neighbor repulsion is investigated as a test case. [1] M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001). [2] A. Houghton, H.-J. Kwon, J. B. Marston, Adv.Phys. 49, 141 (2000); P. Kopietz, Bosonization of interacting fermions in arbitrary dimensions, (Springer, Berlin, 1997). [3] H.-H. Lin, L. Balents, M. P. A. Fisher, Phys. Rev. B 56, 6569 6593 (1997); J. O. Fjaerestad, J. B. Marston, U. Schollwoeck, Ann. Phys. (N.Y.) 321, 894 (2006).

  2. 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.

  3. 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.

  4. 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.

  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. Causal hydrodynamics from kinetic theory by doublet scheme in renormalization-group method

    NASA Astrophysics Data System (ADS)

    Tsumura, Kyosuke; Kikuchi, Yuta; Kunihiro, Teiji

    2016-12-01

    We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by zero modes. We call this framework the doublet scheme. The validity of the doublet scheme is first tested and demonstrated by taking the Lorenz model as a simple three-dimensional dynamical system; it is shown that the two-dimensional reduced dynamics on the attractive manifold composed of the would-be zero and a fast modes are successfully obtained in a natural way. We then apply the doublet scheme to construct causal hydrodynamics as a mesoscopic dynamics of kinetic theory, i.e., the Boltzmann equation, in a systematic manner with no ad-hoc assumption. It is found that our equation has the same form as Grad's thirteen-moment causal hydrodynamic equation, but the microscopic formulae of the transport coefficients and relaxation times are different. In fact, in contrast to the Grad equation, our equation leads to the same expressions for the transport coefficients as given by the Chapman-Enskog expansion method and suggests novel formulae of the relaxation times expressed in terms of relaxation functions which allow a natural physical interpretation of the relaxation times. Furthermore, our theory nicely gives the explicit forms of the distribution function and the thirteen hydrodynamic variables in terms of the linearized collision operator, which in turn clearly suggest the proper ansatz forms of them to be adopted in the method of moments.

  8. 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.

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

    SciTech Connect

    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 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, 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.

  10. 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

  11. 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.

  12. An Overview of the Monte Carlo Methods, Codes, & Applications Group

    SciTech Connect

    Trahan, Travis John

    2016-08-30

    This report sketches the work of the Group to deliver first-principle Monte Carlo methods, production quality codes, and radiation transport-based computational and experimental assessments using the codes MCNP and MCATK for such applications as criticality safety, non-proliferation, nuclear energy, nuclear threat reduction and response, radiation detection and measurement, radiation health protection, and stockpile stewardship.

  13. A Functional Generalization of the Field-Theoretical Renormalization Group Approach for the Single-Impurity Anderson Model

    NASA Astrophysics Data System (ADS)

    Freire, Hermann; Corrêa, Eberth

    2012-02-01

    We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta et al. (in Phys. Rev. Lett. 85:4940, 2000), which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.

  14. Renormalization group flow of the Luttinger-Ward functional: Conserving approximations and application to the Anderson impurity model

    NASA Astrophysics Data System (ADS)

    Rentrop, J. F.; Meden, V.; Jakobs, S. G.

    2016-05-01

    We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle-irreducible vertex functions, given a cutoff in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to nonconserving approximations introduced in an earlier publication [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015), 10.1088/1751-8113/48/14/145002]. We apply the different approximate flow equations to the single-impurity Anderson model in thermal equilibrium at vanishing temperature. Numerical results for the effective mass, the spin susceptibility, the charge susceptibility, and the linear conductance reflect the similarity of the methods to the fluctuation exchange approximation. We find the majority of the approximations to deviate stronger from the exact results than one-particle-irreducible functional renormalization group schemes. However, we identify a simple static two-particle-irreducible flow scheme which performs remarkably well and produces an exponential Kondo-like scale in the renormalized level position.

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

    PubMed

    Nakatani, Naoki; Chan, Garnet Kin-Lic

    2013-04-07

    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.

  16. 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 .

  17. Real-Space Renormalization-Group Approach to the Integer Quantum Hall Effect

    NASA Astrophysics Data System (ADS)

    Cain, Philipp; Römer, Rudolf A.

    We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2 up to RL 20h/e2 when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance R H∝ R Lκ is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization

  18. 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.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

    The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.

  1. 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.

  2. Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

    NASA Astrophysics Data System (ADS)

    Duclut, Charlie; Delamotte, Bertrand

    2017-01-01

    We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization-group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent z . This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the principle of minimal sensitivity (PMS) is employed to optimize the critical exponents η , ν , and z , the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.

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

    PubMed

    Liu, X M; Cheng, W W; Liu, J-M

    2016-01-19

    We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.

  4. Renormalization-group evolution of the B-meson light-cone distribution amplitude.

    PubMed

    Lange, Björn O; Neubert, Matthias

    2003-09-05

    An integro-differential equation governing the evolution of the leading-order B-meson light-cone distribution amplitude is derived. The anomalous dimension in this equation contains a logarithm of the renormalization scale, whose coefficient is identified with the cusp anomalous dimension of Wilson loops. The exact solution of the evolution equation is obtained, from which the asymptotic behavior of the distribution amplitude is derived. These results can be used to resum Sudakov logarithms entering the hard-scattering kernels in QCD factorization theorems for exclusive B decays.

  5. Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

    NASA Astrophysics Data System (ADS)

    Das, Sourin; Rao, Sumathi; Saha, Arijit

    2009-04-01

    We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an S matrix representing small deviations from a given fixed point S matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k ]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

  6. Nonequilibrium dynamics of active matter with correlated noise: A dynamical renormalization group study

    NASA Astrophysics Data System (ADS)

    Kachan, Devin; Levine, Alex; Bruinsma, Robijn

    2014-03-01

    Biology is rife with examples of active materials - soft matter systems driven into nonequilibrium steady states by energy input at the micro scale. For example, solutions of active micron scale swimmers produce active fluids showing phenomena reminiscent of turbulent convection at low Reynolds number; cytoskeletal networks driven by endogenous molecular motors produce active solids whose mechanics and low frequency strain fluctuations depend sensitively on motor activity. One hallmark of these systems is that they are driven at the micro scale by temporally correlated forces. In this talk, we study how correlated noise at the micro scale leads to novel long wavelength and long time scale dynamics at the macro scale in a simple model system. Specifically, we study the fluctuations of a ϕ4 scalar field obeying model A dynamics and driven by noise with a finite correlation time τ. We show that the effective dynamical system at long length and time scales is driven by white noise with a renormalized amplitude and renormalized transport coefficients. We discuss the implications of this result for a broad class of active matter systems driven at the micro scale by colored noise.

  7. 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.

  8. Effects of Random Environment on a Self-Organized Critical System: Renormalization Group Analysis of a Continuous Model

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t - t')/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction - the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa-Kardar model is irrelevant) and to the "pure" Hwa-Kardar model (the advection is irrelevant). For the special case ξ = 2(4 - d)/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.

  9. 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

    2011-11-02

    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.

  10. Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches.

    PubMed

    Langari, A; Pollmann, F; Siahatgar, M

    2013-10-09

    We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.

  11. Renormalization group approach for the wave packet dynamics in golden-mean and silver-mean labyrinth tilings

    NASA Astrophysics Data System (ADS)

    Thiem, Stefanie; Schreiber, Michael

    2012-06-01

    We study the quantum diffusion in quasiperiodic tight-binding models in one, two, and three dimensions. First, we investigate a class of one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated generalized labyrinth tilings in d dimensions are then constructed from the direct product of d such chains, which allows us to consider rather large systems numerically. The electronic transport is studied by computing the scaling behavior of the mean-square displacement of the wave packets with respect to time. The results reveal the occurrence of anomalous diffusion in these systems. By extending a renormalization group approach, originally proposed for the golden-mean chain, we show also for the silver-mean chain as well as for the higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic modulation the wave-packet dynamics are governed by the underlying quasiperiodic structure.

  12. 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.

  13. 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.

  14. 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.

  15. 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.; ...

    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

  16. 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.

  17. Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes.

    PubMed

    Chan, Garnet Kin-Lic; Van Voorhis, Troy

    2005-05-22

    We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.

  18. 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.

  19. In-medium spectral functions of vector- and axial-vector mesons from the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Jung, Christopher; Rennecke, Fabian; Tripolt, Ralf-Arno; von Smekal, Lorenz; Wambach, Jochen

    2017-02-01

    In this work, we present the first results on vector- and axial-vector meson spectral functions as obtained by applying the nonperturbative functional renormalization group approach to an effective low-energy theory motivated by the gauged linear sigma model. By using a recently proposed analytic continuation method, we study the in-medium behavior of the spectral functions of the ρ and a1 mesons in different regimes of the phase diagram. In particular, we demonstrate explicitly how these spectral functions degenerate at high temperatures as well as at large chemical potentials, as a consequence of the restoration of chiral symmetry. In addition, we also compute the momentum dependence of the ρ and a1 spectral functions and discuss the various timelike and spacelike processes that can occur.

  20. Critical behaviour of a fluid in a random shear flow: renormalization group analysis of a simplified model

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Ignatieva, A. A.

    2006-11-01

    Critical behaviour of a fluid (binary mixture or liquid crystal), subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order parameter, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with a correlation function of the form ~δ(t - t')/|kbottom|d+ξ, where kbottom is the component of the wave vector, perpendicular to the distinguished direction ('direction of the flow')—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381) within the context of passive scalar advection. It is shown that, depending on the relation between the exponent ξ and the space dimensionality d, the system exhibits various types of large-scale self-similar behaviour, associated with different infrared attractive fixed points of the renormalization group equations. In addition to well-known asymptotic regimes (model A of equilibrium critical dynamics and a passively advected scalar with no self-interaction), the existence of a new, non-equilibrium and strongly anisotropic type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the second order of the double expansion in ξ and ɛ = 4 - d (two-loop approximation). The most realistic values of the model parameters (for example, d = 3 and the Kolmogorov exponent ξ = 4/3) belong to this class. The scaling behaviour appears anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different. The results are in qualitative agreement with the results, obtained in experiments and simulations of fluid systems subjected to various kinds of regular and chaotic anisotropic flows.

  1. High-performance ab initio density matrix renormalization group method: Applicability to large-scale multireference problems for metal compounds

    NASA Astrophysics Data System (ADS)

    Kurashige, Yuki; Yanai, Takeshi

    2009-06-01

    This article presents an efficient and parallelized implementation of the density matrix renormalization group (DMRG) algorithm for quantum chemistry calculations. The DMRG method as a large-scale multireference electronic structure model is by nature particularly efficient for one-dimensionally correlated systems, while the present development is oriented toward applications for polynuclear transition metal compounds, in which the macroscopic one-dimensional structure of electron correlation is absent. A straightforward extension of the DMRG algorithm is proposed with further improvements and aggressive optimizations to allow its application with large multireference active space, which is often demanded for metal compound calculations. Special efficiency is achieved by making better use of sparsity and symmetry in the operator and wave function representations. By accomplishing computationally intensive DMRG calculations, the authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Potential energy curve calculations for the Cr2 molecule near the known equilibrium precisely predicted the full configuration interaction energies with a correlation space of 24 electrons in 30 orbitals [denoted by (24e,30o)]. The energies are demonstrated to be accurate to 0.6mEh (the error from the extrapolated best value) when as many as 10 000 renormalized basis states are employed for the left and right DMRG block representations. The relative energy curves for [Cu2O2]2+ along the isomerization coordinate were obtained from DMRG and other correlated calculations, for which a fairly large orbital space (32e,62o) is modeled as a full correlation space. The DMRG prediction nearly overlaps

  2. Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

    The model of landscape erosion, introduced in (1998 Phys. Rev. Lett. 80 4349, 1998 J. Stat. Phys. 93 477) and modified in (2016 Theor. Math. Phys. in press (arXiv:1602.00432)), is advected by anisotropic velocity field. The field is Gaussian with vanishing correlation time and the pair correlation function of the form \\propto δ ≤ft(t-{{t}\\prime}\\right)/k\\botd-1+ξ , where {{k}\\bot}=|{{\\mathbf{k}}\\bot}| and {{\\mathbf{k}}\\bot} is the component of the wave vector, perpendicular to a certain preferred direction—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381). Analogous to the case without advection, the model is multiplicatively renormalizable and has infinitely many coupling constants. The one-loop counterterm is derived in a closed form in terms of the certain function V(h), entering the original stochastic equation, and its derivatives with respect to the height field h≤ft(t,\\mathbf{x}\\right) . The full infinite set of the one-loop renormalization constants, β-functions and anomalous dimensions is obtained from the Taylor expansion of the counter-term. Instead of a two-dimensional surface of fixed points there are two such surfaces; they are likely to contain infrared attractive region(s). If that is the case, the model exhibits scaling behaviour in the infrared range. The corresponding critical exponents are non-universal because they depend on the coordinates of the fixed points on the surface; they also satisfy certain universal exact relation.

  3. Self-affinities for the amplitude and the wavelength of folds: A general renormalization-group argument

    NASA Astrophysics Data System (ADS)

    Kikuchi, K.; Nagahama, H.

    2013-12-01

    A method to analyze self-affinities is introduced and applied to the large scale fold geometries of Quaternary and Tertiary sediments in the inner belt of the Northeast Honshu Arc, Japan (Kikuchi et al. 2013). Based on this analysis, their geometries are self-affine and can be differently scaled in different directions. They recognize the self-affinities for the amplitude and the wavelength of folds and a crossover from local to global altitude (vertical) variation of the geometries of folds in the Northeast Honshu Arc. Moreover, they discuss self-affinity for the crustal deformation is related to the b-value in Gutenberg-Richter's law, the fractal dimension and the uniformity of the crustal fragmentation. Softening behaviour can lead to localisation of fold packets in layered materials and a progression to chaos with fractal geometries (Hunt and Wadee, 1991). Why do fractal geometries exist and what is the control on the fractal dimension that is responsible for temperature and strain-rate dependence?(Ord and Hobbs, 2011). Shimamoto (1974) examined the conditions of similarity for geometrically similar systems of inhomogeneous viscous Newtonian fluids under similar boundary conditions, making use of the method of dimensional analysis (Buckingham's Pi-theorem). Then, based on the completely similarity, he vividly derived a relationship between the wavelength of fold and initial thickness of folded layer. Buckingham's Pi-theorem is sufficient to the first problems of fold systems. But the complete similarity can not give us the self-affinities of folds. A general renormalization-group argument is proposed to the applicability of the incomplete self-similarity theory (Barenblatt, 1979). So in this paper, based on the general renormalization-group argument, we derive the self-affinities for the amplitude and the wavelength of folds. Keywords: Fold, Self-Affinities, Dimensional Analysis, Pi-theorem, Incomplete self-similarity R e f e r e n c e s Barenblatt, G.I. (1979

  4. 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

  5. Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations

    NASA Astrophysics Data System (ADS)

    Nakatani, Naoki; Guo, Sheng

    2017-03-01

    This paper describes an interface between the density matrix renormalization group (DMRG) method and the complete active-space self-consistent field (CASSCF) method and its analytical gradient, as well as an extension to the second-order perturbation theory (CASPT2) method. This interfacing allows large active-space multi-reference computations to be easily performed. The interface and its extension are both implemented in terms of reduced density matrices (RDMs) which can be efficiently computed via the DMRG sweep algorithm. We also present benchmark results showing that, in practice, the DMRG-CASSCF calculations scale with active-space size in a polynomial manner in the case of quasi-1D systems. Geometry optimization of a binuclear iron-sulfur cluster using the DMRG-CASSCF analytical gradient is demonstrated, indicating that the inclusion of the valence p-orbitals of sulfur and double-shell d-orbitals of iron lead to non-negligible changes in the geometry compared to the results of small active-space calculations. With the exception of the selection of M values, many computational settings in these practical DMRG calculations have been tuned and black-boxed in our interface, and so the resulting DMRG-CASSCF and DMRG-CASPT2 calculations are now available to novice users as a common tool to compute strongly correlated electronic wavefunctions.

  6. Formation of selfbound states in a one-dimensional nuclear model—a renormalization group based density functional study

    NASA Astrophysics Data System (ADS)

    Kemler, Sandra; Pospiech, Martin; Braun, Jens

    2017-01-01

    In nuclear physics, density functional theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and renormalization group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of N identical fermions interacting via a general two-body interaction. Moreover, we discuss the control of spuriously emerging fermion self-interactions in DFT studies within our framework. In general, our approach may help to guide the development of energy functionals for future quantitative DFT studies of heavy nuclei from microscopic interactions.

  7. Interplay between Magnetism, Superconductivity, and Orbital Order in 5-Pocket Model for Iron-Based Superconductors: Parquet Renormalization Group Study.

    PubMed

    Classen, Laura; Xing, Rui-Qi; Khodas, Maxim; Chubukov, Andrey V

    2017-01-20

    We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of d_{xz}, d_{yz}, and d_{xy} orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under the RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one d_{xy} hole pocket and two electron pockets or a 4-pocket model made of two d_{xz}/d_{yz} hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by s^{+-} superconductivity. In the effective 3-pocket model, orbital fluctuations are weaker, and the system develops either s^{+-} superconductivity or a stripe spin-density wave. In the latter case, nematicity is induced by composite spin fluctuations.

  8. Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: Pseudofermion functional renormalization group perspective

    NASA Astrophysics Data System (ADS)

    Buessen, Finn Lasse; Trebst, Simon

    2016-12-01

    Quantum magnets on kagome lattice geometries in two and three spatial dimensions are archetypal examples of spin systems in which geometric frustration inhibits conventional magnetic ordering and instead benefits the emergence of long-range entangled spin liquids at low temperature. Here we employ a recently developed pseudofermion functional renormalization group (pf-FRG) approach to study the low-temperature quantum magnetism of kagome and hyperkagome spin systems with exchange interactions beyond the nearest-neighbor coupling. We find that next-nearest-neighbor couplings stabilize a variety of magnetic orders as well as induce additional spin liquid regimes, giving rise to rather rich phase diagrams, which we characterize in detail. On a technical level, we find that the pf-FRG approach is in excellent quantitative agreement with high-temperature series expansions over their range of validity and it exhibits a systematic finite-size convergence in the temperature regime below. We discuss notable advantages and some current limitations of the pf-FRG approach in the ongoing search for unconventional forms of quantum magnetism.

  9. 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/.

  10. Renormalization group calculations for wetting transitions of infinite order and continuously varying order: local interface Hamiltonian approach.

    PubMed

    Indekeu, J O; Koga, K; Hooyberghs, H; Parry, A O

    2013-08-01

    We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

  11. The Renormalization Group and Its Applications to Generating Coarse-Grained Models of Large Biological Molecular Systems.

    PubMed

    Koehl, Patrice; Poitevin, Frédéric; Navaza, Rafael; Delarue, Marc

    2017-03-14

    Understanding the dynamics of biomolecules is the key to understanding their biological activities. Computational methods ranging from all-atom molecular dynamics simulations to coarse-grained normal-mode analyses based on simplified elastic networks provide a general framework to studying these dynamics. Despite recent successes in studying very large systems with up to a 100,000,000 atoms, those methods are currently limited to studying small- to medium-sized molecular systems due to computational limitations. One solution to circumvent these limitations is to reduce the size of the system under study. In this paper, we argue that coarse-graining, the standard approach to such size reduction, must define a hierarchy of models of decreasing sizes that are consistent with each other, i.e., that each model contains the information of the dynamics of its predecessor. We propose a new method, Decimate, for generating such a hierarchy within the context of elastic networks for normal-mode analysis. This method is based on the concept of the renormalization group developed in statistical physics. We highlight the details of its implementation, with a special focus on its scalability to large systems of up to millions of atoms. We illustrate its application on two large systems, the capsid of a virus and the ribosome translation complex. We show that highly decimated representations of those systems, containing down to 1% of their original number of atoms, still capture qualitatively and quantitatively their dynamics. Decimate is available as an OpenSource resource.

  12. Interplay between Magnetism, Superconductivity, and Orbital Order in 5-Pocket Model for Iron-Based Superconductors: Parquet Renormalization Group Study

    NASA Astrophysics Data System (ADS)

    Classen, Laura; Xing, Rui-Qi; Khodas, Maxim; Chubukov, Andrey V.

    2017-01-01

    We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of dx z, dy z, and dx y orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under the RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one dx y hole pocket and two electron pockets or a 4-pocket model made of two dx z/dy z hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by s+- superconductivity. In the effective 3-pocket model, orbital fluctuations are weaker, and the system develops either s+- superconductivity or a stripe spin-density wave. In the latter case, nematicity is induced by composite spin fluctuations.

  13. Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Oriti, Daniele; Rivasseau, Vincent

    2014-04-01

    We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.

  14. BRST Renormalization

    NASA Astrophysics Data System (ADS)

    Lavrov, P. M.; Shapiro, I. L.

    2012-09-01

    We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.

  15. Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal.

    PubMed

    Stadler, K M; Yin, Z P; von Delft, J; Kotliar, G; Weichselbaum, A

    2015-09-25

    We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

  16. Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal

    NASA Astrophysics Data System (ADS)

    Stadler, K. M.; Yin, Z. P.; von Delft, J.; Kotliar, G.; Weichselbaum, A.

    2015-09-01

    We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1 /3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

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

    NASA Astrophysics Data System (ADS)

    Katanin, A. A.

    2015-06-01

    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 DMF2RG 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.

  18. Renormalization-group study of a superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations

    NASA Astrophysics Data System (ADS)

    Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.

    2014-11-01

    We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.

  19. Pseudo-random renormalization group forward and inverse modeling of the electrical properties of some carbonate rocks

    NASA Astrophysics Data System (ADS)

    Gomaa, Mohamed M.; Kassab, Mohamed A.

    2016-12-01

    Electrical properties of carbonate rocks from North Sinai, Egypt, were investigated experimentally in the frequency domain (100 Hz to 100 kHz). Changes between electrical properties were attributed to changes in mineral composition and texture of samples. Asymmetric mixture laws cannot describe electrical behavior of heterogeneous rocks in the mentioned frequency range. A theoretical pseudo-random renormalization group (PRNG) method was developed to model electrical behavior of rock mixtures. The main goal of this paper is to make forward and inverse modeling using PRNG method for the electrical properties as a function of frequency for carbonate rocks with texture. In PRNG method four phases were used to take into account the texture in the samples. Four phases are the best that we could use in the model. We are trying to increase the competence of the model in the near future. In these four phases mainly conducting constituents (silt and clay) and mainly insulating constituents (sand, air and carbonate) may coat each other. With appropriately chosen coatings for the four phases, the PRNG method can reasonably model the electrical properties of the samples in the measured frequency range. Thus, an inverse problem is used to find the detailed structure of the four phases, which leads to the measured electrical properties of the samples, taking into account the measured concentrations of the different constituents of the samples. The inverse problem is based on minimizing the misfit between the measured frequency response for the conductivity and the dielectric constant and those obtained theoretically from the PRNG method. It was shown that the texture plays an important role in determining the A.C. electrical properties of heterogeneous samples.

  20. 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.

  1. Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function.

    PubMed

    Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi

    2013-07-28

    We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.

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

    NASA Astrophysics Data System (ADS)

    Roemelt, Michael

    2015-07-01

    Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.

  3. Matrix product state renormalization

    NASA Astrophysics Data System (ADS)

    Bal, M.; Rams, M. M.; Zauner, V.; Haegeman, J.; Verstraete, F.

    2016-11-01

    The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multiscale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015), 10.1088/1367-2630/17/5/053002] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states.

  4. 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)

  5. 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.

  6. Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

    NASA Astrophysics Data System (ADS)

    Rodrigues, Davi C.; Mauro, Sebastião; de Almeida, Álefe O. F.

    2016-10-01

    General relativity extensions based on renormalization group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post-Newtonian limits of a realization called renormalization group extended general relativity (RGGR). Special attention is given to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter ν¯⊙, and this parameter is such that for ν¯⊙=0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν¯ ⊙|≲10-21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the parametrized post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ν¯⊙, either considering or not the external potential effect. With the external potential effect the new bound reads |ν¯ ⊙|≲10-16 . We discuss the possible consequences of this bound on the dark matter abundance in galaxies.

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

    PubMed

    Yunus, Çağın; Renklioğlu, 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.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

    Endres, Michael G.; Brower, Richard C.; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V.

    2015-12-01

    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.

  10. Linear perturbation renormalization group for the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions in a field

    NASA Astrophysics Data System (ADS)

    Sznajd, J.

    2016-12-01

    The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

  11. Linear perturbation renormalization group for the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions in a field.

    PubMed

    Sznajd, J

    2016-12-01

    The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J) and interchain nearest-neighbor (J_{1}) and next-nearest-neighbor (J_{2}) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J_{2}=-J_{1}/2 for a rectangular lattice and J_{2}=-J_{1} for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

  12. 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.

  13. Renormalization of Lorentz violating theories

    SciTech Connect

    Anselmi, Damiano; Halat, Milenko

    2007-12-15

    We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a ''weighted power-counting'' criterion. The theories contain a dimensionful parameter {lambda}{sub L}, yet a set of models are classically invariant under a weighted scale transformation, which is anomalous at the quantum level. Formulas for the weighted trace anomaly are derived. The renormalization-group properties are studied.

  14. Real-time density matrix renormalization group dynamics of spin and charge transport in push-pull polyenes and related systems

    NASA Astrophysics Data System (ADS)

    Dutta, Tirthankar; Ramasesha, S.

    2012-01-01

    In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)x-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)x-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)x-A, systems in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a “quasi-static” state.

  15. Can the renormalization group improved effective potential be used to estimate the Higgs mass in the conformal limit of the standard model?

    SciTech Connect

    Chishtie, F. A.; Jia, J.; Hanif, T.; Mann, R. B.; McKeon, D. G. C.; Sherry, T. N.; Steele, T. G.

    2011-05-15

    We consider the effective potential V in the standard model with a single Higgs doublet in the limit that the only mass scale {mu} present is radiatively generated. Using a technique that has been shown to determine V completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to V using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling x, the quartic coupling of the Higgs field y, the SU(3) gauge coupling z, and the SU(2)xU(1) couplings r and s). We then employ the two loop RG functions with the three couplings x, y, z to sum the next-to-leading-log (NLL) contributions to V and then the three to five loop RG functions with one coupling y to sum all the N{sup 2}LL...N{sup 4}LL contributions to V. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the LL result is m{sub H}=219 GeV/c{sup 2} and decreases to m{sub H}=188 GeV/c{sup 2} at N{sup 2}LL order and m{sub H}=163 GeV/c{sup 2} at N{sup 4}LL order. No reasonable estimate of m{sub H} can be made at orders V{sub NLL} or V{sub N}{sup 3}{sub LL} since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for m{sub H} from the LL, N{sup 2}LL, and N{sup 4}LL approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of m{sub H}. The mass 163 GeV/c{sup 2} is argued to be an upper bound on m{sub H}.

  16. Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension.

    PubMed

    Kastening, Boris; Dohm, Volker

    2010-06-01

    Finite-size effects are investigated in the Gaussian model with isotropic and anisotropic short-range interactions in film geometry with nonperiodic boundary conditions (bc) above, at, and below the bulk critical temperature Tc. We have obtained exact results for the free energy and the Casimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixed bc in 1renormalized and reformulated as one-loop contributions of the φ4 field theory at fixed dimension d and are then compared with the ε=4-d expansion results at ε=1 as well as with d=3 Monte Carlo data. For d=2 , the Gaussian results for the Casimir force scaling function are compared with those for the Ising model with periodic, antiperiodic, and free bc; unexpected exact relations are found between the Gaussian

  17. Group membership prediction when known groups consist of unknown subgroups: a Monte Carlo comparison of methods

    PubMed Central

    Finch, W. Holmes; Bolin, Jocelyn H.; Kelley, Ken

    2014-01-01

    Classification using standard statistical methods such as linear discriminant analysis (LDA) or logistic regression (LR) presume knowledge of group membership prior to the development of an algorithm for prediction. However, in many real world applications members of the same nominal group, might in fact come from different subpopulations on the underlying construct. For example, individuals diagnosed with depression will not all have the same levels of this disorder, though for the purposes of LDA or LR they will be treated in the same manner. The goal of this simulation study was to examine the performance of several methods for group classification in the case where within group membership was not homogeneous. For example, suppose there are 3 known groups but within each group two unknown classes. Several approaches were compared, including LDA, LR, classification and regression trees (CART), generalized additive models (GAM), and mixture discriminant analysis (MIXDA). Results of the study indicated that CART and mixture discriminant analysis were the most effective tools for situations in which known groups were not homogeneous, whereas LDA, LR, and GAM had the highest rates of misclassification. Implications of these results for theory and practice are discussed. PMID:24904445

  18. 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

  19. A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the One-Dimensional Driven Asymmetric Chain

    NASA Astrophysics Data System (ADS)

    Georgiev, Ivan T.; McKay, Susan R.

    2001-03-01

    We present a position-space renormalization-group method for nonequilibrium systems, and illustrate its application using the one-dimensional driven asymmetric chain. The dynamics in this case are characterized by three parameters: the probability α that a particle will enter the chain from the left boundary, the probability β that a particle will exit the chain at the right boundary, and the probability p that a particle will jump to its right neighboring site if that site is empty. Rescaling trajectories flow in the space of these probabilities and the dynamics are implemented sequentially. The phase diagram for the steady states consists of three distinct regions, one with high current and two others distinguished by their average densities. This method yields a multicritical point at α_c=β_c=0.5, in agreement with the exact solution.(B. Derrida, et al., J. Phys. A: Math. Gen. 26), 1493 (1993); G. Schutz and E. Domany, J. Stat. Phys. 72, 277 (1993). We find the exponent ν = 2.71 associated with this fixed point, as compared with the exact value of 2.00.

  20. 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).

  1. Dynamics of the reaction between the free end of a tethered self-avoiding polymer and a flat penetrable surface: A renormalization group study

    NASA Astrophysics Data System (ADS)

    Cherayil, Binny J.; Bhattacharyya, Pinaki

    2014-06-01

    The average time τr for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a "sink" term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of τr on N mirrors the behavior of the average time τc of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which τr ˜ N2.2. A simulation study by Cheng and Makarov [J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N2.2 behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react.

  2. Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ɛ K ' /ɛK in the Standard Model and beyond

    NASA Astrophysics Data System (ADS)

    Kitahara, Teppei; Nierste, Ulrich; Tremper, Paul

    2016-12-01

    The standard analytic solution of the renormalization group (RG) evolution for the Δ S = 1 Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of ɛ K ' , the measure of direct CP violation in K → ππ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio ɛ K ' /ɛ K (with ɛ K quantifying indirect CP violation) in the Standard Model (SM) at NLO to ɛ K ' /ɛ K = (1.06 ± 5.07) × 10- 4, which is 2 .8 σ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: if the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100%. Our solution contains a term of order α EM 2 / α s 2 , which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.

  3. Nonperturbative functional renormalization-group approach to transport in the vicinity of a (2 +1 ) -dimensional O(N )-symmetric quantum critical point

    NASA Astrophysics Data System (ADS)

    Rose, F.; Dupuis, N.

    2017-01-01

    Using a nonperturbative functional renormalization-group approach to the two-dimensional quantum O (N ) model, we compute the low-frequency limit ω →0 of the zero-temperature conductivity in the vicinity of the quantum critical point. Our results are obtained from a derivative expansion to second order of a scale-dependent effective action in the presence of an external (i.e., nondynamical) non-Abelian gauge field. While in the disordered phase the conductivity tensor σ (ω ) is diagonal, in the ordered phase it is defined, when N ≥3 , by two independent elements, σA(ω ) and σB(ω ) , respectively associated to SO (N ) rotations which do and do not change the direction of the order parameter. For N =2 , the conductivity in the ordered phase reduces to a single component σA(ω ) . We show that limω→0σ (ω ,δ ) σA(ω ,-δ ) /σq2 is a universal number, which we compute as a function of N (δ measures the distance to the quantum critical point, q is the charge, and σq=q2/h the quantum of conductance). On the other hand we argue that the ratio σB(ω →0 ) /σq is universal in the whole ordered phase, independent of N and, when N →∞ , equal to the universal conductivity σ*/σq at the quantum critical point.

  4. Instability of three-band Tomonaga-Luttinger liquid: Renormalization group analysis and possible application to K2Cr3As3

    NASA Astrophysics Data System (ADS)

    Miao, Jian-Jian; Zhang, Fu-Chun; Zhou, Yi

    2016-11-01

    Motivated by recently discovered quasi-one-dimensional superconductor K2Cr3As3 with D3 h lattice symmetry, we study a one-dimensional three-orbital Hubbard model with generic electron repulsive interaction described by intraorbital repulsion U , interorbital repulsion U', and Hund's coupling J . As extracted from density functional theory calculation, two of the three atomic orbitals are degenerate (E' states) and the third one is nondegenerate (A1'), and the system is at incommensurate filling. With the help of bosonization, the normal state is described by a three-band Tomonaga-Luttinger liquid. Possible charge density wave (CDW), spin density wave (SDW), and superconducting (SC) instabilities are analyzed by renormalization group method. The ground state depends on the ratio J /U and is sensitive to the degeneracy of E' bands. The spin-singlet SC state is favored at 0 U /2 . When the twofold degeneracy of E' bands is lifted, the SDW instability has the tendency to dominate over the spin-singlet SC state at 0

  5. Nonperturbative O(a) improvement of the Wilson quark action with the renormalization-group-improved gauge action using the Schroedinger functional method

    SciTech Connect

    Aoki, S.; Takeda, S.; Taniguchi, Y.; Fukugita, M.; Hashimoto, S.; Kaneko, T.; Yamada, N.; Ishikawa, K-I.; Okawa, M.; Ishizuka, N.; Iwasaki, Y.; Kanaya, K.; Kuramashi, Y.; Ukawa, A.; Yoshie, T.; Tsutsui, N.

    2006-02-01

    We perform a nonperturbative determination of the O(a)-improvement coefficient c{sub SW} and the critical hopping parameter {kappa}{sub c} for N{sub f}=3, 2, and 0 flavor QCD with the (RG) renormalization-group-improved gauge action using the Schroedinger functional method. In order to interpolate c{sub SW} and {kappa}{sub c} as a function of the bare coupling, a wide range of {beta} from the weak coupling region to the moderately strong coupling points used in large-scale simulations is studied. Corrections at finite lattice size of O(a/L) turned out to be large for the RG-improved gauge action, and hence we make the determination at a size fixed in physical units using a modified improvement condition. This enables us to avoid O(a) scaling violations which would remain in physical observables if c{sub SW} determined for a fixed lattice size L/a is used in numerical simulations.

  6. Low-lying excitations of poly-fused thiophene within Pariser-Parr-Pople model: A density matrix renormalization group study.

    PubMed

    Das, Mousumi

    2010-05-21

    We studied the nature of the ground and low-lying excited states of poly-fused thiophene oligomers within long-range Pariser-Parr-Pople (PPP) model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. Our results show that the lowest dipole-allowed state lies below the lowest dipole forbidden two-photon state, indicating that poly-fused thiophenes are strongly fluorescent. The lowest triplet state lies below the two-photon state, which is in agreement with the general trend in conjugated polymers. The charge density and bond order calculations of three low-lying excited states, along with the ground state of fused thiophene oligomers, show a significant transfer of charge from sulfur to adjacent carbon atom in the middle of the largest system size and these excitations are localized. The charge density and bond order calculations on singly and doubly doped states show that bipolarons are not stable entity in these systems. The calculations of low-lying excitations on radical cation and anion of fused thiophene oligomers show a new energy band in the low energy region, which is strongly coupled to its hole and electron conductivity. This implies that poly-fused thiophenes posses novel field-effect transistor properties.

  7. 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.

  8. Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models

    NASA Astrophysics Data System (ADS)

    Carpentier, David; Le Doussal, Pierre

    2001-02-01

    We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>=1 it exhibits a transition at T=Tc>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this ``marginal glass'' case (energy fluctuation exponent θ=0) and disappears if correlations grow faster (single ground-state dominance θ>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting similarities with the weak- to strong-coupling transition in Liouville (c=1 barrier) and with a transition that we conjecture for the sinh-Gordon model, with correspondence in some exact results and RG analysis. Glassy freezing of the particle is associated with the generation under RG of new local operators and of nonsmooth configurations in Liouville. Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar ``quasilocalized'' regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.

  9. 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.

  10. Phase diagram of electronic systems with quadratic Fermi nodes in 2 renormalization group

    NASA Astrophysics Data System (ADS)

    Janssen, Lukas; Herbut, Igor F.

    2017-02-01

    Several materials in the regime of strong spin-orbit interaction such as HgTe, the pyrochlore iridate Pr2Ir2O7 , and the half-Heusler compound LaPtBi, as well as various systems related to these three prototype materials, are believed to host a quadratic band touching point at the Fermi level. Recently, it has been proposed that such a three-dimensional gapless state is unstable to a Mott-insulating ground state at low temperatures when the number of band touching points N at the Fermi level is smaller than a certain critical number Nc. We further substantiate and quantify this scenario by various approaches. Using ɛ expansion near two spatial dimensions, we show that Nc=64 /(25 ɛ2) +O (1 /ɛ ) and demonstrate that the instability for N renormalization group equations in the dynamical bosonization scheme which we show to agree to one-loop order with the results from ɛ expansion both near two as well as near four dimensions, and which smoothly interpolates between these two perturbatively accessible limits for general 2

  11. 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; ...

    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

  12. Inertial-Range Behavior of a Passive Scalar Field in a Random Shear Flow: Renormalization Group Analysis of a Simple Model

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Malyshev, A. V.

    2012-01-01

    Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form ∝δ(t-t') / k_{bot}^{d-1+ξ}, where k ⊥=| k ⊥| and k ⊥ is the component of the wave vector, perpendicular to the distinguished direction (`direction of the flow')—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan's rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum {E} ∝ k_{bot}^{1-\\varepsilon} and in the dispersion law ω∝ k_{bot}^{2-η}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray η=0, ɛ>0 in the ɛ- η plane. The physical (Kolmogorov) point ɛ=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.

  13. Optimal caliper width for propensity score matching of three treatment groups: a Monte Carlo study.

    PubMed

    Wang, Yongji; Cai, Hongwei; Li, Chanjuan; Jiang, Zhiwei; Wang, Ling; Song, Jiugang; Xia, Jielai

    2013-01-01

    Propensity score matching is a method to reduce bias in non-randomized and observational studies. Propensity score matching is mainly applied to two treatment groups rather than multiple treatment groups, because some key issues affecting its application to multiple treatment groups remain unsolved, such as the matching distance, the assessment of balance in baseline variables, and the choice of optimal caliper width. The primary objective of this study was to compare propensity score matching methods using different calipers and to choose the optimal caliper width for use with three treatment groups. The authors used caliper widths from 0.1 to 0.8 of the pooled standard deviation of the logit of the propensity score, in increments of 0.1. The balance in baseline variables was assessed by standardized difference. The matching ratio, relative bias, and mean squared error (MSE) of the estimate between groups in different propensity score-matched samples were also reported. The results of Monte Carlo simulations indicate that matching using a caliper width of 0.2 of the pooled standard deviation of the logit of the propensity score affords superior performance in the estimation of treatment effects. This study provides practical solutions for the application of propensity score matching of three treatment groups.

  14. Renormalized halo bias

    SciTech Connect

    Assassi, Valentin; Baumann, Daniel; Green, Daniel; Zaldarriaga, Matias E-mail: dbaumann@damtp.cam.ac.uk E-mail: matiasz@ias.edu

    2014-08-01

    This paper provides a systematic study of renormalization in models of halo biasing. Building on work of McDonald, we show that Eulerian biasing is only consistent with renormalization if non-local terms and higher-derivative contributions are included in the biasing model. We explicitly determine the complete list of required bias parameters for Gaussian initial conditions, up to quartic order in the dark matter density contrast and at leading order in derivatives. At quadratic order, this means including the gravitational tidal tensor, while at cubic order the velocity potential appears as an independent degree of freedom. Our study naturally leads to an effective theory of biasing in which the halo density is written as a double expansion in fluctuations and spatial derivatives. We show that the bias expansion can be organized in terms of Galileon operators which aren't renormalized at leading order in derivatives. Finally, we discuss how the renormalized bias parameters impact the statistics of halos.

  15. 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

  16. Renormalized jellium model for colloidal mixtures

    NASA Astrophysics Data System (ADS)

    García de Soria, María Isabel; Álvarez, Carlos E.; Trizac, Emmanuel

    2016-10-01

    In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge, and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from one species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corresponding predictions are compared to the results of Monte Carlo simulations of binary mixtures, where Coulombic interactions are accounted for exactly, at the primitive model level (structureless solvent with fixed dielectric permittivity). An excellent agreement is found.

  17. Renormalized jellium model for colloidal mixtures.

    PubMed

    García de Soria, María Isabel; Álvarez, Carlos E; Trizac, Emmanuel

    2016-10-01

    In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge, and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from one species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corresponding predictions are compared to the results of Monte Carlo simulations of binary mixtures, where Coulombic interactions are accounted for exactly, at the primitive model level (structureless solvent with fixed dielectric permittivity). An excellent agreement is found.

  18. Thermodynamics and renormalized quasiparticles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

    NASA Astrophysics Data System (ADS)

    Krieg, Jan; Strassel, Dominik; Streib, Simon; Eggert, Sebastian; Kopietz, Peter

    2017-01-01

    We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature T and chemical potential μ . We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at μ =0 to finite values of μ . To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-1 /2 quantum X Y model with coupling J in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for μ ≤0 rather accurately up to relatively high temperatures T ≲0.1 J .

  19. 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.

  20. Loop Optimization for Tensor Network Renormalization

    NASA Astrophysics Data System (ADS)

    Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

    2017-03-01

    We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.

  1. Complete renormalization of QCD at five loops

    NASA Astrophysics Data System (ADS)

    Luthe, Thomas; Maier, Andreas; Marquard, Peter; Schröder, York

    2017-03-01

    We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.

  2. 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.

  3. Controlling sign problems in spin models using tensor renormalization

    SciTech Connect

    Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

    2014-01-09

    We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

  4. Holographic renormalization and supersymmetry

    NASA Astrophysics Data System (ADS)

    Genolini, Pietro Benetti; Cassani, Davide; Martelli, Dario; Sparks, James

    2017-02-01

    Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.

  5. 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.

  6. Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

    NASA Astrophysics Data System (ADS)

    Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna

    2014-12-01

    We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

  7. Simulation of Quantum Many-Body Systems with Strings of Operators and Monte Carlo Tensor Contractions

    SciTech Connect

    Schuch, Norbert; Wolf, Michael M.; Cirac, J. Ignacio; Verstraete, Frank

    2008-02-01

    We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.0.

  8. 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.

  9. 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.

  10. A nonperturbative parametrization and scenario for EFT renormalization

    NASA Astrophysics Data System (ADS)

    Yang, Ji-Feng

    2009-03-01

    We present a universal form of the T-matrices renormalized in nonperturbative regime and the ensuing notions and properties that fail conventional wisdoms. A universal scale is identified and shown to be renormalization group invariant. The effective range parameters are derived in a nonperturbative scenario with some new predictions within the realm of contact potentials. Some controversies are shown to be due to the failure of conventional wisdoms.

  11. The NSVZ β-function in supersymmetric theories with different regularizations and renormalization prescriptions

    NASA Astrophysics Data System (ADS)

    Kataev, A. L.; Stepanyantz, K. V.

    2014-12-01

    We briefly review the calculations of quantum corrections related to the exact Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β-function in N= 1 supersymmetric theories, paying special attention to the scheme dependence of the results. We explain how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. We also describe how to construct a special renormalization prescription that gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories regularized by higher derivatives and discuss the scheme dependence of the NSVZ β-function (for the renormalization group functions defined in terms of the renormalized coupling constant) in the non-Abelian case. We show that in this case, the NSVZ β-function leads to a certain scheme-independent equality.

  12. 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.

  13. 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) .

  14. Nonperturbative Renormalization of Composite Operators with Overlap Fermions

    SciTech Connect

    J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams

    2005-12-01

    We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

  15. 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.

  16. Evidence of a short-range incommensurate d-wave charge order from a fermionic two-loop renormalization group calculation of a 2D model with hot spots

    SciTech Connect

    Carvalho, Vanuildo S de; Freire, Hermann

    2014-09-15

    The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.

  17. 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!!!

  18. Detection of Differential Item Functioning for More than Two Groups: A Monte Carlo Comparison of Methods

    ERIC Educational Resources Information Center

    Finch, W. Holmes

    2016-01-01

    Differential item functioning (DIF) assessment is a crucial component in test construction, serving as the primary way in which instrument developers ensure that measures perform in the same way for multiple groups within the population. When such is not the case, scores may not accurately reflect the trait of interest for all individuals in the…

  19. 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.

  20. Competing instabilities, orbital ordering, and splitting of band degeneracies from a parquet renormalization group analysis of a four-pocket model for iron-based superconductors: Application to FeSe

    NASA Astrophysics Data System (ADS)

    Xing, Rui-Qi; Classen, Laura; Khodas, Maxim; Chubukov, Andrey V.

    2017-02-01

    We report the results of a parquet renormalization group (RG) study of competing instabilities in the full 2D four-pocket, three-orbital low-energy model for iron-based superconductors. We derive and analyze the RG flow of the couplings, which describes all symmetry-allowed interactions between low-energy fermions. Despite that the number of the couplings is large, we argue that there are only two stable fixed trajectories of the RG flow and one weakly unstable fixed trajectory with a single unstable direction. Each fixed trajectory has a finite basin of attraction in the space of initial system parameters. On the stable trajectories, either interactions involving only dx z and dy z or only dx y orbital components on electron pockets dominate, while on the weakly unstable trajectory interactions involving dx z (dy z) and dx y orbital states on electron pockets remain comparable. The behavior along the two stable fixed trajectories has been analyzed earlier [Chubukov, Khodas, and Fernandes, Phys. Rev. X 6, 041045 (2016), 10.1103/PhysRevX.6.041045]. Here we focus on the system behavior along the weakly unstable trajectory and apply the results to FeSe. We find, based on the analysis of susceptibilities along this trajectory, that the leading instability upon lowering the temperature is towards a three-component d -wave orbital nematic order. Two components are the differences between fermionic densities on dx z and dy z orbitals on hole pockets and on electron pockets, and the third one is the difference between the densities of dx y orbitals on the two electron pockets. We argue that this order is consistent with the splitting of band degeneracies, observed in recent photoemission data on FeSe by Fedorov et al. [Sci. Rep. 6, 36834 (2016), 10.1038/srep36834].

  1. Recursive renormalization group theory based subgrid modeling

    NASA Technical Reports Server (NTRS)

    Zhou, YE

    1991-01-01

    Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.

  2. Renormalization Group Analysis of October Market Crashes

    NASA Astrophysics Data System (ADS)

    Gluzman, S.; Yukalov, V. I.

    The self-similar analysis of time series, suggested earlier by the authors, is applied to the description of market crises. The main attention is payed to the October 1929, 1987 and 1997 stock market crises, which can be successfully treated by the suggested approach. The analogy between market crashes and critical phenomena is emphasized.

  3. Renormalization group running of neutrino parameters.

    PubMed

    Ohlsson, Tommy; Zhou, Shun

    2014-10-17

    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.

  4. Four loop renormalization of the Gross-Neveu model

    NASA Astrophysics Data System (ADS)

    Gracey, J. A.; Luthe, T.; Schröder, Y.

    2016-12-01

    We renormalize the S U (N ) Gross-Neveu model in the modified minimal subtraction scheme at four loops and determine the β function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-Fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.

  5. Evidence for Fisher renormalization in the compressible phi4 model.

    PubMed

    Tröster, A

    2008-04-11

    We present novel Fourier Monte Carlo simulations of a compressible phi4-model on a simple-cubic lattice with linear-quadratic coupling of order parameter and strain, focusing on the detection of fluctuation-induced first-order transitions and deviations from standard critical behavior. The former is indeed observed in the constant stress ensemble and for auxetic systems at constant strain, while for regular isotropic systems at constant strain, we find strong evidence for Fisher-renormalized critical behavior and are led to predict the existence of a tricritical point.

  6. 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.

  7. Concepts of renormalization in physics.

    PubMed

    Alexandre, Jean

    2005-01-01

    A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, and then show how similar ideas appear in particle physics. This short review is written for non-particle physicists and/or students aiming at studying particle physics.

  8. Disordered holographic systems: Functional renormalization

    NASA Astrophysics Data System (ADS)

    Adams, Allan; Yaida, Sho

    2015-12-01

    We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance, or marginality of quenched disorder holds.

  9. Renormalization constants from string theory.

    NASA Astrophysics Data System (ADS)

    di Vecchia, P.; Magnea, L.; Lerda, A.; Russo, R.; Marotta, R.

    The authors review some recent results on the calculation of renormalization constants in Yang-Mills theory using open bosonic strings. The technology of string amplitudes, supplemented with an appropriate continuation off the mass shell, can be used to compute the ultraviolet divergences of dimensionally regularized gauge theories. The results show that the infinite tension limit of string amplitudes corresponds to the background field method in field theory.

  10. The renormalization scale-setting problem in QCD

    SciTech Connect

    Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

    2013-09-01

    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

  11. LETTER: Fisher renormalization for logarithmic corrections

    NASA Astrophysics Data System (ADS)

    Kenna, Ralph; Hsu, Hsiao-Ping; von Ferber, Christian

    2008-10-01

    For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogues. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.

  12. RENORMALIZATION OF POLYAKOV LOOPS IN FUNDAMENTAL AND HIGHER REPRESENTATIONS

    SciTech Connect

    KACZMAREK,O.; GUPTA, S.; HUEBNER, K.

    2007-07-30

    We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal entent of the lattice and find that both prescriptions are equivalent, resulting in renormalization constants that depend on the bare coupling. Furthermore these renormalization constants show Casimir scaling for higher representations of the Polyakov loops. The analysis of Polyakov loops in different representations of the color SU(3) group indicates that a simple perturbative inspired relation in terms of the quadratic Casimir operator is realized to a good approximation at temperatures T{approx}>{Tc}, for renormalized as well as bare loops. In contrast to a vanishing Polyakov loop in representations with non-zero triality in the confined phase, the adjoint loops are small but non-zero even for temperatures below the critical one. The adjoint quark-antiquark pairs exhibit screening. This behavior can be related to the binding energy of glue-lump states.

  13. Renormalizing chiral nuclear forces: Triplet channels

    NASA Astrophysics Data System (ADS)

    Long, Bingwei; Yang, C.-J.

    2012-03-01

    We discuss the subleading contact interactions, or counterterms, of the triplet channels of nucleon-nucleon scattering in the framework of chiral effective field theory, with S and P waves as the examples. The triplet channels are special in that they allow the singular attraction of one-pion exchange to modify Weinberg's original power-counting (WPC) scheme. With renormalization group invariance as the constraint, our power counting for the triplet channels can be summarized as a modified version of naive dimensional analysis in which, when compared with WPC, all of the counterterms in a given partial wave (leading or subleading) are enhanced by the same amount. More specifically, this means that WPC needs no modification in 3S1-3D1 and 3P1, whereas a two-order enhancement is necessary in both 3P0 and 3P2-3F2.

  14. Renormalizing Chiral Nuclear Forces: Triplet Channels

    SciTech Connect

    Bingwei Long, Chieh-Jen Yang

    2012-03-01

    We discuss the subleading contact interactions, or counterterms, of the triplet channels of nucleon-nucleon scattering in the framework of chiral effective field theory, with S and P waves as the examples. The triplet channels are special in that it allows the singular attraction of one-pion exchange to modify Weinberg's original power counting (WPC) scheme. With renormalization group invariance as the constraint, our power counting for the triplet channels can be summarized as a modified version of naive dimensional analysis that, when compared with WPC, the subleading counterterms are enhanced as much as the leading one. More specifically, this means that WPC needs no modification in {sup 3}S{sub 1}-{sup 3}D{sub 1} and {sup 3}P{sub 1} whereas a two-order enhancement is necessary in both {sup 3}P{sub 0} and {sup 3}P{sub 2} - {sup 3}F{sub 2}.

  15. Systematic all-orders method to eliminate renormalization-scale and scheme ambiguities in perturbative QCD.

    PubMed

    Mojaza, Matin; Brodsky, Stanley J; Wu, Xing-Gang

    2013-05-10

    We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of perturbative QCD predictions, exposes the general pattern of nonconformal {β(i)} terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in perturbative QCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.

  16. 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.

  17. Algorithms for tensor network renormalization

    NASA Astrophysics Data System (ADS)

    Evenbly, G.

    2017-01-01

    We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. First, we recall established techniques for how the partition function of a 2 D classical many-body system or the Euclidean path integral of a 1 D quantum system can be represented as a network of tensors, before describing how TNR can be implemented to efficiently contract the network via a sequence of coarse-graining transformations. The efficacy of the TNR approach is then benchmarked for the 2 D classical statistical and 1 D quantum Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining transformations, even at a critical point, is demonstrated.

  18. 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.

  19. 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.

  20. 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

  1. 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.; ...

    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

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

    SciTech Connect

    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 the 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

    We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.

  4. 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

  5. Higher derivatives and renormalization in quantum cosmology

    NASA Astrophysics Data System (ADS)

    Mazzitelli, Francisco D.

    1992-04-01

    In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change completely the Hamiltonian structure of the theory, not making clear the relation between the renormalized theory and the original one. We show that it is possible to avoid this problem. We replace the higher-derivative theory by a second-order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities, and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson-Walker minisuperspace with a quantum scalar field.

  6. 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

  7. Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model

    NASA Astrophysics Data System (ADS)

    Hewson, A. C.

    2016-11-01

    We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.

  8. 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.

  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. 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.

  11. 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.

  12. A Monte Carlo based nodal diffusion model for criticality analysis, and, Application of high-order cross section homogenization method to two-group nodal diffusion

    NASA Astrophysics Data System (ADS)

    Ilas, Germina

    In the first part, an accurate and fast computational method is presented as an alternative to the Monte Carlo or deterministic transport theory codes currently used to determine the subcriticality of spent fuel storage lattices. The method is capable of analyzing storage configurations with simple or complex lattice cell geometry. It is developed based on two-group nodal diffusion theory, with the nodal cross sections and discontinuity factors determined from continuous-energy Monte Carlo simulations of each unique node (spent fuel assembly type). Three different approaches are developed to estimate the node-averaged diffusion coefficient. The applicability and the accuracy of the nodal method are assessed in two-dimensional geometry through several benchmark configurations typical at Savannah River Site. It is shown that the multiplication constant of the analyzed configurations is within 1% of the MCNP results. In the second part, the high-order cross section homogenization method, recently developed by McKinley and Rahnema, is implemented in the context of two-group nodal diffusion theory. The method corrects the generalized equivalence theory homogenization parameters for the effect of the core environment. The reconstructed fine-mesh (fuel pin) flux and power distributions are a natural byproduct of this method. The method was not tested for multigroup problems, where it was assumed that the multigroup flux expansion in terms of the perturbation parameter is a convergent series. Here the applicability of the method to two-group problems is studied, and it is shown that the perturbation expansion series converges for the multigroup case. A two-group nodal diffusion code with a bilinear intra-nodal flux shape is developed for the implementation of the high-order homogenization method in the context of the generalized equivalence theory. The method is tested by using as a benchmark a core configuration typical of a BWR in slab geometry, which has large

  13. 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.

  14. Charge Renormalization and Charge Oscillation in Asymmetric Primitive Model of Electrolytes

    NASA Astrophysics Data System (ADS)

    Ding, Mingnan; Liang, Yihao; Lu, Bing-Sui; Xing, Xiangjun

    2016-12-01

    Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of the system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upward by ionic correlations, while those of smaller ions remain approximately the same. For sufficiently high density, the system exhibits charge oscillations. The threshold ion density for charge oscillation is much lower than the corresponding values for symmetric electrolytes. Our results agree well with large-scale Monte Carlo simulations, and find good agreement in general, except for the case of small ion sizes (d = 4 Å) near the charge oscillation threshold.

  15. Renormalization transformation of periodic and aperiodic lattices

    SciTech Connect

    Macia, Enrique; Rodriguez-Oliveros, Rogelio

    2006-10-01

    In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order (i.e., periodic or quasiperiodic) of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process.

  16. Relativistic causality and position space renormalization

    NASA Astrophysics Data System (ADS)

    Todorov, Ivan

    2016-11-01

    The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior) in the case of the massless φ4 theory and display the dilation and the conformal anomaly.

  17. 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.

  18. On background-independent renormalization of spin foam models

    NASA Astrophysics Data System (ADS)

    Bahr, Benjamin

    2017-04-01

    In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical consistency of path integral measures gives a natural analogue of Wilson’s RG flow equations for background-independent systems. We discuss the conditions for the continuum measures to be diffeomorphism-invariant, and consider both exact and approximate examples.

  19. 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.

  20. A self-consistent renormalized jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions.

    PubMed

    Colla, Thiago E; Levin, Yan; Trizac, Emmanuel

    2009-08-21

    An approach is proposed which allows to self-consistently calculate the structural and the thermodynamic properties of highly charged aqueous colloidal suspensions. The method is based on the renormalized jellium model with the background charge distribution related to the colloid-colloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspensions containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with Monte Carlo simulations.

  1. 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.

  2. 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.

  3. Critical mass renormalization in renormalized ϕ4 theories in two and three dimensions

    NASA Astrophysics Data System (ADS)

    Pelissetto, Andrea; Vicari, Ettore

    2015-12-01

    We consider the O (N)-symmetric ϕ4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the ϕ4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative series in the massive renormalization scheme, taking into account their Borel summability and the known large-order behavior of the coefficients. The results are in good agreement with those obtained in lattice calculations.

  4. 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!!!

  5. Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

    NASA Astrophysics Data System (ADS)

    Gu, Zheng-Cheng; Wen, Xiao-Gang

    2009-10-01

    We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors Tinv plus the symmetry group Gsym of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (Gsym,Tinv) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (Gsym,Tinv) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.

  6. 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.

  7. Monte Carlo method for critical systems in infinite volume: The planar Ising model.

    PubMed

    Herdeiro, Victor; Doyon, Benjamin

    2016-10-01

    In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.

  8. Monte Carlo simulations of the disordered three-color quantum Ashkin-Teller chain

    NASA Astrophysics Data System (ADS)

    Ibrahim, Ahmed K.; Vojta, Thomas

    2017-02-01

    We investigate the zero-temperature quantum phase transitions of the disordered three-color quantum Ashkin-Teller spin chain by means of large-scale Monte Carlo simulations. We find that the first-order phase transitions of the clean system are rounded by the quenched disorder. For weak intercolor coupling, the resulting emergent quantum critical point between the paramagnetic phase and the magnetically ordered Baxter phase is of infinite-randomness type and belongs to the universality class of the random transverse-field Ising model, as predicted by recent strong-disorder renormalization group calculations. We also find evidence for unconventional critical behavior in the case of strong intercolor coupling, even though an unequivocal determination of the universality class is beyond our numerical capabilities. We compare our results to earlier simulations, and we discuss implications for the classification of phase transitions in the presence of disorder.

  9. MBR Monte Carlo Simulation in PYTHIA8

    NASA Astrophysics Data System (ADS)

    Ciesielski, R.

    We present the MBR (Minimum Bias Rockefeller) Monte Carlo simulation of (anti)proton-proton interactions and its implementation in the PYTHIA8 event generator. We discuss the total, elastic, and total-inelastic cross sections, and three contributions from diffraction dissociation processes that contribute to the latter: single diffraction, double diffraction, and central diffraction or double-Pomeron exchange. The event generation follows a renormalized-Regge-theory model, successfully tested using CDF data. Based on the MBR-enhanced PYTHIA8 simulation, we present cross-section predictions for the LHC and beyond, up to collision energies of 50 TeV.

  10. Renormalized vacuum polarization of rotating black holes

    NASA Astrophysics Data System (ADS)

    Ferreira, Hugo R. C.

    2015-04-01

    Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

  11. Monte Carlo Simulation of Plumes Spectral Emission

    DTIC Science & Technology

    2005-06-07

    Henyey − Greenstein scattering indicatrix SUBROUTINE Calculation of spectral (group) phase function of Monte - Carlo Simulation of Plumes...calculations; b) Computing code SRT-RTMC-NSM intended for narrow band Spectral Radiation Transfer Ray Tracing Simulation by the Monte - Carlo method with...project) Computing codes for random ( Monte - Carlo ) simulation of molecular lines with reference to a problem of radiation transfer

  12. 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

  13. The Physical Renormalization of Quantum Field Theories

    SciTech Connect

    Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC

    2007-02-20

    The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi

  14. Improved Epstein-Glaser renormalization in x-space versus differential renormalization

    NASA Astrophysics Data System (ADS)

    Gracia-Bondía, José M.; Gutiérrez, Heidy; Várilly, Joseph C.

    2014-09-01

    Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.

  15. 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.

  16. 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.

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

    SciTech Connect

    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 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 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.

  18. Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems

    NASA Astrophysics Data System (ADS)

    Wu, Wei; Xu, Jing-Bo

    2016-08-01

    We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with the real-space quantum renormalization group method. As illustration examples, a one-dimensional and a two-dimensional XY models are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find that the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points.

  19. The proton and carbon therapy experience of the medical physics group at the Italian Southern Laboratories: Monte Carlo simulation and experiment

    NASA Astrophysics Data System (ADS)

    Cirrone, G. A. Pablo; Agodi, C.; Candiano, G.; Cuttone, G.; di Rosa, F.; Mongelli, E.; Lojacono, P.; Mazzaglia, S.; Russo, G.; Romano, F.; Valastro, L. M.; Lo Nigro, S.; Pittera, S.; Sabini, M. G.; Rafaele, L.; Salamone, V.; Morone, C.; Randazzo, N.; Sipala, V.; Bucciolini, M.; Bruzzi, M.; Menichelli, D.

    2008-03-01

    At the Italian Southern Laboratories (LNS) of the Italian National Institute for Nuclear Physics the first, and actually unique, Italian proton therapy center is installed and operating. Up to now, 140 patients have been treated. In this environment a big effort is devoted towards Monte Carlo simulation expeciallt with the GEANT4 Toolkit. The authors of this work belong to the Geant4 Collaboration and they use the toolkit in their research programs. They maintain a Monte Carlo application devoted to the complete simulation of a generic hadron-therapy beam line and take active part in the study of fragmentation processes. Moreover they are working in the development of a prototype of a proton Computed tomographic system. In this work we will report our results in the field of proton and carbon therapy either in the simulation as well in the experimental side of our activity.

  20. Naturalness and renormalization group in the standard model

    NASA Astrophysics Data System (ADS)

    Pivovarov, Grigorii B.

    2016-10-01

    I define a naturalness criterion formalizing the intuitive notion of naturalness discussed in the literature. After that, using ϕ4 as an example, I demonstrate that a theory may be natural in the MS-scheme and, at the same time, unnatural in the Gell-Mann-Low scheme. Finally, I discuss the prospects of using a version of the Gell-Mann-Low scheme in the Standard Model.

  1. Naturalness and Renormalization Group in the Standard Model

    NASA Astrophysics Data System (ADS)

    Pivovarov, Grigorii B.

    I define a naturalness criterion formalizing the intuitive notion of naturalness discussed in the literature. After that, using ϕ4 as an example, I demonstrate that a theory may be natural in the MS-scheme and, at the same time, unnatural in the Gell-Mann-Low scheme. Finally, I discuss the prospects of using a version of the Gell-Mann-Low scheme in the Standard Model.

  2. 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.

  3. 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.

  4. 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.

  5. Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function

    NASA Astrophysics Data System (ADS)

    Ananthanarayan, B.; Das, Diganta

    2016-12-01

    We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the s -quark mass relevant in τ -decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass ms(2 GeV )=106.70 ±9.36 MeV and ms(2 GeV )=74.47 ±7.77 MeV from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

  6. Emergent space-time via a geometric renormalization method

    NASA Astrophysics Data System (ADS)

    Rastgoo, Saeed; Requardt, Manfred

    2016-12-01

    We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of space-time can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group (RG). Furthermore, we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which, e.g., for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e., quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is noninteger. At the end of the paper we briefly mention the possibility that our network carries a translocal far order that leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.

  7. Renormalized one-loop theory of correlations in polymer blends.

    PubMed

    Qin, Jian; Morse, David C

    2009-06-14

    The renormalized one-loop theory is a coarse-grained theory of corrections to the random phase approximation (RPA) theory of composition fluctuations. We present predictions of corrections to the RPA for the structure function S(k) and to the random walk model of single-chain statics in binary homopolymer blends. We consider an apparent interaction parameter chi(a) that is defined by applying the RPA to the small k limit of S(k). The predicted deviation of chi(a) from its long chain limit is proportional to N(-1/2), where N is the chain length. This deviation is positive (i.e., destabilizing) for weakly nonideal mixtures, with chi(a)N less than or approximately 1, but negative (stabilizing) near the critical point. The positive correction to chi(a) for low values of chi(a)N is a result of the fact that monomers in mixtures of shorter chains are slightly less strongly shielded from intermolecular contacts. The predicted depression in chi(a) near the critical point is a result of long-wavelength composition fluctuations. The one-loop theory predicts a shift in the critical temperature of O(N(-1/2)), which is much greater than the predicted O(N(-1)) width of the Ginzburg region. Chain dimensions are found to deviate slightly from those of a random walk even in a one-component melt and contract slightly as thermodynamic repulsion is increased. Predictions for S(k) and single-chain properties are compared to published lattice Monte Carlo simulations.

  8. Renormalizing chiral nuclear forces: A case study of 3P0

    NASA Astrophysics Data System (ADS)

    Long, Bingwei; Yang, C.-J.

    2011-11-01

    We discuss in this Brief Report the subleading contact interactions, or counterterms, in the 3P0 channel of nucleon-nucleon scattering up to O(Q3), where, already at leading order, Weinberg's original power counting (WPC) scheme fails to fulfill renormalization group invariance due to the singular attraction of one-pion exchange. Treating the subleading interactions as perturbations and using renormalization group invariance as the criterion, we investigate whether WPC, although missing the leading order, could prescribe correct subleading counterterms. We find that the answer is negative and, instead, that the structure of counterterms agrees with a modified version of naive dimensional analysis. Using 3P0 as an example, we also study the cutoffs where the subleading potential can be iterated together with the leading one.

  9. Fragmentation scaling of percolation clusters in two and three dimensions: Large-cell Monte Carlo RG approach

    NASA Astrophysics Data System (ADS)

    Cheon, M.; Chang, I.

    1999-04-01

    The scaling behavior for a binary fragmentation of critical percolation clusters is investigated by a large-cell Monte Carlo real-space renormalization group method in two and three dimensions. We obtain accurate values of critical exponents λ and phi describing the scaling of fragmentation rate and the distribution of fragments' masses produced by a binary fragmentation. Our results for λ and phi show that the fragmentation rate is proportional to the size of mother cluster, and the scaling relation σ = 1 + λ - phi conjectured by Edwards et al. to be valid for all dimensions is satisfied in two and three dimensions, where σ is the crossover exponent of the average cluster number in percolation theory, which excludes the other scaling relations.

  10. 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.

  11. 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

  12. 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

  13. 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

  14. 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.

  15. 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.

  16. Correlation matrix renormalization approximation for total energy calculations of correlated electron systems

    NASA Astrophysics Data System (ADS)

    Yao, Y. X.; Liu, C.; Liu, J.; Lu, W. C.; Wang, C. Z.; Ho, K. M.

    2013-03-01

    The recently introduced correlation matrix renormalization approximation (CMRA) was further developed by adopting a completely factorizable form for the renormalization z-factors, which assumes the validity of the Wick's theorem with respect to Gutzwiller wave function. This approximation (CMR-II) shows better dissociation behavior than the original one (CMR-I) based on the straightforward generalization of the Gutzwiller approximation to two-body interactions. We further improved the performance of CMRA by redefining the z-factors as a function of f(z) in CMR-II, which we call CMR-III. We obtained an analytical expression of f(z) by enforcing the equality in energy functional between CMR-III and full configuration interaction for the benchmark minimal basis H2. We show that CMR-III yields quite good binding energies and dissociation behaviors for various hydrogen clusters with converged basis set. Finally, we apply CMR-III to hydrogen crystal phases and compare the results with quantum Monte Carlo. Research supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

  17. Monte Carlo Benchmark

    SciTech Connect

    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.

  18. Nonlinear scale separation and a renormalization interpretation in seismic envelope inversion

    NASA Astrophysics Data System (ADS)

    Luo, J.; Wu, R. S.

    2015-12-01

    Envelope inversion can nonlinearly separate the response of large-scale structure from the fine-structure. The convergence behavior of envelope inversion can be well-explained by renormalization and renormalization group (RG) theory/method. The local integration (local interaction) of the envelope operator and the local re-linearization of the envelope inversion solve the divergence problem, although it can only recover the large-scale background structure (low resolution inversion). The combined inversion of envelope inversion and waveform inversion (SEI+FWI) can substantially reduce the starting model dependence of the regular full-waveform inversion. Numerical examples from the Marmousi model and the Overthrust model are shown to demonstrate the method.

  19. Conformal gauges and renormalized equations of motion in massless quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Petkova, V. B.; Sotkov, G. M.; Todorov, I. T.

    1985-03-01

    A formulation of massless QED is studied with a non-singular Lagrangian and conformal invariant equations of motion. It makes use of non-decomposable representations of the conformal group G and involves two dimensionless scalar fields (in addition to the conventional charged field and electromagnetic potential) but gauge invariant Green functions are shown to coincide with those of standard (massless) QED. Assuming that the (non-elementary) representation of G for the 5-potential which leaves the equations of motion invariant and leads to the free photon propagator of Johnson-Baker-Adler (JBA) conformal QED remains unaltered by renormalization, we prove that consistency requirements for conformal invariant 2-, 3-, and 4-point Green functions satisfying (renormalized) equations of motion and standard Ward identities lead to either a trivial solution (with eψ=0) or to a subcanonical dimension d=1/2 for the charged field.

  20. 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.

  1. Renormalization of tracer turbulence leading to fractional differential equations.

    PubMed

    Sánchez, R; Carreras, B A; Newman, D E; Lynch, V E; van Milligen, B Ph

    2006-07-01

    For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

  2. 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.

  3. 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.

  4. 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.

  5. Renormalization of an Inverse Scattering Theory for Inhomogeneous Dielectrics.

    DTIC Science & Technology

    2014-09-26

    approximation is the solution obtained by assuming small phase shifts in the scattered field. The radius of convergence for this approximation is limited...paper we investigate a method to increase the radius of convergence of approximate solu- tions of inverse scattering problems by using renormalization. We...boundary-layer theory. The results of Table 1 show that the renormalized inversion theory has a larger radius of conver- gence than the Born approximation

  6. Aspects of renormalization in finite-density field theory

    SciTech Connect

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

    2015-05-26

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

  7. Renormalization of aperiodic model lattices: spectral properties

    NASA Astrophysics Data System (ADS)

    Kroon, Lars; Riklund, Rolf

    2003-04-01

    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schrödinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubling sequence are purely singular continuous.

  8. 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.

  9. Renormalization of the unitary evolution equation for coined quantum walks

    NASA Astrophysics Data System (ADS)

    Boettcher, Stefan; Li, Shanshan; Portugal, Renato

    2017-03-01

    We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.

  10. Effective viscosity of puller-like microswimmers: a renormalization approach

    PubMed Central

    Gluzman, Simon; Karpeev, Dmitry A.; Berlyand, Leonid V.

    2013-01-01

    Effective viscosity (EV) of suspensions of puller-like microswimmers (pullers), for example Chlamydamonas algae, is difficult to measure or simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytical determination of the passive EV for all concentrations remains unsatisfactory. At the same time, the EV of bacterial suspensions is closely linked to collective motion in these systems and is biologically significant. We develop an approach for determining analytical EV estimates at all concentrations for suspensions of pullers as well as for passive suspensions. The proposed methods are based on the ideas of renormalization group (RG) theory and construct the EV formula based on the known asymptotics for small concentrations and near the critical point (i.e. approaching dense packing). For passive suspensions, the method is verified by comparison against known theoretical results. We find that the method performs much better than an earlier RG-based technique. For pullers, the validation is done by comparing them to experiments conducted on Chlamydamonas suspensions. PMID:24068178

  11. Monte Carlo Example Programs

    SciTech Connect

    Kalos, M.

    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.

  12. Renormalization of position space amplitudes in a massless QFT

    NASA Astrophysics Data System (ADS)

    Todorov, Ivan

    2017-03-01

    Ultraviolet renormalization of position space massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree is determined by the degree of divergence while their order—the highest power of logarithm in the dilation anomaly—is given by the number of (sub)divergences. In the present paper we review these results and observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformally invariant theory internal integration is also proven to preserve the order of associate homogeneity. The renormalized 4-point amplitudes in the φ4 theory (in four space-time dimensions) are written as (non-analytic) translation invariant functions of four complex variables with calculable conformal anomaly. Our conclusion concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless φ4 theory agrees with the old result of Lowenstein and Zimmermann [23].

  13. 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.

  14. Efficient and Accurate Computation of Non-Negative Anisotropic Group Scattering Cross Sections for Discrete Ordinates and Monte Carlo Radiation Transport

    DTIC Science & Technology

    2002-07-01

    angular flux is a distribution function in space, energy, and angle. It can be described as a neutron path length rate density with units such as 3...The group angular flux , gy , is a distribution function in space and angle, and a bin integrated function in energy. It has units of 3 . neutron cm s...g), element/ordinate (n) angular flux 5 A Ratio of atomic mass to neutron mass 32 E’ Incident energy 4 Es Secondary energy after either elastic

  15. 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}.

  16. Dispersion coefficients from a field-theoretic renormalization of fluid mechanics.

    PubMed

    Deem, M W; Park, J M

    2001-10-22

    We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Péclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Péclet numbers.

  17. 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.

  18. Monte Carlo Ground State Energy for Trapped Boson Systems

    NASA Astrophysics Data System (ADS)

    Rudd, Ethan; Mehta, N. P.

    2012-06-01

    Diffusion Monte Carlo (DMC) and Green's Function Monte Carlo (GFMC) algorithms were implemented to obtain numerical approximations for the ground state energies of systems of bosons in a harmonic trap potential. Gaussian pairwise particle interactions of the form V0e^-|ri-rj|^2/r0^2 were implemented in the DMC code. These results were verified for small values of V0 via a first-order perturbation theory approximation for which the N-particle matrix element evaluated to N2 V0(1 + 1/r0^2)^3/2. By obtaining the scattering length from the 2-body potential in the perturbative regime (V0φ 1), ground state energy results were compared to modern renormalized models by P.R. Johnson et. al, New J. Phys. 11, 093022 (2009).

  19. 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.

  20. 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.

  1. RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

    SciTech Connect

    Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

    2010-05-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  2. Relativistic Magnetohydrodynamics: Renormalized Eigenvectors and Full Wave Decomposition Riemann Solver

    NASA Astrophysics Data System (ADS)

    Antón, Luis; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Aloy, Miguel A.; Mimica, Petar

    2010-05-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  3. Renormalization constants for 2-twist operators in twisted mass QCD

    SciTech Connect

    Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.

    2011-01-01

    Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to {beta}=3.9, 4.05, 4.20. Subtraction of O(a{sup 2}) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a{sup 2}). The renormalization conditions are defined in the RI{sup '}-MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.

  4. Two-loop renormalization of Feynman gauge QED

    SciTech Connect

    Adkins, Gregory S.; Fell, Richard N.; Sapirstein, J.

    2001-06-15

    We calculate the two-loop renormalization constants {delta}m, Z{sub 1}, and Z{sub 2} in Feynman gauge QED using dimensional regularization to control ultraviolet divergences and a non-zero photon mass to regulate infrared divergences.

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

    SciTech Connect

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

    2016-05-31

    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 k{sup 2} 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.

  6. A GPU-based large-scale Monte Carlo simulation method for systems with long-range interactions

    NASA Astrophysics Data System (ADS)

    Liang, Yihao; Xing, Xiangjun; Li, Yaohang

    2017-06-01

    In this work we present an efficient implementation of Canonical Monte Carlo simulation for Coulomb many body systems on graphics processing units (GPU). Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD) architectures, and adopts the sequential updating scheme of Metropolis algorithm. It makes no approximation in the computation of energy, and reaches a remarkable 440-fold speedup, compared with the serial implementation on CPU. We further use this method to simulate primitive model electrolytes, and measure very precisely all ion-ion pair correlation functions at high concentrations. From these data, we extract the renormalized Debye length, renormalized valences of constituent ions, and renormalized dielectric constants. These results demonstrate unequivocally physics beyond the classical Poisson-Boltzmann theory.

  7. Renormalization in the Coulomb gauge and order parameter for confinement in QCD

    NASA Astrophysics Data System (ADS)

    Zwanziger, Daniel

    1998-05-01

    Renormalization of the Coulomb gauge is studied in the phase space formalism, where one integrates over both the vector potential A, and its canonical momentum Π as well as the usual Faddeev-Popov auxiliary fields. A proof of renormalizability is not attempted. Instead, algebraic identities are derived from BRST invariance which renormalization must satisfy if the Coulomb gauge is renormalizable. In particular, a Ward identity is derived which holds at a fixed time t, and which is an analog of Gauss's law in the BRST formalism, and which we call the Gauss-BRST identity. The familiar Zinn-Justin equation results when this identity is integrated over all t. It is shown that in the Coulomb gauge, g2D0.0 is a renormalization-group invariant, as is its instantaneous part V( R), which we call the color-Coulomb potential. (Here D0.0 is the time-time component of the gluon propagator.) The contribution of V( R) to the Wilson loop exponentiates. It is proposed that the string tension defined by KCoul = lim R→∞ CV( R)/ R may serve as an order parameter for confinement, where C = (2 N) -1( N2 - 1) for SU( N) gauge theory. A remarkable consequence of the above-mentioned Ward identity is that the Fourier transform V( k) of V( R) is of the product form V( k) = [ k2D C,C ∗ ( k)] 2L( k) , where D C,C ∗ ( k) is the ghost propagator, and L( k) is a correlation function of longitudinal gluons. This exact equation combines with a previous analysis of the Gribov problem according to which k2D C,C ∗ ( k) diverges at k = 0 , to provide a scenario for confinement.

  8. Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model.

    PubMed

    O'Brien, Aroon; Bartlett, Stephen D; Doherty, Andrew C; Flammia, Steven T

    2015-10-01

    We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model in which the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization-group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.

  9. Auxiliary field quantum Monte Carlo with a localized basis--applications to atoms and molecules

    NASA Astrophysics Data System (ADS)

    Al-Saidi, Wissam A.; Zhang, Shiwei; Krakauer, Henry

    2006-03-01

    We extended the recently introduced phaseless auxiliary field quantum Monte Carlo approach [1] to any single-particle basis, and applied it to study atoms and molecules using localized Gaussian basis. This method maps the interacting many-body problem into a linear combination of non-interacting problems using a complex Hubbard-Stratonovich transformation, and controls the phase/sign problem using a trial wave function. It employs a random walk approach in Slater determinant space to project the many-body ground state of the system. The computational cost scales as a low power of system size. In all of the presented results the trial wave function was from a Hartree-Fock calculation. The obtained total energies of the atoms and molecules agree to within a few milli Hartrees with the exact value from full configuration interaction or density matrix renormalization group. The results are comparable in accuracy to those of CCSD(T) for equilibrium geometries but are superior for bond breaking. [1] S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003).

  10. Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors

    NASA Astrophysics Data System (ADS)

    Detmold, William; Endres, Michael G.

    2016-12-01

    We demonstrate the applicability of a recently proposed multiscale thermalization algorithm to two-color quantum chromodynamics (QCD) with two mass-degenerate fermion flavors. The algorithm involves refining an ensemble of gauge configurations that had been generated using a renormalization group (RG) matched coarse action, thereby producing a fine ensemble that is close to the thermalized distribution of a target fine action; the refined ensemble is subsequently rethermalized using conventional algorithms. Although the generalization of this algorithm from pure Yang-Mills theory to QCD with dynamical fermions is straightforward, we find that in the latter case, the method is susceptible to numerical instabilities during the initial stages of rethermalization when using the hybrid Monte Carlo algorithm. We find that these instabilities arise from large fermion forces in the evolution, which are attributed to an accumulation of spurious near-zero modes of the Dirac operator. We propose a simple strategy for curing this problem, and demonstrate that rapid thermalization—as probed by a variety of gluonic and fermionic operators—is possible with the use of this solution. In addition, we study the sensitivity of rethermalization rates to the RG matching of the coarse and fine actions, and identify effective matching conditions based on a variety of measured scales.

  11. Effects of the mean velocity field on the renormalized turbulent viscosity and correlation function

    NASA Astrophysics Data System (ADS)

    Kumar, Abhishek; Verma, Mahendra

    2015-11-01

    We perform renormalization group analysis of the Navier Stokes equation in the Eulerian framework in the presence of mean velocity field U0, and observe that that the renormalized viscosity ν (k) is independent of U0, where k is the wavenumber. Thus we show that ν (k) in the Eulerian field theory is Galilean invariant. We also compute ν (k) using numerical simulations and verify the above theoretical prediction. The velocity-velocity correlation function however exhibits damped oscillations whose time period of oscillation and damping time scales are given by 1 / kU0 and 1 / (ν (k) k2) respectively. In a modified form of Kraichnan's direct interaction approximation (DIA), the ``random mean velocity field'' of the large eddies sweeps the small-scale fluctuations. The DIA calculations also reveal that in the weak turbulence limit, the energy spectrum E (k) ~k - 3 / 2 , but for the strong turbulence limit, the random velocity field of the large-scale eddies is scale-dependent that leads to Kolmogorov's energy spectrum.

  12. 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.

  13. Improved description of metal oxide stability: Beyond the random phase approximation with renormalized kernels

    NASA Astrophysics Data System (ADS)

    Jauho, Thomas S.; Olsen, Thomas; Bligaard, Thomas; Thygesen, Kristian S.

    2015-09-01

    The renormalized adiabatic PBE (rAPBE) method has recently been shown to comprise a significant improvement over the random phase approximation (RPA) for total energy calculations of simple solids and molecules. Here we consider the formation energies of 19 group I and II metal oxides and a few transition-metal oxides. The mean absolute error relative to experiments is 0.21 eV and 0.38 eV per oxygen atom for rAPBE and RPA, respectively, and thus the rAPBE method greatly improves the description of metal-oxygen bonds across a wide range of oxides. The failure of the RPA can be partly attributed to the lack of error cancellation between the correlation energy of the oxide on the one hand and the bulk metal and oxygen molecule on the other hand, which are all separately predicted much too negative by the RPA. We ascribe the improved performance of the rAPBE to its significantly better description of absolute correlation energies which reduces the need for error cancellation. The rAPBE is just one out of an entire class of renormalized exchange-correlation kernels which should be further investigated.

  14. Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence

    NASA Astrophysics Data System (ADS)

    Singha, Tapas; Dutta, Kishore; Nandy, Malay K.

    2017-03-01

    We apply a renormalized perturbative scheme to the Navier–Stokes equation for an incompressible isotropic turbulent velocity field. This allows us to obtain the renormalized expressions for second- and third-order cumulants of the velocity derivative directly from the corresponding Feynman diagrams. The resulting expressions are integrated numerically by excluding and including the dissipation range assuming Kolmogorov and Pao’s phenomenological expressions for the energy spectrum. The ensuing values for skewness are found to be S  =  ‑0.647 (when the dissipation range is excluded) and S=-0.682 (when the dissipation is included). These estimated values are compared with various experimental, numerical and theoretical results.

  15. Renormalization flow of the hierarchical Anderson model at weak disorder

    NASA Astrophysics Data System (ADS)

    Metz, F. L.; Leuzzi, L.; Parisi, G.

    2014-02-01

    We study the flow of the renormalized model parameters obtained from a sequence of simple transformations of the 1D Anderson model with long-range hierarchical hopping. Combining numerical results with a perturbative approach for the flow equations, we identify three qualitatively different regimes at weak disorder. For a sufficiently fast decay of the hopping energy, the Cauchy distribution is the only stable fixed point of the flow equations, whereas for sufficiently slowly decaying hopping energy the renormalized parameters flow to a δ-peak fixed-point distribution. In an intermediate range of the hopping decay, both fixed-point distributions are stable and the stationary solution is determined by the initial configuration of the random parameters. We present results for the critical decay of the hopping energy separating the different regimes.

  16. Matrix product density operators: Renormalization fixed points and boundary theories

    NASA Astrophysics Data System (ADS)

    Cirac, J. I.; Pérez-García, D.; Schuch, N.; Verstraete, F.

    2017-03-01

    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  17. 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.

  18. Nonperturbative Quark Mass and Coupling Renormalization in Two Flavor QCD

    NASA Astrophysics Data System (ADS)

    Blum, Thomas Charles

    1995-01-01

    Nonperturbative bare quark mass and coupling renormalization is studied for two flavor quantum chromodynamics (QCD). In particular, the beta function for the case of Kogut-Susskind quarks is determined over the parameter space of existing lattice (spectrum) simulations from the existing spectrum data. This beta function is combined with a series of finite temperature lattice simulations (N_{t} = 4 ) to calculate the interaction measure, varepsilon-3p, which together with the pressure yields the thermal equation of state. A method of computing the asymmetry, or Karsch, coefficients, is also given. These coefficients give the parameter renormalizations for anisotropic lattices. However, for the three points in parameter space that we studied (one using Wilson fermions and two using Kogut-Susskind fermions), a clear determination of the asymmetry coefficients could not be made because of the remarkable fact that ratios of masses measured in different directions on lattices with anisotropic couplings were Euclidean invariant.

  19. A Dynamical Role for Acetylcholine in Synaptic Renormalization

    PubMed Central

    Fink, Christian G.; Murphy, Geoffrey G.; Zochowski, Michal; Booth, Victoria

    2013-01-01

    Although sleep is a fundamental behavior observed in virtually all animal species, its functions remain unclear. One leading proposal, known as the synaptic renormalization hypothesis, suggests that sleep is necessary to counteract a global strengthening of synapses that occurs during wakefulness. Evidence for sleep-dependent synaptic downscaling (or synaptic renormalization) has been observed experimentally, but the physiological mechanisms which generate this phenomenon are unknown. In this study, we propose that changes in neuronal membrane excitability induced by acetylcholine may provide a dynamical mechanism for both wake-dependent synaptic upscaling and sleep-dependent downscaling. We show in silico that cholinergically-induced changes in network firing patterns alter overall network synaptic potentiation when synaptic strengths evolve through spike-timing dependent plasticity mechanisms. Specifically, network synaptic potentiation increases dramatically with high cholinergic concentration and decreases dramatically with low levels of acetylcholine. We demonstrate that this phenomenon is robust across variation of many different network parameters. PMID:23516342

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

    DOE PAGES

    Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; ...

    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

  1. Classical Renormalization of Codimension-two Brane Couplings

    SciTech Connect

    Rham, Claudia de

    2007-11-20

    The curvature on codimension-two and higher branes is not regular for arbitrary matter sources. Nevertheless, the low-energy theory for an observer on such a brane should be well-defined and independent to any regularization procedure. This is achieved via appropriate classical renormalization of the brane couplings, and leads to a natural hierarchy between standard model couplings and couplings to gravity.

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

    SciTech Connect

    Führer, Florian; Rigopoulos, Gerasimos E-mail: gerasimos.rigopoulos@ncl.ac.uk

    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.

  3. Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations

    NASA Astrophysics Data System (ADS)

    Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun

    2016-10-01

    Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m :-n electrolyte. A perturbation series is developed in terms of g =4 π κ b , where b a n d 1 /κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m ≠n ), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

  4. Renormalizing SMD: The Renormalization Approach and Its Use in Long Time Simulations and Accelerated PMF Calculations of Macromolecules

    PubMed Central

    Dryga, Anatoly; Warshel, Arieh

    2010-01-01

    Simulations of long time process in condensed phases in general and in biomolecules in particular, presents a major challenge that cannot be overcome at present by brute force molecular dynamics (MD) approaches. This work takes the renormalization method, intruded by us sometime ago, and establishes its reliability and potential in extending the time scale of molecular simulations. The validation involves a truncated gramicidin system in the gas phase that is small enough to allow very long explicit simulation and sufficiently complex to present the physics of realistic ion channels. The renormalization approach is found to be reliable and arguably presents the first approach that allows one to exploit the otherwise problematic steered molecular dynamics (SMD) treatments in quantitative and meaningful studies. It is established that we can reproduce the long time behavior of large systems by using Langevin dynamics (LD) simulations of a renormalized implicit model. This is done without spending the enormous time needed to obtain such trajectories in the explicit system. The present study also provides a promising advance in accelerated evaluation of free energy barriers. This is done by adjusting the effective potential in the implicit model to reproduce the same passage time as that obtained in the explicit model, under the influence of an external force. Here having a reasonable effective friction provides a way to extract the potential of mean force (PMF) without investing the time needed for regular PMF calculations. The renormalization approach, which is illustrated here in realistic calculations, is expected to provide a major help in studies of complex landscapes and in exploring long time dynamics of biomolecules. PMID:20836533

  5. 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.

  6. 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.

  7. The metric on field space, functional renormalization, and metric–torsion quantum gravity

    SciTech Connect

    Reuter, Martin Schollmeyer, Gregor M.

    2016-04-15

    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.

  8. Real Space Renormalization of Majorana Fermions in Quantum Nano-Wire Superconductors

    NASA Astrophysics Data System (ADS)

    Jafari, R.; Langari, A.; Akbari, Alireza; Kim, Ki-Seok

    2017-02-01

    We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As an example we focus on the Kitaev chain to investigate the topological quantum phase transition (TQPT) in the one-dimensional spinless p-wave superconductor. Studying the behaviour of local compressibility and ground-state fidelity, show that the TQPT is signalled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point are used as proper indicators for the TQPT, which signals the appearance of Majorana fermions. Finally, we present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the TQPT, which reveals two different scaling behaviors as we approach the critical point and thermodynamic limit.

  9. 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.

  10. Renormalized dynamics of the Dean-Kawasaki model.

    PubMed

    Bidhoodi, Neeta; Das, Shankar P

    2015-07-01

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

  11. Electronic Quasiparticle Renormalization on the Spin Wave Energy Scale

    NASA Astrophysics Data System (ADS)

    Schäfer, J.; Schrupp, D.; Rotenberg, Eli; Rossnagel, K.; Koh, H.; Blaha, P.; Claessen, R.

    2004-03-01

    High-resolution photoemission data of the (110) iron surface reveal the existence of well-defined metallic surface resonances in good correspondence to band calculations. Close to the Fermi level, their dispersion and momentum broadening display anomalies characteristic of quasiparticle renormalization due to coupling to bosonic excitations. Its energy scale exceeds that of phonons by far, and is in striking coincidence with that of the spin wave spectrum in iron. The self-energy behavior thus gives spectroscopic evidence of a quasiparticle mass enhancement due to electron-magnon coupling.

  12. 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.

  13. Renormalized entanglement entropy flow in mass-deformed ABJM theory

    NASA Astrophysics Data System (ADS)

    Kim, Kyung Kiu; Kwon, O.-Kab; Park, Chanyong; Shin, Hyeonjoon

    2014-08-01

    We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in (2+1)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in (2+1)-dimensions are consistent with the Zamolodchikov c-function proposed in (1+1)-dimensional conformal field theory.

  14. The Number Self-Consistent Renormalized Random Phase Approximation

    NASA Astrophysics Data System (ADS)

    Mariano, A.

    RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigen-values for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

  15. The Number Self-Consistent Renormalized Random Phase Approximation

    NASA Astrophysics Data System (ADS)

    Mariano, A.

    RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigenvalues for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

  16. The Number Self-Consistent Renormalized Random Phase Approximation

    NASA Astrophysics Data System (ADS)

    Mariano, A.

    2006-09-01

    RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigenvalues for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

  17. 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.

  18. Monte Carlo Reliability Analysis.

    DTIC Science & Technology

    1987-10-01

    to Stochastic Processes , Prentice-Hall, Englewood Cliffs, NJ, 1975. (5) R. E. Barlow and F. Proscham, Statistical TheorX of Reliability and Life...Lewis and Z. Tu, "Monte Carlo Reliability Modeling by Inhomogeneous ,Markov Processes, Reliab. Engr. 16, 277-296 (1986). (4) E. Cinlar, Introduction

  19. Landau quantization and Fermi velocity renormalization in twisted graphene bilayers

    NASA Astrophysics Data System (ADS)

    Yin, Long-Jing; Qiao, Jia-Bin; Wang, Wen-Xiao; Zuo, Wei-Jie; Yan, Wei; Xu, Rui; Dou, Rui-Fen; Nie, Jia-Cai; He, Lin

    2015-11-01

    Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction not only in different twisted bilayers, but also in twisted bilayers with the same rotation angle. Below the VHSs, the observed Landau quantization in the twisted bilayers is identical to that of massless Dirac fermions in graphene monolayer, which allows us to measure the Fermi velocity directly. Our result indicates that the Fermi velocity of the twisted bilayers depends remarkably on both the twisted angles and the interlayer coupling strengths. This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data.

  20. Block renormalization study on the nonequilibrium chiral Ising model.

    PubMed

    Kim, Mina; Park, Su-Chan; Noh, Jae Dong

    2015-01-01

    We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any u<1 exhibiting the power-law scaling of the characteristic length scale ξ∼t(1/z) and the domain-wall density ρ∼t(-δ). The scaling exponents z and δ were found to vary continuously with the parameter u. To establish the anomalous power-law scaling firmly, we perform the block renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.

  1. Theory and renormalization of the gauge-invariant effective action

    NASA Astrophysics Data System (ADS)

    Hart, C. F.

    1983-10-01

    The different methods for constructing a gauge-invariant effective action (GIEA) for quantum non-Abelian gauge field theories proposed by 't Hooft, DeWitt, Boulware, and Abbott are all shown to be equivalent. In the course of proving this equivalence we show how to extend the usual background-field method so as to construct what may be considered the prototypical GIEA and discuss in some detail the invariance and gauge transformation properties of both the usual theory and the new theory using the GIEA. All solutions to the GIEA field equations are shown to be physical-being solutions to the usual field equations with an arbitrary gauge condition. The renormalization program based upon the GIEA is shown to differ from the standard theory and we outline the modifications which are needed in the present proof of renormalizability. In particular we prove that the physical renormalization is independent of any gauge-fixing choice. Finally, we prove that the S-matrix elements derived from the GIEA for an arbitrary background-field solution to the field equations are the same as those derived using the usual effective action.

  2. 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.

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Bates, Jefferson E.; Furche, Filipp

    2013-11-01

    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.

  5. 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.

  6. Renormalization screening and collision-induced quantum interference in dense plasmas

    SciTech Connect

    Jung, Young-Dae; Rasheed, A.; Jamil, M.

    2014-07-15

    The influence of renormalization screening and collision-induced quantum interference in electron-electron collisions is investigated in partially ionized dense hydrogen plasmas. The effective interaction potential with the total spin-states of the collision system is considered to obtain the differential electron-electron scattering cross section. The results show that the renormalization plasma screening effect suppresses the electron-electron scattering cross section, including the quantum interference effect, especially, except for the forward and backward scattering directions. It is also shown that the renormalization plasma screening effect on the scattering cross section decreases with increasing collision energy. However, the renormalization screening effect is found to be important for the forward directions in the scattering cross section neglecting the quantum interference effect. The variations of the renormalization screening and collision-induced quantum interference effects are also discussed.

  7. Fundamentals of Monte Carlo

    SciTech Connect

    Wollaber, Allan Benton

    2016-06-16

    This is a powerpoint presentation which serves as lecture material for the Parallel Computing summer school. It goes over the fundamentals of the Monte Carlo calculation method. The material is presented according to the following outline: Introduction (background, a simple example: estimating π), Why does this even work? (The Law of Large Numbers, The Central Limit Theorem), How to sample (inverse transform sampling, rejection), and An example from particle transport.

  8. Monte Carlo eikonal scattering

    NASA Astrophysics Data System (ADS)

    Gibbs, W. R.; Dedonder, J. P.

    2012-08-01

    Background: The eikonal approximation is commonly used to calculate heavy-ion elastic scattering. However, the full evaluation has only been done (without the use of Monte Carlo techniques or additional approximations) for α-α scattering.Purpose: Develop, improve, and test the Monte Carlo eikonal method for elastic scattering over a wide range of nuclei, energies, and angles.Method: Monte Carlo evaluation is used to calculate heavy-ion elastic scattering for heavy nuclei including the center-of-mass correction introduced in this paper and the Coulomb interaction in terms of a partial-wave expansion. A technique for the efficient expansion of the Glauber amplitude in partial waves is developed.Results: Angular distributions are presented for a number of nuclear pairs over a wide energy range using nucleon-nucleon scattering parameters taken from phase-shift analyses and densities from independent sources. We present the first calculations of the Glauber amplitude, without further approximation, and with realistic densities for nuclei heavier than helium. These densities respect the center-of-mass constraints. The Coulomb interaction is included in these calculations.Conclusion: The center-of-mass and Coulomb corrections are essential. Angular distributions can be predicted only up to certain critical angles which vary with the nuclear pairs and the energy, but we point out that all critical angles correspond to a momentum transfer near 1 fm-1.

  9. Renormalization and Universality of Van der Waals forces

    NASA Astrophysics Data System (ADS)

    Ruiz Arriola, Enrique; Calle Cordón, Alvaro

    2010-04-01

    Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals force between neutral atoms. The dominance of the leading power law is highlighted both in the scattering as well as in the bound state problem. The role of off-shell two-body unitarity and causality within the Effective Field Theory framework on the light of universality and scaling at low energies is analyzed. Presented by E. Ruiz Arriola at 19th International IUPAP Conference On Few-Body Problems In Physics (FB 19) 31 Aug - 5 Sep 2009, Bonn, Germany

  10. Sorption kinetics considered as a renormalized diffusion process

    SciTech Connect

    Ravera, F.; Liggieri, L. ); Steinchen, A. )

    1993-03-01

    A theoretical study, of the sorption kinetics is performed by using a new approach in which the adsorption-desorption process is considered as an extended diffusion process with a renormalized diffusion coefficient taking into account an interfacial potential barrier. This model allows one to describe the time dependence of the process by considering both the crossing of an interfacial potential barrier and the diffusion in the neighboring phase. This model leads one to write an expression for the surface concentration as a function of the time, in terms of the molecular activation energies of adsorption and desorption. The possibility of using this theoretical approach to interpret experimental data of dynamic interfacial tension during the absorption at liquid-liquid and liquid-gas interfaces is discussed.

  11. Renormalization of vacuum expectation values in spontaneously broken gauge theories

    NASA Astrophysics Data System (ADS)

    Sperling, Marcus; Stöckinger, Dominik; Voigt, Alexander

    2013-07-01

    We compute one-loop and two-loop β-functions for vacuum expectation values (VEVs) in gauge theories. In R ξ gauge the VEVs renormalize differently from the respective scalar fields. We focus particularly on the origin and behaviour of this difference and show that it can be interpreted as the anomalous dimension of a certain scalar background field, leading to simple direct computation and qualitative understanding. The results are given for generic as well as supersymmetric gauge theories. These complement the set of well-known γ- and β-functions of Machacek/Vaughn. As an application, we compute the β-functions for VEVs and tan β in the MSSM, NMSSM, and E6SSM.

  12. Clothed particle representation in quantum field theory: Mass renormalization

    SciTech Connect

    Korda, V.Yu.; Shebeko, A.V.

    2004-10-15

    We consider the neutral pion and nucleon fields interacting via the pseudoscalar (PS) Yukawa-type coupling. The method of unitary clothing transformations is used to handle the so-called clothed particle representation, where the total field Hamiltonian and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled (at least, partly) by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands depend on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization. The present results prove to be equivalent to the results obtained by Feynman techniques.

  13. Improved quasi parton distribution through Wilson line renormalization

    NASA Astrophysics Data System (ADS)

    Chen, Jiunn-Wei; Ji, Xiangdong; Zhang, Jian-Hui

    2017-02-01

    Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a "mass" counterterm in the auxiliary z-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

  14. Renormalized stress-energy tensor for stationary black holes

    NASA Astrophysics Data System (ADS)

    Levi, Adam

    2017-01-01

    We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the t -splitting variant of the method, which was first presented for ⟨ϕ2⟩ren , to compute the RSET in a stationary, asymptotically flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.

  15. 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.

  16. Space and time renormalization in phase transition dynamics

    DOE PAGES

    Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; ...

    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. Space and time renormalization in phase transition dynamics

    SciTech Connect

    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 investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.

  18. Consistent regularization and renormalization in models with inhomogeneous phases

    NASA Astrophysics Data System (ADS)

    Adhikari, Prabal; Andersen, Jens O.

    2017-02-01

    In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in 1 +1 dimensions in the large-Nc limit and in the 3 +1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

  19. 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.

  20. 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.