Sample records for charge renormalization

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590

    2016-01-15

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

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

    PubMed

    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=4πκb, where band1/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.

  3. Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach.

    PubMed

    Camargo, Manuel; Téllez, Gabriel

    2008-04-07

    The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

  4. Charge independence, charge symmetry breaking in the S-wave nucleon-nucleon interaction, and renormalization

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Alvaro Calle Cordon,Manuel Pavon Valderrama,Enrique Ruiz Arriola

    2012-02-01

    We study the interplay between charge symmetry breaking and renormalization in the NN system for S-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.

  5. The quantum-field renormalization group in the problem of a growing phase boundary

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Antonov, N.V.; Vasil`ev, A.N.

    1995-09-01

    Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik`s assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants ({open_quotes}charge{close_quotes}). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundarymore » and time, {delta}{sub h} and {delta}{sub t}, which satisfy the exact relationship 2 {delta}{sub h}= {delta}{sub t} + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab.« less

  6. Renormalization-group constraints on Yukawa alignment in multi-Higgs-doublet models

    NASA Astrophysics Data System (ADS)

    Ferreira, P. M.; Lavoura, L.; Silva, João P.

    2010-05-01

    We write down the renormalization-group equations for the Yukawa-coupling matrices in a general multi-Higgs-doublet model. We then assume that the matrices of the Yukawa couplings of the various Higgs doublets to right-handed fermions of fixed quantum numbers are all proportional to each other. We demonstrate that, in the case of the two-Higgs-doublet model, this proportionality is preserved by the renormalization-group running only in the cases of the standard type-I, II, X, and Y models. We furthermore show that a similar result holds even when there are more than two Higgs doublets: the Yukawa-coupling matrices to fermions of a given electric charge remain proportional under the renormalization-group running if and only if there is a basis for the Higgs doublets in which all the fermions of a given electric charge couple to only one Higgs doublet.

  7. Fluctuation-enhanced electric conductivity in electrolyte solutions.

    PubMed

    Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

    2017-10-10

    We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

  8. Fluctuation-enhanced electric conductivity in electrolyte solutions

    PubMed Central

    Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

    2017-01-01

    We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

  9. Noncommutative Jackiw-Pi model: One-loop renormalization

    NASA Astrophysics Data System (ADS)

    Bufalo, R.; Ghasemkhani, M.; Alipour, M.

    2018-06-01

    In this paper, we study the quantum behavior of the noncommutative Jackiw-Pi model. After establishing the Becchi-Rouet-Store-Tyutin (BRST) invariant action, the perturbative renormalizability is discussed, allowing us to introduce the renormalized mass and gauge coupling. We then proceed to compute the one-loop correction to the basic 1PI functions, necessary to determine the renormalized parameters (mass and charge), next we discuss the physical behavior of these parameters.

  10. Fluctuation-enhanced electric conductivity in electrolyte solutions

    DOE PAGES

    Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

    2017-09-26

    In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

  11. Fluctuation-enhanced electric conductivity in electrolyte solutions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

    In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

  12. Sign Reversal of Coulom Interaction Between Two Quasiparticles in Momentum Space

    NASA Astrophysics Data System (ADS)

    Fan, J. D.; Malozovsky, Yuriy M.

    2013-06-01

    The main misconception regarding the interaction between quasiparticles stems from the assertion that the interaction energy between two quasiparticles is exactly identical to that of the renormalized interaction between two particles due to interparticle interaction in the Fermi system. If the main concept regarding the definition of quasiparticle as a weakly excited state of the Fermi system with conservation of charge and spin is paramount (except for the charge and spin separation models), the concept of the interaction between quasiparticles is very different from the assumption in the common sense. In this paper, we will prove a general theorem that the interaction between two quasiparticles is very much different from the renormalized interaction between two particles. The major difference lies in two places: the interaction between two quasiparticles is just negative to the renormalized interaction between two particles, and the interaction energy between the two particles is proportional to the product of two Fermi liquid renormalization factors. The result shed light on the reinterpretation of Cooper's pairing without invoking electron-photon interaction.

  13. Charge renormalization and inversion of a highly charged lipid bilayer: effects of dielectric discontinuities and charge correlations.

    PubMed

    Taheri-Araghi, Sattar; Ha, Bae-Yeun

    2005-08-01

    We reexamine the problem of charge renormalization and inversion of a highly charged surface of a low dielectric constant immersed in ionic solutions. To be specific, we consider an asymmetrically charged lipid bilayer, in which only one layer is negatively charged. In particular, we study how dielectric discontinuities and charge correlations (among lipid charges and condensed counterions) influence the effective charge of the surface. When counterions are monovalent (e.g., Na+), our mean-field approach implies that dielectric discontinuities can enhance counterion condensation. A simple scaling picture shows how the effects of dielectric discontinuities and surface-charge distributions are intertwined: Dielectric discontinuities diminish condensation if the backbone charge is uniformly smeared out while counterions are localized in space; they can, however, enhance condensation when the backbone charge is discrete. In the presence of asymmetric salts such as CaCl2 , we find that the correlation effect, treated at the Gaussian level, is more pronounced when the surface has a lower dielectric constant, inverting the sign of the charge at a smaller value of Ca2+ concentration.

  14. A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution

    NASA Astrophysics Data System (ADS)

    Krishnan, M.

    2017-05-01

    We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or rapid, reliable predictions are desired.

  15. Charged polymers in high dimensions

    NASA Technical Reports Server (NTRS)

    Kantor, Yacov

    1990-01-01

    A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

  16. Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi

    The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

  17. BPS-like bound and thermodynamics of the charged BTZ black hole

    NASA Astrophysics Data System (ADS)

    Cadoni, Mariano; Monni, Cristina

    2009-07-01

    The charged Bañados-Teitelboim-Zanelli (BTZ) black hole is plagued by several pathologies: (a) Divergent boundary terms are present in the action; hence, we have a divergent black-hole mass. (b) Once a finite, renormalized, mass M is defined, black-hole states exist for arbitrarily negative values of M. (c) There is no upper bound on the charge Q. We show that these pathological features are an artifact of the renormalization procedure. They can be completely removed by using an alternative renormalization scheme leading to a different definition M0 of the black-hole mass, which is the total energy inside the horizon. The new mass satisfies a BPS-like bound M0≥(π)/(2)Q2, and the heat capacity of the hole is positive. We also discuss the black-hole thermodynamics that arises when M0 is interpreted as the internal energy of the system. We show, using three independent approaches (black-hole thermodynamics, Einstein equations, and Euclidean action formulation), that M0 satisfies the first law if a term describing the mechanical work done by the electrostatic pressure is introduced.

  18. Effects of long-range interactions on curvature energies of viral shells

    NASA Astrophysics Data System (ADS)

    Shojaei, Hamid R.; Božič, Anže Lošdorfer; Muthukumar, Murugappan; Podgornik, Rudolf

    2016-05-01

    We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.

  19. Topological terms, AdS2 n gravity, and renormalized entanglement entropy of holographic CFTs

    NASA Astrophysics Data System (ADS)

    Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

    2018-05-01

    We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS /CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2 n -dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

  20. Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

    NASA Astrophysics Data System (ADS)

    Lee, Yu-Wen; Lee, Yu-Li

    2018-01-01

    We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

  1. Physical renormalization condition for de Sitter QED

    NASA Astrophysics Data System (ADS)

    Hayashinaka, Takahiro; Xue, She-Sheng

    2018-05-01

    We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions including the identical asymptotic behavior of the scalar and spinor currents, the removal of the IR hyperconductivity from the scalar current, and the finite current for the massless fermion.

  2. Effective electrostatic interactions among charged thermo-responsive microgels immersed in a simple electrolyte

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    González-Mozuelos, P.

    This work explores the nature and thermodynamic behavior of the effective electrostatic interactions among charged microgels immersed in a simple electrolyte, taking special interest in the effects due to the thermally induced variation of the microgel size while the remaining parameters (microgel charge and concentration, plus the amount of added salt) are kept constant. To this end, the rigorous approach obtained from applying the precise methodology of the dressed ion theory to the proper definition of the effective direct correlation functions, which emerge from tracing-out the degrees of freedom of the microscopic ions, is employed to provide an exact descriptionmore » of the parameters characterizing such interactions: screening length, effective permittivity, and renormalized charges. A model solution with three components is assumed: large permeable anionic spheres for the microgels, plus small charged hard spheres of equal size for the monovalent cations and anions. The two-body correlations among the components of this model suspension, used as the input for the determination of the effective interaction parameters, are here calculated by using the hyper-netted chain approximation. It is then found that at finite microgel concentrations the values of these parameters change as the microgel size increases, even though the ionic strength of the supporting electrolyte and the bare charge of the microgels remain fixed during this process. The variation of the screening length, as well as that of the effective permittivity, is rather small, but still interesting in view of the fact that the corresponding Debye length stays constant. The renormalized charges, in contrast, increase markedly as the microgels swell. The ratio of the renormalized charge to the corresponding analytic result obtained in the context of an extended linear response theory allows us to introduce an effective charge that accounts for the non-linear effects induced by the short-ranged association of microions to the microgels. The behavior of these effective charges as a function of the amount of added salt and the macroion charge, size, and concentration reveals the interplay among all these system parameters.« less

  3. Electron-lattice interactions strongly renormalize the charge-transfer energy in the spin-chain cuprate Li 2CuO 2

    DOE PAGES

    Johnston, Steve; Monney, Claude; Bisogni, Valentina; ...

    2016-02-17

    Strongly correlated insulators are broadly divided into two classes: Mott–Hubbard insulators, where the insulating gap is driven by the Coulomb repulsion U on the transition-metal cation, and charge-transfer insulators, where the gap is driven by the charge-transfer energy Δ between the cation and the ligand anions. The relative magnitudes of U and Δ determine which class a material belongs to, and subsequently the nature of its low-energy excitations. These energy scales are typically understood through the local chemistry of the active ions. Here we show that the situation is more complex in the low-dimensional charge-transfer insulator Li 2CuO 2, wheremore » Δ has a large non-electronic component. Combining resonant inelastic X-ray scattering with detailed modelling, we determine how the elementary lattice, charge, spin and orbital excitations are entangled in this material. This results in a large lattice-driven renormalization of Δ, which significantly reshapes the fundamental electronic properties of Li 2CuO 2.« less

  4. Renormalized Energy Concentration in Random Matrices

    NASA Astrophysics Data System (ADS)

    Borodin, Alexei; Serfaty, Sylvia

    2013-05-01

    We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, 2012; 1D log-gases and the renormalized energy, 2013). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.

  5. The Poisson-Boltzmann theory for the two-plates problem: some exact results.

    PubMed

    Xing, Xiang-Jun

    2011-12-01

    The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

  6. A simple derivation of Lorentz self-force

    NASA Astrophysics Data System (ADS)

    Haque, Asrarul

    2014-09-01

    We derive the Lorentz self-force for a charged particle in arbitrary non-relativistic motion by averaging the retarded fields. The derivation is simple and at the same time pedagogically accessible. We obtain the radiation reaction for a charged particle moving in a circle. We pin down the underlying concept of mass renormalization.

  7. Amplitude-Mode Spectroscopy of Charge Excitations in PTB7 π -Conjugated Donor-Acceptor Copolymer for Photovoltaic Applications

    NASA Astrophysics Data System (ADS)

    Baniya, Sangita; Vardeny, Shai R.; Lafalce, Evan; Peygambarian, Nasser; Vardeny, Z. Valy

    2017-06-01

    We measure the spectra of resonant Raman scattering and doping-induced absorption of pristine films of the π -conjugated donor-acceptor (D -A ) copolymer, namely, thieno[3,4 b]thiophene-alt-benzodithiophene (PTB7), as well as photoinduced absorption spectrum in a blend of PTB7 with fullerene phenyl-C61-butyric acid methyl ester molecules used for organic photovoltaic (OPV) applications. We find that the D -A copolymer contains six strongly coupled vibrational modes having relatively strong Raman-scattering intensity, which are renormalized upon adding charge polarons onto the copolymer chains either by doping or photogeneration. Since the lower-energy charge-polaron absorption band overlaps with the renormalized vibrational modes, they appear as antiresonance lines superposed onto the induced polaron absorption band in the photoinduced absorption spectrum but less so in the doping-induced absorption spectrum. We show that the Raman-scattering, doping-, and photoinduced absorption spectra of PTB7 are well explained by the amplitude mode model, where a single vibrational propagator describes the renormalized modes and their related intensities in detail. From the relative strengths of the induced infrared activity of the polaron-related vibrations and electronic transitions, we obtain the polaron effective kinetic mass in PTB7 using the amplitude mode model to be approximately 3.8 m* , where m* is the electron effective mass. The enhanced polaronic mass in PTB7 may limit the charge mobility, which, in turn, reduces the OPV solar-cell efficiency based on the PTB7-fullerene blend.

  8. Is the Luttinger Liquid a New State of Matter?

    NASA Astrophysics Data System (ADS)

    Afonin, V. V.; Petrov, V. Y.

    2010-02-01

    We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau’s theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.

  9. Charge and Spin Dynamics of the Hubbard Chains

    NASA Technical Reports Server (NTRS)

    Park, Youngho; Liang, Shoudan

    1999-01-01

    We calculate the local correlation functions of charge and spin for the one-chain and two-chain Hubbard model using density matrix renormalization group method and the recursion technique. Keeping only finite number of states we get good accuracy for the low energy excitations. We study the charge and spin gaps, bandwidths and weights of the spectra for various values of the on-site Coulomb interaction U and the electron filling. In the low energy part, the local correlation functions are different for the charge and spin. The bandwidths are proportional to t for the charge and J for the spin respectively.

  10. Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis

    NASA Astrophysics Data System (ADS)

    Tsuchiizu, Masahisa; Kawaguchi, Kouki; Yamakawa, Youichi; Kontani, Hiroshi

    2018-04-01

    Recently, complex rotational symmetry-breaking phenomena have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various unconventional charge susceptibilities in an unbiased way by applying the functional-renormalization-group method to the d -p Hubbard model. Without assuming the wave vector of the order parameter, we reveal that the most dominant instability is the uniform (q =0 ) charge modulation on the px and py orbitals, which possesses d symmetry. This uniform nematic order triggers another nematic p -orbital density wave along the axial (Cu-Cu) direction at Qa≈(π /2 ,0 ) . It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at q =Qa is triggered by the uniform order. The predicted multistage nematic transitions are caused by Aslamazov-Larkin-type fluctuation-exchange processes.

  11. Universality for shape dependence of Casimir effects from Weyl anomaly

    NASA Astrophysics Data System (ADS)

    Miao, Rong-Xin; Chu, Chong-Sun

    2018-03-01

    We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We also test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization. Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

  12. Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

    PubMed

    Tsiper, E V

    2006-08-18

    The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

  13. Antiferromagnetism, charge density wave, and d-wave superconductivity in the extended t-J-U model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory.

    PubMed

    Abram, M; Zegrodnik, M; Spałek, J

    2017-09-13

    In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.

  14. Nucleon scalar and tensor charges using lattice QCD simulations at the physical value of the pion mass

    NASA Astrophysics Data System (ADS)

    Alexandrou, C.; Constantinou, M.; Dimopoulos, P.; Frezzotti, R.; Hadjiyiannakou, K.; Jansen, K.; Kallidonis, C.; Kostrzewa, B.; Koutsou, G.; Mangin-Brinet, M.; Vaquero Avilès-Casco, A.; Wenger, U.

    2017-06-01

    We present results on the light, strange and charm nucleon scalar and tensor charges from lattice QCD, using simulations with Nf=2 flavors of twisted mass clover-improved fermions with a physical value of the pion mass. Both connected and disconnected contributions are included, enabling us to extract the isoscalar, strange and charm charges for the first time directly at the physical point. Furthermore, the renormalization is computed nonperturbatively for both isovector and isoscalar quantities. We investigate excited state effects by analyzing several sink-source time separations and by employing a set of methods to probe ground state dominance. Our final results for the scalar charges are gSu=5.20 (42 )(15 )(12 ), gSd=4.27 (26 )(15 )(12 ), gSs=0.33 (7 )(1 )(4 ), and gSc=0.062 (13 )(3 )(5 ) and for the tensor charges gTu=0.794 (16 )(2 )(13 ), gTd=-0.210 (10 )(2 )(13 ), gTs=0.00032 (24 )(0 ), and gTc=0.00062 (85 )(0 ) in the MS ¯ scheme at 2 GeV. The first error is statistical, the second is the systematic error due to the renormalization and the third the systematic arising from estimating the contamination due to the excited states, when our data are precise enough to probe the first excited state.

  15. Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

    PubMed Central

    Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

    2016-01-01

    The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363

  16. Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

    NASA Astrophysics Data System (ADS)

    Fang, Tie-Feng; Guo, Ai-Min; Sun, Qing-Feng

    2018-06-01

    We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction U is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing a negative-U charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. 8, 395 (2017), 10.1038/s41467-017-00495-7].

  17. Scalar quantum electrodynamics via Duffin-Kemmer-Petiau gauge theory in the Heisenberg picture: Vacuum polarization

    NASA Astrophysics Data System (ADS)

    Beltran, J.; Maia, N. T.; Pimentel, B. M.

    2018-04-01

    Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization.

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  19. Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states.

    PubMed

    Iftikhar, Z; Jezouin, S; Anthore, A; Gennser, U; Parmentier, F D; Cavanna, A; Pierre, F

    2015-10-08

    Many-body correlations and macroscopic quantum behaviours are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo effect, which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems and can be explored with tunable nanostructures. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum. Here we demonstrate the previously elusive 'charge' Kondo effect in a hybrid metal-semiconductor implementation of a single-electron transistor, with a quantum pseudospin of 1/2 constituted by two degenerate macroscopic charge states of a metallic island. In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel, thereby providing unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics. Using a weakly coupled probe, we find the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point. Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality.

  20. Gauge mediation scenario with hidden sector renormalization in MSSM

    NASA Astrophysics Data System (ADS)

    Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika

    2010-02-01

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

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gu Zhengcheng; Wen Xiaogang

    2009-10-15

    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 T{sub inv} plus the symmetry group G{sub sym} 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, asmore » 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 (G{sub sym},T{sub inv}) 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 (G{sub sym},T{sub inv}) 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.« less

  2. Charge transfer polarisation wave and carrier pairing in the high T(sub c) copper oxides

    NASA Technical Reports Server (NTRS)

    Chakraverty, B. K.

    1990-01-01

    The High T(sub c) oxides are highly polarizable materials and are charge transfer insulators. The charge transfer polarization wave formalism is developed in these oxides. The dispersion relationships due to long range dipole-dipole interaction of a charge transfer dipole lattice are obtained in 3-D and 2-D. These are high frequency bosons and their coupling with carriers is weak and antiadiabatic in nature. As a result, the mass renormalization of the carriers is negligible in complete contrast to conventional electron-phonon interaction, that give polarons and bipolarons. Both bound and superconducting pairing is discussed for a model Hamiltonian valid in the antiadiabatic regime, both in 3-D and 2-D. The stability of the charge transfer dipole lattice has interesting consequences that are discussed.

  3. Nuclear axial currents in chiral effective field theory

    DOE PAGES

    Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; ...

    2016-01-11

    Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less

  4. Non-local geometry inside Lifshitz horizon

    NASA Astrophysics Data System (ADS)

    Hu, Qi; Lee, Sung-Sik

    2017-07-01

    Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

  5. Renormalization of the weak hadronic current in the nuclear medium

    NASA Astrophysics Data System (ADS)

    Siiskonen, T.; Hjorth-Jensen, M.; Suhonen, J.

    2001-05-01

    The renormalization of the weak charge-changing hadronic current as a function of the reaction energy release is studied at the nucleonic level. We have calculated the average quenching factors for each type of current (vector, axial vector, and induced pseudoscalar). The obtained quenching in the axial vector part is, at zero momentum transfer, 19% for the 1s0d shell and 23% in the 1p0f shell. We have extended the calculations also to heavier systems such as 56Ni and 100Sn, where we obtain stronger quenchings, 44% and 59%, respectively. Gamow-Teller-type transitions are discussed, along with the higher-order matrix elements. The quenching factors are constant up to roughly 60 MeV momentum transfer. Therefore the use of energy-independent quenching factors in beta decay is justified. We also found that going beyond the zeroth and first order operators (in inverse nucleon mass) does not give any substantial contribution. The extracted renormalization to the ratio CP/CA at q=100 MeV is -3.5%, -7.1%, -28.6%, and +8.7% for mass 16, 40, 56, and 100, respectively.

  6. The long flow to freedom

    DOE PAGES

    Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan; ...

    2017-02-10

    Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one)more » and a non-zero Fayet-Iliopoulos term, and pure SU( N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. As a result, we expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.« less

  7. Cosmological constant and quantum gravitational corrections to the running fine structure constant.

    PubMed

    Toms, David J

    2008-09-26

    The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.

  8. Origin of the 1 eV-reflectivity edges in high-T c superconducting cuprates

    NASA Astrophysics Data System (ADS)

    Tajima, S.; Uchida, S.; Kaneko, T.; Tomeno, I.; Kosuge, M.; Yamauchi, H.; Koshizuka, N.

    1992-05-01

    The reflectivity edge commonly observed at around 1 eV in the optical spectrum is investigated for a number of high- Tc superconducting cuprates. We have found that the edge energy ( ωedge) is almost independent of doping concentration in each material but varies widely among the materials dependent on the average CuO 2-plane spacing d c. This is consistent with a view supposing that the observed reflectivity edge corresponds to the plasma edge associated with the renormalized two-dimensional band, which would be nearly half-filled and has been reconstructed on doping from the gap-separated states of the charge transfer insulator as a result of reduced renormalization. We could not find a universal correlation between Tc and ω'p2.

  9. Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field [rapid communication

    NASA Astrophysics Data System (ADS)

    Yao, K. L.; Li, Y. C.; Sun, X. Z.; Liu, Q. M.; Qin, Y.; Fu, H. H.; Gao, G. Y.

    2005-10-01

    By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge charge and spin spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge charge and the spin spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute.

  10. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Krebs, H., E-mail: hermann.krebs@rub.de; Epelbaum, E., E-mail: evgeny.epelbaum@rub.de; Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016

    We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of themore » continuity equation.« less

  11. DMRG study of fractional quantum Hall effect and valley skyrmions in graphene

    NASA Astrophysics Data System (ADS)

    Shibata, Naokazu

    2011-12-01

    The ground state and low-energy excitations of graphene and its bilayer are investigated by the density matrix renormalization group (DMRG) method. We analyze the effect of Coulomb interaction between the electrons including valley degrees of freedoms. The obtained results show finite charge excitation gap at various fractional fillings νn = 1/3, 2/5, 2/3 in the n = 0 and 1 Landau levels of single-layer graphene (SLG) and n = 2 Landau level of bilayer graphene (BLG). The lowest charge excitations at ν = 1/3, and 1 in SLG are valley skyrmions.

  12. Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

    DOE PAGES

    Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

    2017-06-06

    Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

  13. Resilience of the quantum Rabi model in circuit QED

    NASA Astrophysics Data System (ADS)

    E Manucharyan, Vladimir; Baksic, Alexandre; Ciuti, Cristiano

    2017-07-01

    In circuit quantum electrodynamics (circuit QED), an artificial ‘circuit atom’ can couple to a quantized microwave radiation much stronger than its real atomic counterpart. The celebrated quantum Rabi model describes the simplest interaction of a two-level system with a single-mode boson field. When the coupling is large enough, the bare multilevel structure of a realistic circuit atom cannot be ignored even if the circuit is strongly anharmonic. We explored this situation theoretically for flux (fluxonium) and charge (Cooper pair box) type multi-level circuits tuned to their respective flux/charge degeneracy points. We identified which spectral features of the quantum Rabi model survive and which are renormalized for large coupling. Despite significant renormalization of the low-energy spectrum in the fluxonium case, the key quantum Rabi feature—nearly-degenerate vacuum consisting of an atomic state entangled with a multi-photon field—appears in both types of circuits when the coupling is sufficiently large. Like in the quantum Rabi model, for very large couplings the entanglement spectrum is dominated by only two, nearly equal eigenvalues, in spite of the fact that a large number of bare atomic states are actually involved in the atom-resonator ground state. We interpret the emergence of the two-fold degeneracy of the vacuum of both circuits as an environmental suppression of flux/charge tunneling due to their dressing by virtual low-/high-impedance photons in the resonator. For flux tunneling, the dressing is nothing else than the shunting of a Josephson atom with a large capacitance of the resonator. Suppression of charge tunneling is a manifestation of the dynamical Coulomb blockade of transport in tunnel junctions connected to resistive leads.

  14. The generalized scheme-independent Crewther relation in QCD

    NASA Astrophysics Data System (ADS)

    Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.

    2017-07-01

    The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton-nucleon scattering times the Adler function, defined from the cross section for electron-positron annihilation into hadrons, has no pQCD radiative corrections. The ;Generalized Crewther Relation; relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd (Q) =∑i≥1 αˆg1 i (Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.

  15. Chemical-potential flow equations for graphene with Coulomb interactions

    NASA Astrophysics Data System (ADS)

    Fräßdorf, Christian; Mosig, Johannes E. M.

    2018-06-01

    We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results are consistent with a charge carrier-independent Fermi velocity v (k ) for small densities n ≲k2/π , supporting the comparison of the zero-density fRG calculation of Bauer et al. [Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409], with the experiment of Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].

  16. Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

    NASA Astrophysics Data System (ADS)

    Caldeira Costa, R. N.

    2012-11-01

    In this work we elaborate on an extension of the AdS/CFT framework to a sub-class of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.

  17. Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

    NASA Astrophysics Data System (ADS)

    Varjas, Daniel; Zaletel, Michael; Moore, Joel

    2014-03-01

    We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

  18. Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

    NASA Astrophysics Data System (ADS)

    Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

    2013-10-01

    We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

  19. Numerical renormalization group method for entanglement negativity at finite temperature

    NASA Astrophysics Data System (ADS)

    Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

    2018-04-01

    We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

  20. Ab initio estimates of the size of the observable universe

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Page, Don N., E-mail: profdonpage@gmail.com

    2011-09-01

    When one combines multiverse predictions by Bousso, Hall, and Nomura for the observed age and size of the universe in terms of the proton and electron charge and masses with anthropic predictions of Carter, Carr, and Rees for these masses in terms of the charge, one gets that the age of the universe should be roughly the inverse 64th power, and the cosmological constant should be around the 128th power, of the proton charge. Combining these with a further renormalization group argument gives a single approximate equation for the proton charge, with no continuous adjustable or observed parameters, and withmore » a solution that is within 8% of the observed value. Using this solution gives large logarithms for the age and size of the universe and for the cosmological constant that agree with the observed values within 17%.« less

  1. Generation of a Nernst Current from the Conformal Anomaly in Dirac and Weyl Semimetals

    NASA Astrophysics Data System (ADS)

    Chernodub, M. N.; Cortijo, Alberto; Vozmediano, María A. H.

    2018-05-01

    We show that a conformal anomaly in Weyl and Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material. We discuss the experimental feasibility of the proposed phenomenon.

  2. Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

    NASA Astrophysics Data System (ADS)

    Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.

    2016-03-01

    We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

  3. One-dimensional Kondo lattice model at quarter filling

    NASA Astrophysics Data System (ADS)

    Xavier, J. C.; Miranda, E.

    2008-10-01

    We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the J1-J2 Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.

  4. Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

    NASA Astrophysics Data System (ADS)

    Pillay, Jason C.; McCulloch, Ian P.

    2018-05-01

    The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

  5. Coulomb energy of uniformly charged spheroidal shell systems.

    PubMed

    Jadhao, Vikram; Yao, Zhenwei; Thomas, Creighton K; de la Cruz, Monica Olvera

    2015-03-01

    We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.

  6. Effective dynamics of a classical point charge

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

    2014-03-15

    The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

  7. Renormalization group and Ward identities for infrared QED4

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mastropietro, Vieri

    2007-10-15

    A regularized version of Euclidean QED4 in the Feynman gauge is considered, with a fixed ultraviolet cutoff, photon mass of the size of the cutoff, and any value, including zero, of the electron mass. We will prove that the Schwinger functions are expressed by convergent series for small values of the charge and verify the Ward identities, up to corrections which are small for momentum scales far from the ultraviolet cutoff.

  8. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bes, D. R.; Civitarese, O.

    The experimental information on isospin-spin excitations around {sup 58}Ni is analyzed by using isoscalar and isovector pairing vibrations, Gamow-Teller (GT) modes, and their couplings. It is found that the proposed coupling scheme accounts for a sizable amount of the strength associated with isospin-spin excitations, which include transitions to both one- and two-phonon states. The calculations are performed within the framework of perturbation theory, accounting for the renormalization of the charge by the collective GT excitations.

  9. Charge modulation as fingerprints of phase-string triggered interference

    NASA Astrophysics Data System (ADS)

    Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen; Qi, Yang; Weng, Zheng-Yu; Zaanen, Jan

    2015-07-01

    Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t -J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

  10. Genesis of charge orders in high temperature superconductors

    PubMed Central

    Tu, Wei-Lin; Lee, Ting-Kuo

    2016-01-01

    One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy. PMID:26732076

  11. Focus Article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges

    NASA Astrophysics Data System (ADS)

    Kjellander, Roland

    2018-05-01

    A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed.

  12. Asymptotically safe standard model extensions?

    NASA Astrophysics Data System (ADS)

    Pelaggi, Giulio Maria; Plascencia, Alexis D.; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

    2018-05-01

    We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1 /NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

  13. Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Livshits, Gideon I., E-mail: livshits.gideon@mail.huji.ac.il

    2014-02-15

    Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBLmore » superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.« less

  14. AdS 2 holographic dictionary

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cvetic, Mirjam; Papadimitriou, Ioannis

    Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetriesmore » and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, the four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries’, while those obtained from the uplift of the constant dilaton ones are new.« less

  15. AdS 2 holographic dictionary

    DOE PAGES

    Cvetic, Mirjam; Papadimitriou, Ioannis

    2016-12-02

    Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetriesmore » and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, the four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries’, while those obtained from the uplift of the constant dilaton ones are new.« less

  16. The generalized scheme-independent Crewther relation in QCD

    DOE PAGES

    Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; ...

    2017-05-10

    The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

  17. The generalized scheme-independent Crewther relation in QCD

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang

    The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

  18. Valence and charge-transfer optical properties for some SinCm (m, n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy

    NASA Astrophysics Data System (ADS)

    Lutz, Jesse J.; Duan, Xiaofeng F.; Ranasinghe, Duminda S.; Jin, Yifan; Margraf, Johannes T.; Perera, Ajith; Burggraf, Larry W.; Bartlett, Rodney J.

    2018-05-01

    Accurate optical characterization of the closo-Si12C12 molecule is important to guide experimental efforts toward the synthesis of nano-wires, cyclic nano-arrays, and related array structures, which are anticipated to be robust and efficient exciton materials for opto-electronic devices. Working toward calibrated methods for the description of closo-Si12C12 oligomers, various electronic structure approaches are evaluated for their ability to reproduce measured optical transitions of the SiC2, Si2Cn (n = 1-3), and Si3Cn (n = 1, 2) clusters reported earlier by Steglich and Maier [Astrophys. J. 801, 119 (2015)]. Complete-basis-limit equation-of-motion coupled-cluster (EOMCC) results are presented and a comparison is made between perturbative and renormalized non-iterative triples corrections. The effect of adding a renormalized correction for quadruples is also tested. Benchmark test sets derived from both measurement and high-level EOMCC calculations are then used to evaluate the performance of a variety of density functionals within the time-dependent density functional theory (TD-DFT) framework. The best-performing functionals are subsequently applied to predict valence TD-DFT excitation energies for the lowest-energy isomers of SinC and Sin-1C7-n (n = 4-6). TD-DFT approaches are then applied to the SinCn (n = 4-12) clusters and unique spectroscopic signatures of closo-Si12C12 are discussed. Finally, various long-range corrected density functionals, including those from the CAM-QTP family, are applied to a charge-transfer excitation in a cyclic (Si4C4)4 oligomer. Approaches for gauging the extent of charge-transfer character are also tested and EOMCC results are used to benchmark functionals and make recommendations.

  19. Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

    NASA Astrophysics Data System (ADS)

    Fugger, Delia M.; Dorda, Antonius; Schwarz, Frauke; von Delft, Jan; Arrigoni, Enrico

    2018-01-01

    We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B. We investigate the interplay between the shift ({ω }B) of the Kondo peak in the spin-resolved density of states (DOS) and the one ({φ }B) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as {φ }B only for | g| {μ }BB\\gg {k}B{T}K. Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

  20. Asymptotics of surface-plasmon redshift saturation at subnanometric separations

    NASA Astrophysics Data System (ADS)

    Schnitzer, Ory; Giannini, Vincenzo; Craster, Richard V.; Maier, Stefan A.

    2016-01-01

    Many promising nanophotonics endeavors hinge upon the unique plasmonic properties of nanometallic structures with narrow nonmetallic gaps, which support superconcentrated bonding modes that singularly redshift with decreasing separations. In this Rapid Communication, we present a descriptive physical picture, complemented by elementary asymptotic formulas, of a nonlocal mechanism for plasmon redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalization of the corresponding local ones. Specifically, the renormalization furnishes an asymptotic plasmon-frequency lower bound that scales with the 1 /4 power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.

  1. Global phase diagram of the spinless Falicov-Kimball model in d = 3 : renormalization-group theory

    NASA Astrophysics Data System (ADS)

    Sariyer, Ozan S.; Hinczewski, Michael; Berker, A. Nihat

    2011-03-01

    The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The phase boundaries are second order, except for an intermediate interaction regime, where a first-order phase boundary between two CO phases occurs. The first-order phase boundary is delimited by special bicritical points. The cross-sections of the global phase diagram with respect to the chemical potentials of the localized and mobile electrons, at all representative interaction and hopping strengths, are calculated and exhibit three distinct topologies. The phase diagrams with respect to electron densities are also calculated. This research was supported by the Alexander von Humboldt Foundation, the Scientific and Technological Research Council of Turkey (TÜBITAK), and the Academy of Sciences of Turkey.

  2. Coulomb Blockade and Multiple Andreev Reflection in a Superconducting Single-Electron Transistor

    NASA Astrophysics Data System (ADS)

    Lorenz, Thomas; Sprenger, Susanne; Scheer, Elke

    2018-06-01

    In superconducting quantum point contacts, multiple Andreev reflection (MAR), which describes the coherent transport of m quasiparticles each carrying an electron charge with m≥3, sets in at voltage thresholds eV = 2Δ /m. In single-electron transistors, Coulomb blockade, however, suppresses the current at low voltage. The required voltage for charge transport increases with the square of the effective charge eV∝ ( me) ^2. Thus, studying the charge transport in all-superconducting single-electron transistors (SSETs) sets these two phenomena into competition. In this article, we present the fabrication as well as a measurement scheme and transport data for a SSET with one junction in which the transmission and thereby the MAR contributions can be continuously tuned. All regimes from weak to strong coupling are addressed. We extend the Orthodox theory by incorporating MAR processes to describe the observed data qualitatively. We detect a new transport process the nature of which is unclear at present. Furthermore, we observe a renormalization of the charging energy when approaching the strong coupling regime.

  3. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen

    Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high T c cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t - J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. Wemore » demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.« less

  4. Fermionic Schwinger effect and induced current in de Sitter space

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hayashinaka, Takahiro; Department of Physics, Graduate School of Science, The University of Tokyo,Bunkyo-ku, Tokyo, 113-0033; Fujita, Tomohiro

    We explore Schwinger effect of spin 1/2 charged particles with static electric field in 1+3 dimensional de Sitter spacetime. We analytically calculate the vacuum expectation value of the spinor current which is induced by the produced particles in the electric field. The renormalization is performed with the adiabatic subtraction scheme. We find that the current becomes negative, namely it flows in the direction opposite to the electric field, if the electric field is weaker than a certain threshold value depending on the fermion mass, which is also known to happen in the case of scalar charged particles in 1+3 demore » Sitter spacetime. Contrary to the scalar case, however, the IR hyperconductivity is absent in the spinor case.« less

  5. Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

    DOE PAGES

    Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor

    2015-05-22

    Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model).We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chainmore » acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U = 0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. In conclusion, our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.« less

  6. Photoinduced Bandgap Renormalization and Exciton Binding Energy Reduction in WS2.

    PubMed

    Cunningham, Paul D; Hanbicki, Aubrey T; McCreary, Kathleen M; Jonker, Berend T

    2017-12-26

    Strong Coulomb attraction in monolayer transition metal dichalcogenides gives rise to tightly bound excitons and many-body interactions that dominate their optoelectronic properties. However, this Coulomb interaction can be screened through control of the surrounding dielectric environment as well as through applied voltage, which provides a potential means of tuning the bandgap, exciton binding energy, and emission wavelength. Here, we directly show that the bandgap and exciton binding energy can be optically tuned by means of the intensity of the incident light. Using transient absorption spectroscopy, we identify a sub-picosecond decay component in the excited-state dynamics of WS 2 that emerges for incident photon energies above the A-exciton resonance, which originates from a nonequilibrium population of charge carriers that form excitons as they cool. The generation of this charge-carrier population exhibits two distinct energy thresholds. The higher threshold is coincident with the onset of continuum states and therefore provides a direct optical means of determining both the bandgap and exciton binding energy. Using this technique, we observe a reduction in the exciton binding energy from 310 ± 30 to 220 ± 20 meV as the excitation density is increased from 3 × 10 11 to 1.2 × 10 12 photons/cm 2 . This reduction is due to dynamic dipolar screening of Coulomb interactions by excitons, which is the underlying physical process that initiates bandgap renormalization and leads to the insulator-metal transition in monolayer transition metal dichalcogenides.

  7. Exact phase boundaries and topological phase transitions of the X Y Z spin chain

    NASA Astrophysics Data System (ADS)

    Jafari, S. A.

    2017-07-01

    Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

  8. Horizon as critical phenomenon

    NASA Astrophysics Data System (ADS)

    Lee, Sung-Sik

    2016-09-01

    We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U( N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

  9. 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.

  10. Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

    NASA Astrophysics Data System (ADS)

    Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

    2017-05-01

    We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

  11. Two-leg ladder systems with dipole–dipole Fermion interactions

    NASA Astrophysics Data System (ADS)

    Mosadeq, Hamid; Asgari, Reza

    2018-05-01

    The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole–dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole–dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.

  12. Superconductivity on the brink of spin-charge order in doped honeycomb bilayer

    NASA Astrophysics Data System (ADS)

    Vafek, Oskar; Murray, James; Cvetkovic, Vladimir

    2014-03-01

    Using a controlled weak-coupling renormalization group approach, we establish the mechanism of unconventional superconductivity in the vicinity of spin or charge ordered excitonic states for the case of electrons on the Bernal stacked bilayer honeycomb lattice. With one electron per site this system exhibits nearly parabolically touching conduction and valence bands. Such a state is unstable towards a spontaneous symmetry breaking, and repulsive interactions favor excitonic order, such as a charge nematic and/or a layer antiferromagnet. We find that upon adding charge carriers to the system, the excitonic order is suppressed, and unconventional superconductivity appears in its place, before it is replaced by a Fermi liquid. We focus on firmly establishing this phenomenon using the RG formalism within an idealized model with parabolic touching. This work was supported by the NSF CAREER award under Grant No. DMR-0955561 (OV), NSF Cooperative Agreement No. DMR-0654118, and the State of Florida (OV,JM,CV), as well as by ICAM-I2CAM (NSF grant DMR-0844115) and by DoE Award DE-FG02-08ER46544 (JM).

  13. Exactly solvable model of the two-dimensional electrical double layer.

    PubMed

    Samaj, L; Bajnok, Z

    2005-12-01

    We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

  14. Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

    NASA Astrophysics Data System (ADS)

    Kais, S.; Bleil, R.

    1995-05-01

    We develop a systematic way to determine an effective nuclear charge ZRD such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z=2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ˜0.2% for Z=2 to ˜0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N=3-18, Z=3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

  15. Local renormalization group functions from quantum renormalization group and holographic bulk locality

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nakayama, Yu

    Here, the bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographicmore » renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.« less

  16. Spin-orbital model of stoichiometric LaMnO3 with tetragonal distortions

    NASA Astrophysics Data System (ADS)

    Snamina, Mateusz; Oleś, Andrzej M.

    2018-03-01

    The spin-orbital superexchange model is derived for the cubic (perovskite) symmetry of LaMnO3, whereas real crystal structure is strongly deformed. We identify and explain three a priori important physical effects arising from tetragonal deformation: (i) the splitting of eg orbitals ∝Ez , (ii) the directional renormalization of d -p hybridization tp d, and (iii) the directional renormalization of charge excitation energies. Using the example of LaMnO3 crystal we evaluate their magnitude. It is found that the major effects of deformation are an enhanced amplitude of x2-y2 orbitals induced in the orbital order by Ez≃300 meV and anisotropic tp d≃2.0 (2.35) eV along the a b (c ) cubic axis, in very good agreement with Harrison's law. We show that the improved tetragonal model analyzed within mean field approximation provides a surprisingly consistent picture of the ground state. Excellent agreement with the experimental data is obtained simultaneously for: (i) eg orbital mixing angle, (ii) spin exchange constants, and (iii) the temperatures of spin and orbital phase transition.

  17. Tunable Kondo physics in a carbon nanotube double quantum dot.

    PubMed

    Chorley, S J; Galpin, M R; Jayatilaka, F W; Smith, C G; Logan, D E; Buitelaar, M R

    2012-10-12

    We investigate a tunable two-impurity Kondo system in a strongly correlated carbon nanotube double quantum dot, accessing the full range of charge regimes. In the regime where both dots contain an unpaired electron, the system approaches the two-impurity Kondo model. At zero magnetic field the interdot coupling disrupts the Kondo physics and a local singlet state arises, but we are able to tune the crossover to a Kondo screened phase by application of a magnetic field. All results show good agreement with a numerical renormalization group study of the device.

  18. Real-space decoupling transformation for quantum many-body systems.

    PubMed

    Evenbly, G; Vidal, G

    2014-06-06

    We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).

  19. Lifshitz gravity for Lifshitz holography.

    PubMed

    Griffin, Tom; Hořava, Petr; Melby-Thompson, Charles M

    2013-02-22

    We argue that Hořava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and a dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

  20. Baryon chiral perturbation theory combined with the 1 /Nc expansion in SU(3): Framework

    NASA Astrophysics Data System (ADS)

    Fernando, I. P.; Goity, J. L.

    2018-03-01

    Baryon chiral perturbation theory combined with the 1 /Nc expansion is implemented for three flavors. Baryon masses, vector charges and axial vector couplings are studied to one-loop and organized according to the ξ -expansion, in which the 1 /Nc and the low-energy power countings are linked according to 1 /Nc=O (ξ )=O (p ). The renormalization to O (ξ3) necessary for the mentioned observables is provided, along with applications to the baryon masses and axial couplings as obtained in lattice QCD calculations.

  1. Photon-Z mixing the Weinberg-Salam model: Effective charges and the a = -3 gauge

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Baulieu, L.; Coquereaux, R.

    1982-04-15

    We study some properties of the Weinberg-Salam model connected with the photon-Z mixing. We solve the linear Dyson-Schwinger equations between full and 1PI boson propagators. The task is made easier, by the two-point function Ward identities that we derive to all orders and in any gauge. Some aspects of the renormalization of the model are also discussed. We display the exact mass-dependent one-loop two-point functions involving the photon and Z field in any linear xi-gauge. The special gauge a = xi/sup -1/ = -3 is shown to play a peculiar role. In this gauge, the Z field is multiplicatively renormalizablemore » (at the one-loop level), and one can construct both electric and weak effective charges of the theory from the photon and Z propagators, with a very simple expression similar to that of the QED Petermann, Stueckelberg, Gell-Mann and Low charge.« less

  2. Intertwined order in a frustrated four-leg t - J cylinder

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dodaro, John F.; Jiang, Hong -Chen; Kivelson, Steven A.

    Here, we report a density-matrix renormalization group study of the t–J model with nearest (t 1 and J 1) and next-nearest (t 2 and J 2) interactions on a four-leg cylinder with concentration δ=1/8 of doped holes. We observe an astonishingly complex interplay between uniform d-wave superconductivity (SC) and strong spin and charge-density wave ordering tendencies (SDW and CDW). Depending on parameters, the CDWs can be commensurate with period 4 or 8. By comparing the charge ordering vectors with 2k F, we rule out Fermi surface nesting-induced density wave order in our model. Magnetic frustration (i.e., J 2/J 1~1/2) significantlymore » quenches SDW correlations with little effect on the CDW. Typically, the SC order is strongly modulated at the CDW ordering vector and exhibits d-wave symmetry around the cylinder. There is no evidence of a near-degenerate tendency to pair-density wave (PDW) ordering, charge 4e SC, or orbital current order.« less

  3. Intertwined order in a frustrated four-leg t - J cylinder

    DOE PAGES

    Dodaro, John F.; Jiang, Hong -Chen; Kivelson, Steven A.

    2017-04-12

    Here, we report a density-matrix renormalization group study of the t–J model with nearest (t 1 and J 1) and next-nearest (t 2 and J 2) interactions on a four-leg cylinder with concentration δ=1/8 of doped holes. We observe an astonishingly complex interplay between uniform d-wave superconductivity (SC) and strong spin and charge-density wave ordering tendencies (SDW and CDW). Depending on parameters, the CDWs can be commensurate with period 4 or 8. By comparing the charge ordering vectors with 2k F, we rule out Fermi surface nesting-induced density wave order in our model. Magnetic frustration (i.e., J 2/J 1~1/2) significantlymore » quenches SDW correlations with little effect on the CDW. Typically, the SC order is strongly modulated at the CDW ordering vector and exhibits d-wave symmetry around the cylinder. There is no evidence of a near-degenerate tendency to pair-density wave (PDW) ordering, charge 4e SC, or orbital current order.« less

  4. Simulations of Coulomb systems with slab geometry using an efficient 3D Ewald summation method

    NASA Astrophysics Data System (ADS)

    dos Santos, Alexandre P.; Girotto, Matheus; Levin, Yan

    2016-04-01

    We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged walls from the electrostatic potential of electrolyte. The electric field produced by the 3d periodic images of the walls is constant inside the simulation cell, with the field produced by the transverse images of the charged plates canceling out. The non-neutral confined electrolyte in an external potential can be simulated using 3d Ewald summation with a suitable renormalization of the electrostatic energy, to remove a divergence, and a correction that accounts for the conditional convergence of the resulting lattice sum. The new algorithm is at least an order of magnitude more rapid than the usual simulation methods for the slab geometry and can be further sped up by adopting a particle-particle particle-mesh approach.

  5. Flux Renormalization in Constant Power Burnup Calculations

    DOE PAGES

    Isotalo, Aarno E.; Aalto Univ., Otaniemi; Davidson, Gregory G.; ...

    2016-06-15

    To more accurately represent the desired power in a constant power burnup calculation, the depletion steps of the calculation can be divided into substeps and the neutron flux renormalized on each substep to match the desired power. Here, this paper explores how such renormalization should be performed, how large a difference it makes, and whether using renormalization affects results regarding the relative performance of different neutronics–depletion coupling schemes. When used with older coupling schemes, renormalization can provide a considerable improvement in overall accuracy. With previously published higher order coupling schemes, which are more accurate to begin with, renormalization has amore » much smaller effect. Finally, while renormalization narrows the differences in the accuracies of different coupling schemes, their order of accuracy is not affected.« less

  6. Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling

    NASA Astrophysics Data System (ADS)

    Wu, Xing-Gang; Shen, Jian-Ming; Du, Bo-Lun; Brodsky, Stanley J.

    2018-05-01

    As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the newly suggested C -scheme coupling, one can obtain a demonstration that the principle of maximum conformality prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the nonsinglet Adler function and for τ decay to ν + hadrons at the four-loop level.

  7. Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity

    NASA Astrophysics Data System (ADS)

    Mandula, Jeffrey E.; Ogilvie, Michael C.

    1997-02-01

    We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

  8. Valence and charge-transfer optical properties for some SinCm (m, n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy.

    PubMed

    Lutz, Jesse J; Duan, Xiaofeng F; Ranasinghe, Duminda S; Jin, Yifan; Margraf, Johannes T; Perera, Ajith; Burggraf, Larry W; Bartlett, Rodney J

    2018-05-07

    Accurate optical characterization of the closo-Si 12 C 12 molecule is important to guide experimental efforts toward the synthesis of nano-wires, cyclic nano-arrays, and related array structures, which are anticipated to be robust and efficient exciton materials for opto-electronic devices. Working toward calibrated methods for the description of closo-Si 12 C 12 oligomers, various electronic structure approaches are evaluated for their ability to reproduce measured optical transitions of the SiC 2 , Si 2 C n (n = 1-3), and Si 3 C n (n = 1, 2) clusters reported earlier by Steglich and Maier [Astrophys. J. 801, 119 (2015)]. Complete-basis-limit equation-of-motion coupled-cluster (EOMCC) results are presented and a comparison is made between perturbative and renormalized non-iterative triples corrections. The effect of adding a renormalized correction for quadruples is also tested. Benchmark test sets derived from both measurement and high-level EOMCC calculations are then used to evaluate the performance of a variety of density functionals within the time-dependent density functional theory (TD-DFT) framework. The best-performing functionals are subsequently applied to predict valence TD-DFT excitation energies for the lowest-energy isomers of Si n C and Si n-1 C 7-n (n = 4-6). TD-DFT approaches are then applied to the Si n C n (n = 4-12) clusters and unique spectroscopic signatures of closo-Si 12 C 12 are discussed. Finally, various long-range corrected density functionals, including those from the CAM-QTP family, are applied to a charge-transfer excitation in a cyclic (Si 4 C 4 ) 4 oligomer. Approaches for gauging the extent of charge-transfer character are also tested and EOMCC results are used to benchmark functionals and make recommendations.

  9. Soft pair excitations and double-log divergences due to carrier interactions in graphene

    NASA Astrophysics Data System (ADS)

    Lewandowski, Cyprian; Levitov, L. S.

    2018-03-01

    Interactions between charge carriers in graphene lead to logarithmic renormalization of observables mimicking the behavior known in (3+1)-dimensional quantum electrodynamics (QED). Here we analyze soft electron-hole (e -h ) excitations generated as a result of fast charge dynamics, a direct analog of the signature QED effect—multiple soft photons produced by the QED vacuum shakeup. We show that such excitations are generated in photon absorption, when a photogenerated high-energy e -h pair cascades down in energy and gives rise to multiple soft e -h excitations. This fundamental process is manifested in a double-log divergence in the emission rate of soft pairs and a characteristic power-law divergence in their energy spectrum of the form 1/ω ln(ω/Δ ) . Strong carrier-carrier interactions make pair production a prominent pathway in the photoexcitation cascade.

  10. A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity.

    PubMed

    Reimers, Jeffrey R; McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S

    2015-10-14

    While diabatic approaches are ubiquitous for the understanding of electron-transfer reactions and have been mooted as being of general relevance, alternate applications have not been able to unify the same wide range of observed spectroscopic and kinetic properties. The cause of this is identified as the fundamentally different orbital configurations involved: charge-transfer phenomena involve typically either 1 or 3 electrons in two orbitals whereas most reactions are typically closed shell. As a result, two vibrationally coupled electronic states depict charge-transfer scenarios whereas three coupled states arise for closed-shell reactions of non-degenerate molecules and seven states for the reactions implicated in the aromaticity of benzene. Previous diabatic treatments of closed-shell processes have considered only two arbitrarily chosen states as being critical, mapping these states to those for electron transfer. We show that such effective two-state diabatic models are feasible but involve renormalized electronic coupling and vibrational coupling parameters, with this renormalization being property dependent. With this caveat, diabatic models are shown to provide excellent descriptions of the spectroscopy and kinetics of the ammonia inversion reaction, proton transfer in N2H7(+), and aromaticity in benzene. This allows for the development of a single simple theory that can semi-quantitatively describe all of these chemical phenomena, as well as of course electron-transfer reactions. It forms a basis for understanding many technologically relevant aspects of chemical reactions, condensed-matter physics, chemical quantum entanglement, nanotechnology, and natural or artificial solar energy capture and conversion.

  11. 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.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Song, Mi-Young; Yoon, Jung-Sik; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

    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 ismore » 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.« less

  13. Effects of renormalizing the chiral SU(2) quark-meson model

    NASA Astrophysics Data System (ADS)

    Zacchi, Andreas; Schaffner-Bielich, Jürgen

    2018-04-01

    We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

  14. Giant Gating Tunability of Optical Refractive Index in Transition Metal Dichalcogenide Monolayers.

    PubMed

    Yu, Yiling; Yu, Yifei; Huang, Lujun; Peng, Haowei; Xiong, Liwei; Cao, Linyou

    2017-06-14

    We report that the refractive index of transition metal dichacolgenide (TMDC) monolayers, such as MoS 2 , WS 2 , and WSe 2 , can be substantially tuned by >60% in the imaginary part and >20% in the real part around exciton resonances using complementary metal-oxide-semiconductor (CMOS) compatible electrical gating. This giant tunablility is rooted in the dominance of excitonic effects in the refractive index of the monolayers and the strong susceptibility of the excitons to the influence of injected charge carriers. The tunability mainly results from the effects of injected charge carriers to broaden the spectral width of excitonic interband transitions and to facilitate the interconversion of neutral and charged excitons. The other effects of the injected charge carriers, such as renormalizing bandgap and changing exciton binding energy, only play negligible roles. We also demonstrate that the atomically thin monolayers, when combined with photonic structures, can enable the efficiencies of optical absorption (reflection) tuned from 40% (60%) to 80% (20%) due to the giant tunability of the refractive index. This work may pave the way toward the development of field-effect photonics in which the optical functionality can be controlled with CMOS circuits.

  15. Weak mixing below the weak scale in dark-matter direct detection

    NASA Astrophysics Data System (ADS)

    Brod, Joachim; Grinstein, Benjamin; Stamou, Emmanuel; Zupan, Jure

    2018-02-01

    If dark matter couples predominantly to the axial-vector currents with heavy quarks, the leading contribution to dark-matter scattering on nuclei is either due to one-loop weak corrections or due to the heavy-quark axial charges of the nucleons. We calculate the effects of Higgs and weak gauge-boson exchanges for dark matter coupling to heavy-quark axial-vector currents in an effective theory below the weak scale. By explicit computation, we show that the leading-logarithmic QCD corrections are important, and thus resum them to all orders using the renormalization group.

  16. Violation of the Wiedemann-Franz law in a single-electron transistor.

    PubMed

    Kubala, Björn; König, Jürgen; Pekola, Jukka

    2008-02-15

    We study the influence of Coulomb interaction on the thermoelectric transport coefficients for a metallic single-electron transistor. By performing a perturbation expansion up to second order in the tunnel-barrier conductance, we include sequential and cotunneling processes as well as quantum fluctuations that renormalize the charging energy and the tunnel conductance. We find that Coulomb interaction leads to a strong violation of the Wiedemann-Franz law: the Lorenz ratio becomes gate-voltage dependent for sequential tunneling, and is increased by a factor 9/5 in the cotunneling regime. Finally, we suggest a measurement scheme for an experimental realization.

  17. Assessing notions of denormalization and renormalization of smoking in light of e-cigarette regulation.

    PubMed

    Sæbø, Gunnar; Scheffels, Janne

    2017-11-01

    The rationale for 'denormalization' of smoking in tobacco policies has been challenged by the emergence of e-cigarettes and the need to regulate e-cigarette use and promotion. Our aim is to assess the research status on e-cigarettes' contribution to 'renormalization' of smoking and to clarify how renormalization of smoking can be appraised at the conceptual and empirical level. Combining conceptual analysis and narrative review, the paper brings out three dimensions of denormalization/renormalization of smoking ('unacceptability/acceptability'; 'invisibility/visibility'; 'phasing out behaviour/maintaining behaviour') and an inherent duality of the e-cigarette as a smoking-like device and a smoking alternative. These analytical dimensions are applied qualitatively to consider the literature identified by searching the Web of Science database for 'e-cigarettes AND renormalization' (and variants thereof). Theoretically, normative changes in smoking acceptability, increased visibility of e-cigarettes and use, and observations of actual use (prevalence, dual use, gateway) can all be applied to illustrate processes of renormalization. However, only acceptability measures and user measures can be said to be empirical tests of renormalization effects. Visibility measures are only based on logical assumptions of a possible renormalization; they are not in themselves indicative of any "real" renormalization effects and can just as well be understood as possible consequences of normalization of e-cigarettes. Just as a downward trend in smoking prevalence is the litmus test of whether denormalization policy works, stagnating or rising smoking prevalence should be the main empirical indicator of renormalization. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

    NASA Astrophysics Data System (ADS)

    Nataf, Pierre; Mila, Frédéric

    2018-04-01

    We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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.

  20. Giant plasmonic energy and momentum transfer on the nanoscale

    NASA Astrophysics Data System (ADS)

    Durach, Maxim

    We have developed a general theory of the plasmonic enhancement of many-body phenomena resulting in a closed expression for the surface plasmon-dressed Coulomb interaction. It is shown that this interaction has a resonant nature. We have also demonstrated that renormalized interaction is a long-ranged interaction whose intensity is considerably increased compared to bare Coulomb interaction over the entire region near the plasmonic nanostructure. We illustrate this theory by re-deriving the mirror charge potential near a metal sphere as well as the quasistatic potential behind the so-called perfect lens at the surface plasmon (SP) frequency. The dressed interaction for an important example of a metal--dielectric nanoshell is also explicitly calculated and analyzed. The renormalization and plasmonic enhancement of the Coulomb interaction is a universal effect, which affects a wide range of many-body phenomena in the vicinity of metal nanostructures: chemical reactions, scattering between charge carriers, exciton formation, Auger recombination, carrier multiplication, etc. We have described the nanoplasmonic-enhanced Forster resonant energy transfer (FRET) between quantum dots near a metal nanoshell. It is shown that this process is very efficient near high-aspect-ratio nanoshells. We have also obtained a general expression for the force exerted by an electromagnetic field on an extended polarizable object. This expression is applicable to a wide range of situations important for nanotechnology. Most importantly, this result is of fundamental importance for processes involving interaction of nanoplasmonic fields with metal electrons. Using the obtained expression for the force, we have described a giant surface-plasmon-induced drag-effect rectification (SPIDER), which exists under conditions of the extreme nanoplasmonic confinement. Under realistic conditions in nanowires, this giant SPIDER generates rectified THz potential differences up to 10V and extremely strong electric fields up to 105--10 6 V/cm. It can serve as a powerful nanoscale source of THz radiation. The giant SPIDER opens up a new field of ultraintense THz nanooptics with wide potential applications in nanotechnology and nanoscience, including microelectronics, nanoplasmonics, and biomedicine. Additionally, the SPIDER is an ultrafast effect whose bandwidth for nanometric wires is 20 THz, which allows for detection of femtosecond pulses on the nanoscale. INDEX WORDS: Nanoplasmonics, Nanoplasmonic renormalization of Coulomb interaction, Surface-plasmon enhanced Forster energy transfer (FRET), Surface-plasmon-induced drag-effect rectification (SPIDER), Nanotechnology, Plasmonics on the nanoscale, Localized surface plasmons (LSPs), Surface plasmon polaritons (SPPs)

  1. Hidden Order and Dimensional Crossover of the Charge Density Waves in TiSe 2

    DOE PAGES

    Chen, P.; Chan, Y. -H.; Fang, X. -Y.; ...

    2016-11-29

    Charge density wave (CDW) formation, a key physics issue for materials, arises from interactions among electrons and phonons that can also lead to superconductivity and other competing or entangled phases. The prototypical system TiSe 2, with a particularly simple (2 × 2 × 2) transition and no Kohn anomalies caused by electron-phonon coupling, is a fascinating but unsolved case after decades of research. Our angle-resolved photoemission measurements of the band structure as a function of temperature, aided by first-principles calculations, reveal a hitherto undetected but crucial feature: a (2 × 2) electronic order in each layer sets in at ~232more » K before the widely recognized three-dimensional structural order at ~205 K. The dimensional crossover, likely a generic feature of such layered materials, involves renormalization of different band gaps in two stages.« less

  2. Critical behavior of the extended Hubbard model with bond dimerization

    NASA Astrophysics Data System (ADS)

    Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.; Fehske, Holger

    2018-05-01

    Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V / U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c = 1 / 2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c = 7 / 10 . We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β = 1 / 8 (1/24) and correlation length ν = 1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

  3. Strong correlation induced charge localization in antiferromagnets

    PubMed Central

    Zhu, Zheng; Jiang, Hong-Chen; Qi, Yang; Tian, Chushun; Weng, Zheng-Yu

    2013-01-01

    The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole's motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system. PMID:24002668

  4. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lee, Gyeong Won; Shim, Jaewon; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

    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 themore » 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.« less

  5. Doping evolution of spin and charge excitations in the Hubbard model

    DOE PAGES

    Kung, Y. F.; Nowadnick, E. A.; Jia, C. J.; ...

    2015-11-05

    We shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, examining the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to 40% hole and 15% electron doping (the range of dopings achievedmore » in the cuprates). Ultimately, these fundamental differences between the doping evolution of single- and multi-particle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multi-particle excitations. Eventually, the system smoothly transitions via a momentum-dependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.« less

  6. Tuning Charge and Correlation Effects for a Single Molecule on a Graphene Device

    NASA Astrophysics Data System (ADS)

    Tsai, Hsin-Zon; Wickenburg, Sebastian; Lu, Jiong; Lischner, Johannes; Omrani, Arash A.; Riss, Alexander; Karrasch, Christoph; Jung, Han Sae; Khajeh, Ramin; Wong, Dillon; Watanabe, Kenji; Taniguchi, Takashi; Zettl, Alex; Louie, Steven G.; Crommie, Michael F.

    Controlling electronic devices down to the single molecule level is a grand challenge of nanotechnology. Single-molecules have been integrated into devices capable of tuning electronic response, but a drawback for these systems is that their microscopic structure remains unknown due to inability to image molecules in the junction region. Here we present a combined STM and nc-AFM study demonstrating gate-tunable control of the charge state of individual F4TCNQ molecules at the surface of a graphene field effect transistor. This is different from previous studies in that the Fermi level of the substrate was continuously tuned across the molecular orbital energy level. Using STS we have determined the resulting energy level evolution of the LUMO, its associated vibronic modes, and the graphene Dirac point (ED). We show that the energy difference between ED and the LUMO increases as EF is moved away from ED due to electron-electron interactions that renormalize the molecular quasiparticle energy. This is attributed to gate-tunable image-charge screening in graphene and corroborated by ab initio calculations.

  7. Axial charges of N(1535) and N(1650) in lattice QCD with two flavors of dynamical quarks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Takahashi, Toru T.; Kunihiro, Teiji

    2008-07-01

    We show the first lattice QCD results on the axial charge g{sub A}{sup N}*{sup N}* of N*(1535) and N*(1650). The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at {beta}=1.95 and the mean-field improved clover quark action with the hopping parameters, {kappa}=0.1375, 0.1390, and 0.1400. In order to properly separate signals of N*(1535) and N*(1650), we construct 2x2 correlation matrices and diagonalize them. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axialmore » charge of N*(1535) takes small values such as g{sub A}{sup N}*{sup N}*{approx}O(0.1), whereas that of N*(1650) is about 0.5, which is found independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model.« less

  8. Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system I. Vacuum charge density

    NASA Astrophysics Data System (ADS)

    Davydov, A.; Sveshnikov, K.; Voronina, Yu.

    2018-01-01

    Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. 1-3, the nonperturbative vacuum polarization effects in the 2+1D supercritical Dirac-Coulomb system with Z > Zcr,1 are explored. Both the vacuum charge density ρV P(r→) and vacuum energy ℰV P are considered. The main result of the work is that in the overcritical region ℰV P turns out to be a rapidly decreasing function ˜-ηeffZ3/R with ηeff > 0 and R being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I, we consider the evaluation and behavior of the vacuum density ρV P, which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for ρV P and behavior of the integral induced charge QV P in the overcritical region.

  9. Covariant electromagnetic field lines

    NASA Astrophysics Data System (ADS)

    Hadad, Y.; Cohen, E.; Kaminer, I.; Elitzur, A. C.

    2017-08-01

    Faraday introduced electric field lines as a powerful tool for understanding the electric force, and these field lines are still used today in classrooms and textbooks teaching the basics of electromagnetism within the electrostatic limit. However, despite attempts at generalizing this concept beyond the electrostatic limit, such a fully relativistic field line theory still appears to be missing. In this work, we propose such a theory and define covariant electromagnetic field lines that naturally extend electric field lines to relativistic systems and general electromagnetic fields. We derive a closed-form formula for the field lines curvature in the vicinity of a charge, and show that it is related to the world line of the charge. This demonstrates how the kinematics of a charge can be derived from the geometry of the electromagnetic field lines. Such a theory may also provide new tools in modeling and analyzing electromagnetic phenomena, and may entail new insights regarding long-standing problems such as radiation-reaction and self-force. In particular, the electromagnetic field lines curvature has the attractive property of being non-singular everywhere, thus eliminating all self-field singularities without using renormalization techniques.

  10. Renormalization of the Lattice Heavy Quark Classical Velocity

    NASA Astrophysics Data System (ADS)

    Mandula, Jeffrey E.; Ogilvie, Michael C.

    1996-03-01

    In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

  11. Renormalization of entanglement entropy from topological terms

    NASA Astrophysics Data System (ADS)

    Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

    2018-05-01

    We propose a renormalization scheme for entanglement entropy of three-dimensional CFTs with a four-dimensional asymptotically AdS gravity dual in the context of the gauge/gravity correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. We provide an explicit prescription for the renormalized entanglement entropy, which is derived via the replica trick. This is achieved by considering a Euclidean gravitational action renormalized by the addition of the Chern form at the spacetime boundary, evaluated in the conically-singular replica manifold. We show that the addition of this boundary term cancels the divergent part of the entanglement entropy, recovering the results obtained by Taylor and Woodhead. We comment on how this prescription for renormalizing the entanglement entropy is in line with the general program of topological renormalization in asymptotically AdS gravity.

  12. Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs.

    PubMed

    Xu, Xiao; Ran, Qidi; Dey, Pradip; Nikam, Rohit; Haag, Rainer; Ballauff, Matthias; Dzubiella, Joachim

    2018-02-12

    Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titration calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding constant shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire analysis demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.

  13. Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results

    DOE PAGES

    Nocera, Alberto; Wang, Yan; Patel, Niravkumar D.; ...

    2018-05-31

    Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gappedmore » spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.« less

  14. Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nocera, Alberto; Wang, Yan; Patel, Niravkumar D.

    Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gappedmore » spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.« less

  15. Quantum critical spin-2 chain with emergent SU(3) symmetry.

    PubMed

    Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

    2015-04-10

    We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

  16. Baryon chiral perturbation theory combined with the 1 / N c expansion in SU(3): Framework

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fernando, I. P.; Goity, J. L.

    Baryon Chiral Perturbation Theory combined with themore » $$1/N_c$$ expansion is implemented for three flavors. Here, Baryon masses, vector charges and axial vector couplings are studied to one-loop and organized according to the $$\\xi$$-expansion, in which the $$1/N_c$$ and the low energy power countings are linked according to $$1/N_c={\\cal{O}}(\\xi)={\\cal{O}}(p)$$. The renormalization to $${\\cal{O}}(\\xi^3)$$ necessary for the mentioned observables is provided, along with applications to the baryon masses and axial couplings as obtained in lattice QCD calculations.« less

  17. Baryon chiral perturbation theory combined with the 1 / N c expansion in SU(3): Framework

    DOE PAGES

    Fernando, I. P.; Goity, J. L.

    2018-03-14

    Baryon Chiral Perturbation Theory combined with themore » $$1/N_c$$ expansion is implemented for three flavors. Here, Baryon masses, vector charges and axial vector couplings are studied to one-loop and organized according to the $$\\xi$$-expansion, in which the $$1/N_c$$ and the low energy power countings are linked according to $$1/N_c={\\cal{O}}(\\xi)={\\cal{O}}(p)$$. The renormalization to $${\\cal{O}}(\\xi^3)$$ necessary for the mentioned observables is provided, along with applications to the baryon masses and axial couplings as obtained in lattice QCD calculations.« less

  18. Quantum spin circulator in Y junctions of Heisenberg chains

    NASA Astrophysics Data System (ADS)

    Buccheri, Francesco; Egger, Reinhold; Pereira, Rodrigo G.; Ramos, Flávia B.

    2018-06-01

    We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin-1 /2 Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin-liquid phases.

  19. N = 2 supersymmetry and Bailey pairs

    NASA Astrophysics Data System (ADS)

    Berkovich, Alexander; McCoy, Barry M.; Schilling, Anne

    1996-02-01

    We demonstrate that the Bailey pair formulation of Rogers-Ramanujan identities unifies the calculations of the characters of N = 1 and N = 2 supersymmetric conformal field theories with the counterpart theory with no supersymmetry. We illustrate this construction for the M(3,4) (Ising) model where the Bailey pairs have been given by Slater. We then present the general unitary case. We demonstrate that the model M( p,p + 1) is derived from M( p - 1, p) by a Bailey renormalization flow and conclude by obtaining the N = 1 model SM( p,p + 2) and the unitary N = 2 model with central charge c = 3(1 - 2/ p).

  20. Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

    NASA Astrophysics Data System (ADS)

    Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

    2018-05-01

    The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

  1. Entanglement renormalization and topological order.

    PubMed

    Aguado, Miguel; Vidal, Guifré

    2008-02-22

    The multiscale entanglement renormalization ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the renormalization group flow associated with entanglement renormalization. All of these results generalize to arbitrary quantum double models.

  2. Aspects of Galileon non-renormalization

    DOE PAGES

    Goon, Garrett; Hinterbichler, Kurt; Joyce, Austin; ...

    2016-11-18

    We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and P ( X) theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. Furthermore, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.

  3. Renormalization-group theory of plasma microturbulence

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Carati, D.; Chriaa, K.; Balescu, R.

    1994-08-01

    The dynamical renormalization-group methods are applied to the gyrokinetic equation describing drift-wave turbulence in plasmas. As in both magnetohydrodynamic and neutral turbulence, small-scale fluctuations appear to act as effective dissipative processes on large-scale phenomena. A linear renormalized gyrokinetic equation is derived. No artificial forcing is introduced into the equations and all the renormalized corrections are expressed in terms of the fluctuating electric potential. The link with the quasilinear limit and the direct interaction approximation is investigated. Simple analytical expressions for the anomalous transport coefficients are derived by using the linear renormalized gyrokinetic equation. Examples show that both quasilinear and Bohmmore » scalings can be recovered depending on the spectral amplitude of the electric potential fluctuations.« less

  4. Comprehensive renormalization group analysis of the littlest seesaw model

    NASA Astrophysics Data System (ADS)

    Geib, Tanja; King, Stephen F.

    2018-04-01

    We present a comprehensive renormalization group analysis of the littlest seesaw model involving two right-handed neutrinos and a very constrained Dirac neutrino Yukawa coupling matrix. We perform the first χ2 analysis of the low energy masses and mixing angles, in the presence of renormalization group corrections, for various right-handed neutrino masses and mass orderings, both with and without supersymmetry. We find that the atmospheric angle, which is predicted to be near maximal in the absence of renormalization group corrections, may receive significant corrections for some nonsupersymmetric cases, bringing it into close agreement with the current best fit value in the first octant. By contrast, in the presence of supersymmetry, the renormalization group corrections are relatively small, and the prediction of a near maximal atmospheric mixing angle is maintained, for the studied cases. Forthcoming results from T2K and NO ν A will decisively test these models at a precision comparable to the renormalization group corrections we have calculated.

  5. Aspects of the zero Λ limit in the AdS/CFT correspondence

    NASA Astrophysics Data System (ADS)

    Caldeira Costa, R. N.

    2014-11-01

    We examine the correspondence between QFT observables and bulk solutions in the context of AdS/CFT in the limit as the cosmological constant Λ →0 . We focus specifically on the spacetime metric and a nonbackreacting scalar in the bulk, compute the one-point functions of the dual operators, and determine the necessary conditions for the correspondence to admit a well-behaved zero-Λ limit. We discuss holographic renormalization in this limit and find that it requires schemes that partially break diffeomorphism invariance of the bulk theory. In the specific case of three bulk dimensions, we compute the zero-Λ limit of the holographic Weyl anomaly and reproduce the central charge that arises in the central extension of bms3 . We compute holographically the energy and momentum of those QFT states dual to flat cosmological solutions and to the Kerr solution and find an agreement with the bulk theory. We also compute holographically the renormalized two-point function of a scalar operator in the zero-Λ limit and find it to be consistent with that of a conformal operator in two dimensions fewer. Finally, our results can be used in a new definition of asymptotic Ricci flatness at null infinity based on the zero-Λ limit of asymptotically Einstein manifolds.

  6. Variational Approach to Monte Carlo Renormalization Group

    NASA Astrophysics Data System (ADS)

    Wu, Yantao; Car, Roberto

    2017-12-01

    We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

  7. 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.

  8. 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.

  9. Nuclear chiral axial currents and applications to few-nucleon systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Baroni, Alessandro

    This Thesis is divided into three main parts. The first part discusses basic aspects of chiral effective field theory and the formalism, based on time ordered perturbation theory, used to to derive the nuclear potentials and currents from the chiral Lagrangians. The second part deals with the actual derivation, up to one loop, of the two-nucleon potential and one- and two-nucleon weak axial charge and current. In both derivations ultraviolet divergences generated by loop corrections are isolated using dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. A completemore » set of contact terms for the axial charge up to the relevant order in the power counting is constructed. The third part of this Thesis discusses two applications: (i) the calculation of the Gamow-Teller matrix element of tritium, used to constrain the single low-energy constant entering the axial current; (ii) the calculation of neutrino-deuteron inclusive cross sections at low energies. These results have confirmed previous predictions obtained in phenomenological approaches. These latter studies have played an important role in the analysis and interpretation of experiments at the Sudbury Neutrino Observatory.« less

  10. Ising tricriticality in the extended Hubbard model with bond dimerization

    NASA Astrophysics Data System (ADS)

    Fehske, Holger; Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.

    We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results. This work was supported by Deutsche Forschungsgemeinschaft (Germany), SFB 652, project B5, and by the EPSRC under Grant No. EP/N01930X/1 (FHLE).

  11. Floquet theory of microwave absorption by an impurity in the two-dimensional electron gas

    NASA Astrophysics Data System (ADS)

    Chepelianskii, Alexei D.; Shepelyansky, Dima L.

    2018-03-01

    We investigate the dynamics of a two-dimensional electron gas (2DEG) under circular polarized microwave radiation in the presence of dilute localized impurities. Inspired by recent developments on Floquet topological insulators we obtain the Floquet wave functions of this system which allow us to predict the microwave absorption and charge density responses of the electron gas; we demonstrate how these properties can be understood from the underlying semiclassical dynamics even for impurities with a size of around a magnetic length. The charge density response takes the form of a rotating charge density vortex around the impurity that can lead to a significant renormalization of the external microwave field which becomes strongly inhomogeneous on the scale of a cyclotron radius around the impurity. We show that this inhomogeneity can suppress the circular polarization dependence which is theoretically expected for microwave induced resistance oscillations but which was not observed in experiments on semiconducting 2DEGs. Our explanation for this so far unexplained polarization independence has close similarities with the Azbel'-Kaner effect in metals where the interaction length between the microwave field and conduction electrons is much smaller than the cyclotron radius due to skin effect generating harmonics of the cyclotron resonance.

  12. Singular Valence Fluctuations at a Kondo Destroyed Quantum Critical Point

    NASA Astrophysics Data System (ADS)

    Pixley, Jedediah; Kirchner, Stefan; Ingersent, Kevin; Si, Qimiao

    2012-02-01

    Recent experiments on the heavy fermion superconductor beta-YbAlB4 have indicated that this compound satisfies quantum critical scaling [1]. Motivated by the observation of mixed valency in this material [2], we study the Kondo destruction physics in the mixed-valence regime [3] of a particle-hole asymmetric Anderson impurity model with a pseudogapped density of states. In the vicinity of the quantum critical point we determine the finite temperature spin and charge susceptibilities by utilizing a continuous time quantum Monte Carlo method [4] and the numerical renormalization group. We show that this mixed-valence quantum critical point displays a Kondo breakdown effect. Furthermore, we find that both dynamic spin and charge susceptibilities obey frequency over temperature scaling, and that the static charge susceptibility diverges with a universal exponent. Possible implications of our results for beta-YbAlB4 are discussed. [1] Matsumoto et al, Science 331, 316 (2011). [2] Okawaet al, Physical Review Letters 104, 247201 (2010). [3] J. H. Pixley, S. Kirchner, Kevin Ingersent and Q. Si, arXiv:1108.5227v1 (2011). [4] M. Glossop, S. Kirchner, J. H. Pixley and Q. Si, Phys. Rev. Lett. 107, 076404 (2011).

  13. Renormalization of the inflationary perturbations revisited

    NASA Astrophysics Data System (ADS)

    Markkanen, Tommi

    2018-05-01

    In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

  14. Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

    NASA Astrophysics Data System (ADS)

    Dao, Vu Hung; Frésard, Raymond

    2017-10-01

    The charge dynamical response function of the t-t'-U Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slightly affects the renormalization of the quasiparticle mass. In contrast a negative t'/t notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density n ≲ 0.5 (n ≳ 1.5) we find that it enhances (reduces) the damping of the zero-sound mode. Furthermore it softens (hardens) the upper-Hubbard-band collective mode at positive (negative) doping. It is also shown that our results differ markedly from the random-phase approximation in the strong-coupling limit, even at high doping, while they compare favorably with existing quantum Monte Carlo numerical simulations.

  15. Entanglement across extended random defects in the XX spin chain

    NASA Astrophysics Data System (ADS)

    Juhász, Róbert

    2017-08-01

    We study the half-chain entanglement entropy in the ground state of the spin-1/2 XX chain across an extended random defect, where the strength of disorder decays with the distance from the interface algebraically as Δ_l∼ l-κ . In the whole regime κ≥slant 0 , the average entanglement entropy is found to increase logarithmically with the system size L as S_L≃\\frac{c_eff(κ)}{6}\\ln L+const , where the effective central charge c_eff(κ) depends on κ. In the regime κ<1/2 , where the extended defect is a relevant perturbation, the strong-disorder renormalization group method gives c_eff(κ)=(1-2κ)\\ln2 , while, in the regime κ≥slant 1/2 , where the extended defect is irrelevant in the bulk, numerical results indicate a non-zero effective central charge, which increases with κ. The variation of c_eff(κ) is thus found to be non-monotonic and discontinuous at κ=1/2 .

  16. Renormalization of the Higgs sector in the triplet model

    NASA Astrophysics Data System (ADS)

    Aoki, Mayumi; Kanemura, Shinya; Kikuchi, Mariko; Yagyu, Kei

    2012-08-01

    We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y = 1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., mH++2 - mH+2 ≃ mH+2 - mA2 and mA2 ≃ mH2, where the CP-even (H), the CP-odd (A) and the doubly-charged (H±±) as well as the singly-charged (H±) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The hhh coupling for the standard model-like Higgs boson (h) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.

  17. Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe 2

    DOE PAGES

    Chen, P.; Chan, Y. -H.; Wong, M. -H.; ...

    2016-09-20

    Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe 2, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission (ARPES) measurements ofmore » films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band-gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework.« less

  18. Nature of a single doped hole in two-leg Hubbard and t - J ladders

    DOE PAGES

    Liu, Shenxiu; Jiang, Hong -Chen; Devereaux, Thomas P.

    2016-10-15

    In this study, we have systematically studied the single-hole problem in two-leg Hubbard and t–J ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In themore » isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.« less

  19. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liu, Shenxiu; Jiang, Hong -Chen; Devereaux, Thomas P.

    In this study, we have systematically studied the single-hole problem in two-leg Hubbard and t–J ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In themore » isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.« less

  20. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    NASA Astrophysics Data System (ADS)

    Nocera, A.; Patel, N. D.; Fernandez-Baca, J.; Dagotto, E.; Alvarez, G.

    2016-11-01

    We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small as U /t ˜2 -3 , although ratios of peak intensities at different momenta continue evolving with increasing U /t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U /t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

  1. Minimally doubled fermions at one loop

    NASA Astrophysics Data System (ADS)

    Capitani, Stefano; Weber, Johannes; Wittig, Hartmut

    2009-10-01

    Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which is linearly divergent. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.

  2. 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.

  3. Temperature and frequency dependent mean free paths of renormalized phonons in nonlinear lattices

    NASA Astrophysics Data System (ADS)

    Li, Nianbei; Liu, Junjie; Wu, Changqin; Li, Baowen

    2018-02-01

    Unraveling general properties of renormalized phonons are of fundamental relevance to the heat transport in the regime of strong nonlinearity. In this work, we directly study the temperature and frequency dependent mean free path (MFP) of renormalized phonons with the newly developed numerical tuning fork method. The typical 1D nonlinear lattices such as Fermi-Pasta-Ulam β lattice and {φ }4 lattice are investigated in detail. Interestingly, it is found that the MFPs are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory.

  4. Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

    NASA Astrophysics Data System (ADS)

    Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

    2018-03-01

    Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

  5. Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

    NASA Astrophysics Data System (ADS)

    Kim, Chungku

    2018-06-01

    We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

  6. The cosmic QCD phase transition with dense matter and its gravitational waves from holography

    NASA Astrophysics Data System (ADS)

    Ahmadvand, M.; Bitaghsir Fadafan, K.

    2018-04-01

    Consistent with cosmological constraints, there are scenarios with the large lepton asymmetry which can lead to the finite baryochemical potential at the cosmic QCD phase transition scale. In this paper, we investigate this possibility in the holographic models. Using the holographic renormalization method, we find the first order Hawking-Page phase transition, between the Reissner-Nordström AdS black hole and thermal charged AdS space, corresponding to the de/confinement phase transition. We obtain the gravitational wave spectra generated during the evolution of bubbles for a range of the bubble wall velocity and examine the reliability of the scenarios and consequent calculations by gravitational wave experiments.

  7. Kondo interactions from band reconstruction in YbInCu 4

    DOE PAGES

    Jarrige, I.; Kotani, A.; Yamaoka, H.; ...

    2015-03-27

    We combine resonant inelastic X-ray scattering (RIXS) and model calculations in the Kondo lattice compound YbInCu₄, a system characterized by a dramatic increase in Kondo temperature and associated valence fluctuations below a first-order valence transition at T≃42 K. In this study, the bulk-sensitive, element-specific, and valence-projected charge excitation spectra reveal an unusual quasi-gap in the Yb-derived state density which drives an instability of the electronic structure and renormalizes the low-energy effective Hamiltonian at the transition. Our results provide long-sought experimental evidence for a link between temperature-driven changes in the low-energy Kondo scale and the higher-energy electronic structure of this system.

  8. Model of large volumetric capacitance in graphene supercapacitors based on ion clustering

    NASA Astrophysics Data System (ADS)

    Skinner, Brian; Fogler, M. M.; Shklovskii, B. I.

    2011-12-01

    Electric double-layer supercapacitors (SCs) are promising devices for high-power energy storage based on the reversible absorption of ions into porous conducting electrodes. Graphene is a particularly good candidate for the electrode material in SCs due to its high conductivity and large surface area. In this paper, we consider SC electrodes made from a stack of graphene sheets with randomly inserted spacer molecules. We show that the large volumetric capacitances C≳100F/cm3 observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.

  9. A model of large volumetric capacitance in graphene supercapacitors based on ion clustering

    NASA Astrophysics Data System (ADS)

    Skinner, Brian; Fogler, Michael; Shklovskii, Boris

    2012-02-01

    Electric double layer supercapacitors are promising devices for high-power energy storage based on the reversible absorption of ions into porous, conducting electrodes. Graphene is a particularly good candidate for the electrode material in supercapacitors due to its high conductivity and large surface area. In this paper we consider supercapacitor electrodes made from a stack of graphene sheets with randomly-inserted ``spacer" molecules. We show that the large volumetric capacitances C > 100 F/cm^3 observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.

  10. Two band model for the cuprates

    NASA Astrophysics Data System (ADS)

    Liu, Shiu; White, Steven

    2009-03-01

    We use a numerical canonical transformation approach to derive an effective two-band model for the hole-doped cuprates, which keeps both oxygen and copper orbitals but removes double occupancy from each. A similar model was considered previously by Frenkel, Gooding, Shraiman, and Siggia (PRB 41, number 1, page 350). We compare the numerically derived model with previously obtained analytical results. In addition to the usual hopping terms between oxygens tpp and Cu-Cu exchange terms Jdd, the model also includes a strong copper-oxygen exchange interaction Jpd and a Kondo-like spin-flip oxygen-oxygen hopping term Kpdp. We use the density matrix renormalization group to study the charge, spin, and pairing properties of the derived model on ladder systems.

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

    PubMed

    Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2012-07-01

    We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

  12. Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene

    NASA Astrophysics Data System (ADS)

    Leblanc, J. P. F.; Carbotte, J. P.; Nicol, E. J.

    2012-02-01

    Motivated by recent tunneling and angle-resolved photoemission (ARPES) work [1,2], we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the density of states of doped graphene. We find that the plasmarons seen in ARPES are also observable in the density of states and appear as structures with quadratic dependence on energy about the minima. Further, we illustrate how knowledge of the slopes of both the density of states and the renormalized dispersion near the Fermi level can allow for the separation of momentum and frequency dependent renormalizations to the Fermi velocity. This analysis should allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. [4pt] [1] Brar et al. Phys. Rev. Lett. 104, 036805 (2010) [2] Bostwick et al. Science 328, p.999 (2010)

  13. Nonrelativistic Conformed Symmetry in 2 + 1 Dimensional Field Theory.

    NASA Astrophysics Data System (ADS)

    Bergman, Oren

    This thesis is devoted to the study of conformal invariance and its breaking in non-relativistic field theories. It is a well known feature of relativistic field theory that theories which are conformally invariant at the classical level can acquire a conformal anomaly upon quantization and renormalization. The anomaly appears through the introduction of an arbitrary, but dimensionful, renormalization scale. One does not usually associate the concepts of renormalization and anomaly with nonrelativistic quantum mechanics, but there are a few examples where these concepts are useful. The most well known case is the two-dimensional delta -function potential. In two dimensions the delta-function scales like the kinetic term of the Hamiltonian, and therefore the problem is classically conformally invariant. Another example of classical conformal invariance is the famous Aharonov-Bohm (AB) problem. In that case each partial wave sees a 1/r^2 potential. We use the second quantized formulation of these problems, namely the nonrelativistic field theories, to compute Green's functions and derive the conformal anomaly. In the case of the AB problem we also solve an old puzzle, namely how to reproduce the result of Aharonov and Bohm in perturbation theory. The thesis is organized in the following manner. Chapter 1 is an introduction to nonrelativistic field theory, nonrelativistic conformal invariance, contact interactions and the AB problem. In Chapter 2 we discuss nonrelativistic scalar field theory, and how its quantization produces the anomaly. Chapter 3 is devoted to the AB problem, and the resolution of the perturbation puzzle. In Chapter 4 we generalize the discussion of Chapter 3 to particles carrying nonabelian charges. The structure of the nonabelian theory is much richer, and deserves a separate discussion. We also comment on the issues of forward scattering and single -valuedness of wavefunctions, which are important for Chapter 3 as well. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

  14. Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

    NASA Astrophysics Data System (ADS)

    Gracey, J. A.; Simms, R. M.

    2018-04-01

    We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

  15. Equilibrium charge fluctuations of a charge detector and its effect on a nearby quantum dot

    NASA Astrophysics Data System (ADS)

    Ruiz-Tijerina, David; Vernek, Edson; Ulloa, Sergio

    2014-03-01

    We study the Kondo state of a spin-1/2 quantum dot (QD), in close proximity to a quantum point contact (QPC) charge detector near the conductance regime of the 0.7 anomaly. The electrostatic coupling between the QD and QPC introduces a remote gate on the QD level, which varies with the QPC gate voltage. Furthermore, models for the 0.7 anomaly [Y. Meir et al., PRL 89,196802(2002)] suggest that the QPC lodges a Kondo-screened level with charge-correlated hybridization, which may be also affected by capacitive coupling to the QD, giving rise to a competition between the two Kondo ground states. We model the QD-QPC system as two capacitively-coupled Kondo impurities, and explore the zero-bias transport of both the QD and the QPC for different local gate voltages and coupling strengths, using the numerical renormalization group and variational methods. We find that the capacitive coupling produces a remote gating effect, non-monotonic in the gate voltages, which reduces the gate voltage window for Kondo screening in either impurity, and which can also drive a quantum phase transition out of the Kondo regime. Our study is carried out for intermediate coupling strengths, and as such is highly relevant to experiments; particularly, to recent studies of decoherence effects on QDs. Supported by MWN/CIAM and NSF PIRE.

  16. Electrostatics-driven shape transitions in soft shells.

    PubMed

    Jadhao, Vikram; Thomas, Creighton K; Olvera de la Cruz, Monica

    2014-09-02

    Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell's surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.

  17. Excited state TBA and renormalized TCSA in the scaling Potts model

    NASA Astrophysics Data System (ADS)

    Lencsés, M.; Takács, G.

    2014-09-01

    We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

  18. Threshold and flavor effects in the renormalization group equations of the MSSM: Dimensionless couplings

    NASA Astrophysics Data System (ADS)

    Box, Andrew D.; Tata, Xerxes

    2008-03-01

    In a theory with broken supersymmetry, gaugino couplings renormalize differently from gauge couplings, as do higgsino couplings from Higgs boson couplings. As a result, we expect the gauge (Higgs boson) couplings and the corresponding gaugino (higgsino) couplings to evolve to different values under renormalization group evolution. We reexamine the renormalization group equations (RGEs) for these couplings in the minimal supersymmetric standard model (MSSM). To include threshold effects, we calculate the β functions using a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We find that the difference between the SM couplings and their SUSY cousins that is ignored in the literature may be larger than two-loop effects which are included, and further that renormalization group evolution induces a nontrivial flavor structure in gaugino interactions. We present here the coupled set of RGEs for these dimensionless gauge and Yukawa-type couplings. The RGEs for the dimensionful soft-supersymmetry-breaking parameters of the MSSM will be presented in a companion paper.

  19. Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves

    NASA Astrophysics Data System (ADS)

    Carpentier, David; Le Doussal, Pierre

    2000-11-01

    We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core energy). By taking into account the fusion of environments (i.e., charge fusion in the replicated Coulomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits traveling wave solutions and exhibits a freezing phenomenon analogous to glassy freezing in Derrida's random energy models. The resulting physical picture is that the distribution of local disorder becomes broad below a freezing temperature and that the transition is controlled by rare favorable regions for the defects, the density of which can be used as the new perturbative parameter. The determination of marginal directions at the disorder induced transition is shown to be related to the well studied front velocity selection problem in the KPP equation and the universality of the novel critical behaviour obtained here to the known universality of the corrections to the front velocity. Applications to other two dimensional problems are mentioned at the end.

  20. Orbital currents in a generalized Hubbard ladder

    NASA Astrophysics Data System (ADS)

    Fjaerestad, John O.

    2004-03-01

    We study a phase with orbital currents (d-density wave (DDW)/staggered flux phase) in a generalized Hubbard model on the two-leg ladder at zero temperature. Bosonization and perturbative renormalization-group calculations are used to identify a parameter region with long-range DDW order in the weakly interacting half-filled ladder. Finite-size density-matrix renormalization-group (DMRG) studies of ladders with up to 200 rungs, for rational hole dopings δ and intermediate-strength interactions, find that currents remain large in the doped DDW phase, with no evidence of decay.^1,2,3 Motivated by these results, we consider an effective bosonization description of the doped DDW phase in which quantum fluctuations in the total charge mode are neglected.^3 This leads to an analytically solvable Frenkel-Kontorova-like model which predicts that the staggered rung current and the rung electron density show periodic spatial oscillations with wavelengths 2/δ and 1/δ, respectively, with the density minima located at the zeros (domain walls) of the staggered rung current, in good agreement with the DMRG results. We comment on the question of the nature of the asymptotic current correlations in the doped DDW phase. ^1U. Schollwöck, S. Chakravarty, J. O. Fjaerestad, J. B. Marston, and M. Troyer, Phys. Rev. Lett. 90, 186401 (2003). ^2M. Troyer, invited talk at this meeting. ^3J. O. Fjaerestad, J. B. Marston, and U. Schollwöck, unpublished.

  1. Products of composite operators in the exact renormalization group formalism

    NASA Astrophysics Data System (ADS)

    Pagani, C.; Sonoda, H.

    2018-02-01

    We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

  2. Functional Renormalization Group Flows on Friedman-Lemaître-Robertson-Walker backgrounds

    NASA Astrophysics Data System (ADS)

    Platania, Alessia; Saueressig, Frank

    2018-06-01

    We revisit the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the causal dynamical triangulations approach to quantum gravity.

  3. Renormalization group approach to power-law modeling of complex metabolic networks.

    PubMed

    Hernández-Bermejo, Benito

    2010-08-07

    In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.

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

    DOE PAGES

    Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; ...

    2015-06-26

    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R δ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfymore » all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R e+e– and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β i}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.« less

  5. Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

    NASA Astrophysics Data System (ADS)

    Baumgarten, Lorenz; Kierfeld, Jan

    2018-05-01

    We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017), 10.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

  6. Modeling the Electrostatics of Hollow Shell Suspensions: Ion Distribution, Pair Interactions, and Many-Body Effects.

    PubMed

    Hallez, Yannick; Meireles, Martine

    2016-10-11

    Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.

  7. Competing orders in the Hofstadter t -J model

    NASA Astrophysics Data System (ADS)

    Tu, Wei-Lin; Schindler, Frank; Neupert, Titus; Poilblanc, Didier

    2018-01-01

    The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t -J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

  8. Rearranging Pionless Effective Field Theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Martin Savage; Silas Beane

    2001-11-19

    We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalizationmore » scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.« less

  9. Integrability in heavy quark effective theory

    NASA Astrophysics Data System (ADS)

    Braun, Vladimir M.; Ji, Yao; Manashov, Alexander N.

    2018-06-01

    It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C( u) of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

  10. Open sd-shell nuclei from first principles

    DOE PAGES

    Jansen, Gustav R.; Signoracci, Angelo J.; Hagen, Gaute; ...

    2016-07-05

    We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20Ne and 24Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory formore » deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.« less

  11. Open sd-shell nuclei from first principles

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jansen, Gustav R.; Signoracci, Angelo J.; Hagen, Gaute

    We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20Ne and 24Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory formore » deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.« less

  12. Phases of unstable conifolds

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Narayan, K.

    2007-03-15

    We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix Q=(n{sub 1}n{sub 2}-n{sub 3}-n{sub 4}), n{sub i}>0, iQ{sub i}{ne}0, initiated by Narayan [J. High Energy Phys. 03 (2006) 036]. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascadelike phase structure containing decays to lower order conifold-like singularities, including, in particular, the supersymmetric conifold and the Y{sup pq} spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometriesmore » include flips and flops.« less

  13. 750 GeV diphoton resonance and inflation

    NASA Astrophysics Data System (ADS)

    Hamada, Yuta; Noumi, Toshifumi; Shiu, Gary; Sun, Sichun

    2016-06-01

    We study the possibility of a heavy scalar or pseudoscalar in TeV-scale beyond the Standard Model scenarios being the inflaton of the early universe in light of the recent O (750 ) GeV diphoton excess at the LHC. We consider a scenario in which the new scalar or pseudoscalar couples to the Standard Model gauge bosons at the loop level through new massive Standard Model charged vectorlike fermions with or without dark fermions. We calculate the renormalization group running of both the Standard Model and the new scalar couplings, and present two different models that are perturbative, with a stabilized vacuum up to near the Planck scale. Thus, the Standard Model Higgs and this possible new resonance may still preserve the minimalist features of Higgs inflation.

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand, E-mail: davi.rodrigues@cosmo-ufes.org, E-mail: Bertrand.Chauvineau@oca.eu, E-mail: oliver.piattella@pq.cnpq.br

    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.

  15. Renormalization in Coulomb-gauge QCD within the Lagrangian formalism

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Niegawa, A.

    2006-08-15

    We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)

  16. Geometry of the theory space in the exact renormalization group formalism

    NASA Astrophysics Data System (ADS)

    Pagani, C.; Sonoda, H.

    2018-01-01

    We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.

  17. A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

    NASA Astrophysics Data System (ADS)

    Mestel, B. D.; Osbaldestin, A. H.

    2004-10-01

    We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

  18. Renormalization group independence of Cosmological Attractors

    NASA Astrophysics Data System (ADS)

    Fumagalli, Jacopo

    2017-06-01

    The large class of inflationary models known as α- and ξ-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters (ns , r) are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular ξ-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.

  19. Flavor unity in SU(7): Low-mass magnetic monopole, doubly charged lepton,and Q = 5/3,-4/3 quarks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kim, J.E.

    1981-06-01

    A specific flavor unification is suggested in the SU(7) gauge group. This model can be trivially extended to O(14). A global symmetry GAMMA forbids mixings of the b (Q = -1/3) quark with the d and s quarks, and of the t (Q = 2/3) quark with the u and c quarks. Since the b and t quarks carry different GAMMA quantum numbers, they do not belong to the same SU(2)/sub L/ doublet. A mechanism for the GAMMA-symmetry violation is suggested, which allows c-t mixing without b-quark mixing. There are unconventionally charged light (masses < or approx. =300 GeV) fermions:more » a doubly charged lepton T/sup - -/, a Q = -4/3 quark x, and a Q = 5/3 quark y. The bare value of the Weinberg angle sin/sup 2/theta/sup 0//sub W/ = 3/20 is renormalized to the low-energy value by introducing an intermediate mass scale M/sub 1/. A topologically stable magnetic monopole is light (massroughly-equalM/sub 1//..cap alpha..) and hence there does not exist a conflict arising from the grand unified theories and the hot-big-bang cosmology.« less

  20. The QCD running coupling

    NASA Astrophysics Data System (ADS)

    Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

    2016-09-01

    We review the present theoretical and empirical knowledge for αs, the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of αs(Q2) on momentum transfer Q encodes the underlying dynamics of hadron physics-from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on αs(Q2) at high Q2, as predicted by perturbative QCD, and its analytic behavior at small Q2, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of αs(Q2) in the high momentum transfer domain of QCD. We review how αs is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as "Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization-scale ambiguity. We also report recent significant measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the "Principle of Maximum Conformality", which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior αs(Q2) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of αs(Q2) in order to bring better unity to the subject.

  1. Watching the brain recalibrate: Neural correlates of renormalization during face adaptation.

    PubMed

    Kloth, Nadine; Rhodes, Gillian; Schweinberger, Stefan R

    2017-07-15

    The face perception system flexibly adjusts its neural responses to current face exposure, inducing aftereffects in the perception of subsequent faces. For instance, adaptation to expanded faces makes undistorted faces appear compressed, and adaptation to compressed faces makes undistorted faces appear expanded. Such distortion aftereffects have been proposed to result from renormalization, in which the visual system constantly updates a prototype according to the adaptors' characteristics and evaluates subsequent faces relative to that. However, although consequences of adaptation are easily observed in behavioral aftereffects, it has proven difficult to observe renormalization during adaptation itself. Here we directly measured brain responses during adaptation to establish a neural correlate of renormalization. Given that the face-evoked occipito-temporal P2 event-related brain potential has been found to increase with face prototypicality, we reasoned that the adaptor-elicited P2 could serve as an electrophysiological indicator for renormalization. Participants adapted to sequences of four distorted (compressed or expanded) or undistorted faces, followed by a slightly distorted test face, which they had to classify as undistorted or distorted. We analysed ERPs evoked by each of the adaptors and found that P2 (but not N170) amplitudes evoked by consecutive adaptor faces exhibited an electrophysiological pattern of renormalization during adaptation to distorted faces: P2 amplitudes evoked by both compressed and expanded adaptors significantly increased towards asymptotic levels as adaptation proceeded. P2 amplitudes were smallest for the first adaptor, significantly larger for the second, and yet larger for the third adaptor. We conclude that the sensitivity of the occipito-temporal P2 to the perceived deviation of a face from the norm makes this component an excellent tool to study adaptation-induced renormalization. Copyright © 2017 Elsevier Inc. All rights reserved.

  2. Transport signatures of topology protected quantum criticality in Majorana islands

    NASA Astrophysics Data System (ADS)

    Papaj, Michal; Zhu, Zheng; Fu, Liang

    Using numerical renormalization group we study a topological superconductor island coupled to three metallic leads in the vicinity of the charge degeneracy point. We show that the system flows to a non-Fermi liquid fixed point at low temperatures with fractional quantized DC conductance of 2 / 3e2 / h . Our proposal is experimentally feasible due to a much larger crossover temperature than in the previously studied cases and the robustness of the setup against the channel coupling anisotropy and charge degeneracy detuning. Including Majorana hybridization drives the system into a Fermi liquid phase at very low temperatures. The two proposed experimental signatures of multi-terminal electron teleportation include nonmonotonic temperature dependence of DC conductance and emergence of a plateau at 2 / 3e2 / h in tunnel coupling dependence of DC conductance. This work is funded by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award de-sc0010526 (ZZ and LF) and the NSF STC ''Center for Integrated Quantum Materials'' under Cooperative Agreement No. DMR-1231319 (MP).

  3. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    DOE PAGES

    Nocera, Alberto; Patel, Niravkumar D.; Fernandez-Baca, Jaime A.; ...

    2016-11-28

    In this paper, we study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small asmore » U/t ~ 2–3, although ratios of peak intensities at different momenta continue evolving with increasing U/t converging only slowly to the Heisenberg limit. Finally, we discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.« less

  4. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nocera, Alberto; Patel, Niravkumar D.; Fernandez-Baca, Jaime A.

    In this paper, we study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small asmore » U/t ~ 2–3, although ratios of peak intensities at different momenta continue evolving with increasing U/t converging only slowly to the Heisenberg limit. Finally, we discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.« less

  5. Phase diagram of the Hubbard-Holstein model on a four-leg tube system at quarter filling

    NASA Astrophysics Data System (ADS)

    Reja, Sahinur; Nishimoto, Satoshi

    2018-06-01

    We derive an effective electronic Hamiltonian for the square lattice Hubbard-Holstein model (HHM) in the strong electron-electron (e -e ) and electron-phonon (e -p h ) coupling regime and under nonadiabatic conditions (t /ω0≤1 ), t and ω0 being the electron hopping and phonon frequency respectively. Using the density matrix renormalization-group method, we simulate this effective electronic model on a four-leg cylinder system at quarter filling and present a phase diagram in the g -U plane where g and U are the e -p h coupling constant and Hubbard on-site interaction respectively. For larger g , we find that a cluster of spins, i.e., phase separation (PS), gives way to a charge density wave (CDW) phase made of nearest-neighbor singlets which abruptly goes to another CDW phase as we increase U . But for smaller g , we find a metallic phase sandwiched between PS and the singlet CDW phase. This phase is characterized by a vanishing charge gap but a finite spin gap, suggesting a singlet superconducting phase.

  6. Two-loop mass splittings in electroweak multiplets: Winos and minimal dark matter

    NASA Astrophysics Data System (ADS)

    McKay, James; Scott, Pat

    2018-03-01

    The radiatively-induced splitting of masses in electroweak multiplets is relevant for both collider phenomenology and dark matter. Precision two-loop corrections of O (MeV ) to the triplet mass splitting in the wino limit of the minimal supersymmetric standard model can affect particle lifetimes by up to 40%. We improve on previous two-loop self-energy calculations for the wino model by obtaining consistent input parameters to the calculation via two-loop renormalization-group running, and including the effect of finite light quark masses. We also present the first two-loop calculation of the mass splitting in an electroweak fermionic quintuplet, corresponding to the viable form of minimal dark matter (MDM). We place significant constraints on the lifetimes of the charged and doubly-charged fermions in this model. We find that the two-loop mass splittings in the MDM quintuplet are not constant in the large-mass limit, as might naively be expected from the triplet calculation. This is due to the influence of the additional heavy fermions in loop corrections to the gauge boson propagators.

  7. Optimizing long-range order, band gap, and group velocities for graphene on close-packed metal surfaces.

    PubMed

    Natterer, F D; Rusponi, S; Papagno, M; Carbone, C; Brune, H

    2012-08-08

    We compare different growth methods with the aim of optimizing the long-range order of a graphene layer grown on Ru(0001). Combining chemical vapor deposition with carbon loading and segregation of the surface layer leads to autocorrelation lengths of 240 Å. We present several routes to band gap and charge carrier mobility engineering for the example of graphene on Ir(111). Ir cluster superlattices self-assembled onto the graphene moiré pattern produce a strong renormalization of the electron group velocity close to the Dirac point, leading to highly anisotropic Dirac cones and the enlargement of the gap from 140 to 340 meV. This gap can further be enhanced to 740 meV by Na co-adsorption onto the Ir cluster superlattice at room temperature. This value is close to that of Ge, and the high group velocity of the charge carriers is fully preserved. We also present data for Na adsorbed without the Ir clusters. In both cases we find that the Na is on top of the graphene layer.

  8. Toward one-loop tunneling rates of near-extremal magnetic black hole pair production

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yi, P.

    Pair production of magnetic Reissner-Nordstroem black holes (of charges [plus minus][ital q]) was recently studied in the leading WKB approximation. Here we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behavior of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for a sufficiently weak field [ital B], the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renormalization procedures, typical one-loop contributions to themore » WKB exponent are shown to be inversely proportional to [ital B], as [ital B][r arrow]0, indicating that the leading Schwinger term is corrected by a small fraction [similar to][h bar]/[ital q][sup 2]. We demonstrate that this correction to the Schwinger term is actually due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. Finally we discuss a few loose ends.« less

  9. Broken Time-Reversal Symmetry in Strongly Correlated Ladder Structures

    NASA Astrophysics Data System (ADS)

    Troyer, Matthias

    2004-03-01

    A decade after the first detailed numerical investigations of strongly correlated ladder models, exotic and interesting phases are still being discovered. Besides charge and spin density wave states with broken translational symmetry, and resonating valence bond (RVB) type superconductivity, a time reversal symmetry borken phase was recently found at half filling [J.B. Marston et al., Phys. Rev. Lett 89, 056404 (2002)]. In this talk I will present our recent results of density matrix renormalization group (DMRG) calculations [Phys. Rev. Lett. 90, 186401 (2003)], where we provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of this state in which long-range ordered orbital currents are arranged in a staggered pattern. This phase, which we found to coexist with a charge density wave, is known in the literature under the names ``staggered flux phase'', ``orbital antiferromagnetism'' or ``d-density wave (DDW)''. This brings us closer to recent proposals that this order might be realized in the enigmatic pseudogap phase of the cuprate high temperature superconductors.

  10. Renormalization of concurrence: The application of the quantum renormalization group to quantum-information systems

    NASA Astrophysics Data System (ADS)

    Kargarian, M.; Jafari, R.; Langari, A.

    2007-12-01

    We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

  11. Quantum corrections to non-Abelian SUSY theories on orbifolds

    NASA Astrophysics Data System (ADS)

    Groot Nibbelink, Stefan; Hillenbach, Mark

    2006-07-01

    We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S/Z and T/Z, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non- Z fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.

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

    PubMed

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

    2015-01-21

    The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

  13. Effective scalar field theory and reduction of couplings

    NASA Astrophysics Data System (ADS)

    Atance, Mario; Cortés, José Luis

    1997-09-01

    A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the possibility to go beyond the renormalizable φ4 theory without losing its predictive power. It is shown that there is a minimal extension with just one additional free parameter (the mass scale of the effective theory expansion) and some of its properties are discussed.

  14. Lorentz symmetry violation with higher-order operators and renormalization

    NASA Astrophysics Data System (ADS)

    Nascimento, J. R.; Petrov, A. Yu; Reyes, C. M.

    2018-01-01

    Effective field theory has shown to be a powerful method in searching for quantum gravity effects and in particular for CPT and Lorentz symmetry violation. In this work we study an effective field theory with higher-order Lorentz violation, specifically we consider a modified model with scalars and modified fermions interacting via the Yukawa coupling. We study its renormalization properties, that is, its radiative corrections and renormalization conditions in the light of the requirements of having a finite and unitary S-matrix.

  15. Hypercuboidal renormalization in spin foam quantum gravity

    NASA Astrophysics Data System (ADS)

    Bahr, Benjamin; Steinhaus, Sebastian

    2017-06-01

    In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

  16. Callan-Symanzik equations for infrared Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Weber, Axel; Dall'Olio, Pietro

    2017-12-01

    Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.

  17. The { β}-expansion formalism in perturbative QCD and its extension

    NASA Astrophysics Data System (ADS)

    Kataev, A. L.; Mikhailov, S. V.

    2016-11-01

    We discuss the { β}-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ R-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the { β}-expansion. We illustrate this feature considering the nonsinglet Adler function D NS in the third order of perturbation. We propose a generalization of the { β}-expansion for the renormalization group covariant quantities — the { β, γ}-expansion.

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

    DOE PAGES

    Johnston, S.; Lee, W. S.; Chen, Y.; ...

    2010-01-01

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

  19. Strong coupling electrostatics for randomly charged surfaces: antifragility and effective interactions.

    PubMed

    Ghodrat, Malihe; Naji, Ali; Komaie-Moghaddam, Haniyeh; Podgornik, Rudolf

    2015-05-07

    We study the effective interaction mediated by strongly coupled Coulomb fluids between dielectric surfaces carrying quenched, random monopolar charges with equal mean and variance, both when the Coulomb fluid consists only of mobile multivalent counterions and when it consists of an asymmetric ionic mixture containing multivalent and monovalent (salt) ions in equilibrium with an aqueous bulk reservoir. We analyze the consequences that follow from the interplay between surface charge disorder, dielectric and salt image effects, and the strong electrostatic coupling that results from multivalent counterions on the distribution of these ions and the effective interaction pressure they mediate between the surfaces. In a dielectrically homogeneous system, we show that the multivalent counterions are attracted towards the surfaces with a singular, disorder-induced potential that diverges logarithmically on approach to the surfaces, creating a singular but integrable counterion density profile that exhibits an algebraic divergence at the surfaces with an exponent that depends on the surface charge (disorder) variance. This effect drives the system towards a state of lower thermal 'disorder', one that can be described by a renormalized temperature, exhibiting thus a remarkable antifragility. In the presence of an interfacial dielectric discontinuity, the singular behavior of counterion density at the surfaces is removed but multivalent counterions are still accumulated much more strongly close to randomly charged surfaces as compared with uniformly charged ones. The interaction pressure acting on the surfaces displays in general a highly non-monotonic behavior as a function of the inter-surface separation with a prominent regime of attraction at small to intermediate separations. This attraction is caused directly by the combined effects from charge disorder and strong coupling electrostatics of multivalent counterions, which dominate the surface-surface repulsion due to the (equal) mean charges on the two surfaces and the osmotic pressure of monovalent ions residing between them. These effects can be quite significant even with a small degree of surface charge disorder relative to the mean surface charge. The strong coupling, disorder-induced attraction is typically much stronger than the van der Waals interaction between the surfaces, especially within a range of several nanometers for the inter-surface separation, where such effects are predicted to be most pronounced.

  20. Exp(1076) Shades of Black: Aspects of Black Hole Microstates

    NASA Astrophysics Data System (ADS)

    Vasilakis, Orestis

    In this thesis we examine smooth supergravity solutions known as "microstate geometries". These solutions have neither a horizon, nor a singularity, yet they have the same asymptotic structure and conserved charges as black holes. Specifically we study supersymmetric and extremal non-supersymmetric solutions. The goal of this program is to construct enough microstates to account for the correct scaling behavior of the black hole entropy with respect to the charges within the supergravity approximation. For supersymmetric systems that are ⅛-BPS, microstate geometries account so far only for Q5/4 of the total entropy S ˜ Q3/2, while for non-supersymmetric systems the known microstate geometries are sporadic. For the supersymmetric case we construct solutions with three and four charges. Five-dimensional systems with three and four charges are ⅛-BPS. Thus they admit macroscopic horizons making the supergravity approximation valid. For the three-charge case we present some steps towards the construction of the superstratum, a microstate geometry depending on arbitrary functions of two variables, which is expected to provide the necessary entropy for this class of solutions. Specifically we construct multiple concentric solutions with three electric and two dipole magnetic charges which depend on arbitrary functions of two variables and examine their properties. These solutions have no KKM charge and thus are singular. For the four-charge case we construct microstate geometries by extending results available in the literature for three charges. We find smooth solutions in terms of bubbled geometries with ambipolar Gibbons-Hawking base space and by constructing the relevant supertubes. In the non-supersymmetric case we work with a three-charge system of extremal black holes known as almost-BPS, which provides a controlled way of breaking sypersymmetry. By using supertubes we construct the first systematic example of a family of almost-BPS microstate geometries and examine the moduli space of solutions. Furthermore by using brane probe analysis we show that, despite the breaking of supersymmetry, almost-BPS solutions receive no quantum corrections and thus must be subject to some kind of non-renormalization theorem.

  1. 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.

  2. Renormalization of spin excitations in hexagonal HoMnO3 by magnon-phonon coupling

    NASA Astrophysics Data System (ADS)

    Kim, Taehun; Leiner, Jonathan C.; Park, Kisoo; Oh, Joosung; Sim, Hasung; Iida, Kazuki; Kamazawa, Kazuya; Park, Je-Geun

    2018-05-01

    Hexagonal HoMnO3, a two-dimensional Heisenberg antiferromagnet, has been studied via inelastic neutron scattering. A simple Heisenberg model with a single-ion anisotropy describes most features of the spin-wave dispersion curves. However, there is shown to be a renormalization of the magnon energies located at around 11 meV. Since both the magnon-magnon interaction and magnon-phonon coupling can affect the renormalization in a noncollinear magnet, we have accounted for both of these couplings by using a Heisenberg XXZ model with 1 /S expansions [1] and the Einstein site phonon model [13], respectively. This quantitative analysis leads to the conclusion that the renormalization effect primarily originates from the magnon-phonon coupling, while the spontaneous magnon decay due to the magnon-magnon interaction is suppressed by strong two-ion anisotropy.

  3. Off-shell renormalization in Higgs effective field theories

    NASA Astrophysics Data System (ADS)

    Binosi, Daniele; Quadri, Andrea

    2018-04-01

    The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

  4. Band gap renormalization and Burstein-Moss effect in silicon- and germanium-doped wurtzite GaN up to 1020 cm-3

    NASA Astrophysics Data System (ADS)

    Feneberg, Martin; Osterburg, Sarah; Lange, Karsten; Lidig, Christian; Garke, Bernd; Goldhahn, Rüdiger; Richter, Eberhard; Netzel, Carsten; Neumann, Maciej D.; Esser, Norbert; Fritze, Stephanie; Witte, Hartmut; Bläsing, Jürgen; Dadgar, Armin; Krost, Alois

    2014-08-01

    The interplay between band gap renormalization and band filling (Burstein-Moss effect) in n-type wurtzite GaN is investigated. For a wide range of electron concentrations up to 1.6×1020cm-3 spectroscopic ellipsometry and photoluminescence were used to determine the dependence of the band gap energy and the Fermi edge on electron density. The band gap renormalization is the dominating effect up to an electron density of about 9×1018cm-3; at higher values the Burstein-Moss effect is stronger. Exciton screening, the Mott transition, and formation of Mahan excitons are discussed. A quantitative understanding of the near gap transition energies on electron density is obtained. Higher energy features in the dielectric functions up to 10eV are not influenced by band gap renormalization.

  5. 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.

  6. Gauge-independent renormalization of the N2HDM

    NASA Astrophysics Data System (ADS)

    Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui

    2017-12-01

    The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

  7. Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wang, Sheng-Quan; Wu, Xing-Gang; Brodsky, Stanley J.

    We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice overmore » the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.« less

  8. The renormalization scale-setting problem in QCD

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 scalemore » 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 BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC–BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.« less

  9. Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN

    NASA Astrophysics Data System (ADS)

    Nery, Jean Paul; Allen, Philip B.

    2016-09-01

    We develop a simple method to study the zero-point and thermally renormalized electron energy ɛk n(T ) for k n the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter i δ to suppress noise in the density-functional integrations. The finite δ also eliminates the polar divergence which is an artifact of the adiabatic approximation. Nonadiabatic Fröhlich polaron methods then provide analytic expressions for the missing part of the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zinc-blende GaN for an 18 ×18 ×18 integration grid. The Fröhlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.

  10. Multiscale unfolding of real networks by geometric renormalization

    NASA Astrophysics Data System (ADS)

    García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

    2018-06-01

    Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Alexandrou, C.; Computation-based Science and Technology Research Center, The Cyprus Institute, 15 Kypranoros Str., 1645 Nicosia; Constantinou, M.

    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 thesemore » 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.« less

  12. Consistent parameter fixing in the quark-meson model with vacuum fluctuations

    NASA Astrophysics Data System (ADS)

    Carignano, Stefano; Buballa, Michael; Elkamhawy, Wael

    2016-08-01

    We revisit the renormalization prescription for the quark-meson model in an extended mean-field approximation, where vacuum quark fluctuations are included. At a given cutoff scale the model parameters are fixed by fitting vacuum quantities, typically including the sigma-meson mass mσ and the pion decay constant fπ. In most publications the latter is identified with the expectation value of the sigma field, while for mσ the curvature mass is taken. When quark loops are included, this prescription is however inconsistent, and the correct identification involves the renormalized pion decay constant and the sigma pole mass. In the present article we investigate the influence of the parameter-fixing scheme on the phase structure of the model at finite temperature and chemical potential. Despite large differences between the model parameters in the two schemes, we find that in homogeneous matter the effect on the phase diagram is relatively small. For inhomogeneous phases, on the other hand, the choice of the proper renormalization prescription is crucial. In particular, we show that if renormalization effects on the pion decay constant are not considered, the model does not even present a well-defined renormalized limit when the cutoff is sent to infinity.

  13. Time-dependent spectral renormalization method

    NASA Astrophysics Data System (ADS)

    Cole, Justin T.; Musslimani, Ziad H.

    2017-11-01

    The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

  14. Perturbative Power Counting, Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

    NASA Astrophysics Data System (ADS)

    Liao, Yi; Ma, Xiao-Dong

    2018-03-01

    We study two aspects of higher dimensional operators in standard model effective field theory. We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension. The power counting is determined by the number of loops and the difference of the indices of the two operators involved, which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power. Then we show that the operators with the lowest index are unique at each mass dimension d, i.e., (H † H) d/2 for even d ≥ 4, and (LT∈ H)C(LT∈ H) T (H † H)(d-5)/2 for odd d ≥ 5. Here H, L are the Higgs and lepton doublet, and ∈, C the antisymmetric matrix of rank two and the charge conjugation matrix, respectively. The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting. We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics. We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights. Supported by the National Natural Science Foundation of China under Grant Nos. 11025525, 11575089, and by the CAS Center for Excellence in Particle Physics (CCEPP)

  15. Zero point motion effect on the electronic properties of diamond, trans-polyacetylene and polyethylene

    NASA Astrophysics Data System (ADS)

    Cannuccia, E.; Marini, A.

    2012-09-01

    It has been recently shown, using ab-initio methods, that bulk diamond is characterized by a large band-gap renormalization (˜0.6 eV) induced by the electron-phonon interaction. In this work we show that in polymers, compared to bulk materials, the larger amplitude of the atomic vibrations makes the real excitations of the system be composed by entangled electron-phonon states. We prove that these states carry only a fraction of the electronic charge, thus leading, inevitably, to the failure of the electronic picture. The present results cast doubts on the accuracy of purely electronic calculations. They also lead to a critical revision of the state-of-the-art description of carbon-based nanostructures, opening a wealth of potential implications.

  16. Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.

    PubMed

    Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R

    2016-05-13

    The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

  17. Holographic entanglement chemistry

    NASA Astrophysics Data System (ADS)

    Caceres, Elena; Nguyen, Phuc H.; Pedraza, Juan F.

    2017-05-01

    We use the Iyer-Wald formalism to derive an extended first law of entanglement that includes variations in the cosmological constant, Newton's constant and—in the case of higher-derivative theories—all the additional couplings of the theory. In Einstein gravity, where the number of degrees of freedom N2 of the dual field theory is a function of Λ and G , our approach allows us to vary N by keeping the field theory scale fixed or to vary the field theory scale by keeping N fixed. We also derive an extended first law of entanglement for Gauss-Bonnet and Lovelock gravity and show that in these cases all the extra variations reorganize nicely in terms of the central charges of the theory. Finally, we comment on the implications for renormalization group flows and c -theorems in higher dimensions.

  18. Leading temperature dependence of the conductance in Kondo-correlated quantum dots.

    PubMed

    Aligia, A A

    2018-04-18

    Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

  19. First Renormalized Parton Distribution Functions from Lattice QCD

    NASA Astrophysics Data System (ADS)

    Lin, Huey-Wen; LP3 Collaboration

    2017-09-01

    We present the first lattice-QCD results on the nonperturbatively renormalized parton distribution functions (PDFs). Using X.D. Ji's large-momentum effective theory (LaMET) framework, lattice-QCD hadron structure calculations are able to overcome the longstanding problem of determining the Bjorken- x dependence of PDFs. This has led to numerous additional theoretical works and exciting progress. In this talk, we will address a recent development that implements a step missing from prior lattice-QCD calculations: renormalization, its effects on the nucleon matrix elements, and the resultant changes to the calculated distributions.

  20. Renormalization group contraction of tensor networks in three dimensions

    NASA Astrophysics Data System (ADS)

    García-Sáez, Artur; Latorre, José I.

    2013-02-01

    We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

  1. Novel formulations of CKM matrix renormalization

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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.

  2. Effective-field renormalization-group method for Ising systems

    NASA Astrophysics Data System (ADS)

    Fittipaldi, I. P.; De Albuquerque, D. F.

    1992-02-01

    A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

  3. Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model

    NASA Astrophysics Data System (ADS)

    Sousa, J. Ricardo de

    A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.

  4. An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

    NASA Astrophysics Data System (ADS)

    de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

    2009-10-01

    In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

  5. Renormalization in Large Momentum Effective Theory of Parton Physics.

    PubMed

    Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong

    2018-03-16

    In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

  6. Surprises in low-dimensional correlated systems

    NASA Astrophysics Data System (ADS)

    Lin, Hsiu-Hau

    In this thesis, correlation effects in low-dimensional systems were studied. In particular, we focus on two systems: a point-contact in the quantum-Hall regime under the influence of ac drive and quasi-one-dimensional ladder materials with generic interactions in weak coupling. Powerful techniques, including renormalization group, quantum field theory, operator product expansions, bosonization,...etc., were employed to extract surprising physics out of these strongly fluctuating systems. We first study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional Quantum Hall fluids at filling nu-1 an odd integer. In a semi-classical limit, the tunneling current exhibits mode-locking, which corresponds to plateaus in the I-V curve at integer multiples of I = ef , with f the ac drive frequency. However, the full quantum model exhibits rounded plateaus centered around the quantized current values due to quantum fluctuations. The locations of these plateaus can serve as an indirect hint of fractional charges. Switching attentions to quasi-one-dimensional coupled-chain systems, we present a systematic weak-coupling renormalization group (RG) technique and find that generally broad regions of the phase space of the ladder materials are unstable to pairing, usually with approximate d-wave symmetry. The dimensional crossovers from 1D to 2D were also discussed. Carbon nanotubes as possible candidates that display such unconventional pairing and interesting physics in weak coupling were discussed. Quite surprisingly, a hidden symmetry was found in the weakly-coupled two-leg ladder. A perturbative renormalization group analysis reveals that at half-filling the model scales onto an exactly soluble SO(8) symmetric Gross-Neveu model. Integrability of the Gross-Neveu model is employed to extract the exact energies, degeneracies and quantum numbers of all the low energy excited states, which fall into degenerate SO(8) multiplets. For generic physical interactions, there are four robust phases which have different SO(8) symmetries but share a common SO(5) symmetry. The effects of marginal chiral interactions were discussed at the end. Finally, we summarize our main results and discuss related open questions for future study.

  7. The use of effective variables in high energy physics

    NASA Astrophysics Data System (ADS)

    Baumgart, Matthew Todd

    In high energy physics, we often gain by systematically reducing the formal description of a physical system or the data sets that come from particle colliders. Converting the naive, original setup results in a more useful set of couplings, fields, or observables, which we call effective variables. This thesis considers several examples of them: We take a φ4 scalar field theory and renormalize it according to the equations of Wilsonian exact renormalization group. Whatever the initial setup of the theory, this results in an infinite number of operators. We demonstrate a procedure to remove all interaction terms except for the quartic. We find its coupling has the same one-loop beta-function as obtained from standard renormalization group. We also examine the relationship between little Higgs and 5d composite models with identical symmetries. By performing an "extreme" deconstruction, one can reduce any warped composite model to a little Higgs theory on a handful of sites. We find that the finiteness of the Higgs potential in 5d is due to the same collective symmetry breaking as in the little Higgs. We compare a 4d and 5d model with the same symmetry to the data. We see that the 5d model has difficulty meeting several constraints simultaneously. By contrast, the Minimal Moose with custodial symmetry is viable in a large region of its parameter space. Finally, we turn our attentions to the hadron collider environment. In the context of SUSY extended by U(1)', production of an initial Z' gauge boson gives us an additional kinematic constraint. We use this to implement a novel method to measure all of the superpartner masses involved in its decay. For certain final states with two invisible particles, one can construct kinematic observables bounded above by parent particle masses. Additionally, we study other effects of extending the MSSM by a Z '. The production cross-section of sleptons is enhanced over the MSSM, so the discovery potential for sleptons is greatly increased. The flavor and charge information in the resulting slepton decay provides a useful handle on the identity of the LSP.

  8. The renormalization group and the implicit function theorem for amplitude equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kirkinis, Eleftherios

    2008-07-15

    This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen et al., Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation formore » both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases.« less

  9. A key heterogeneous structure of fractal networks based on inverse renormalization scheme

    NASA Astrophysics Data System (ADS)

    Bai, Yanan; Huang, Ning; Sun, Lina

    2018-06-01

    Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

  10. One-loop renormalization of a gravity-scalar system

    NASA Astrophysics Data System (ADS)

    Park, I. Y.

    2017-05-01

    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the "mass" term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.

  11. NLO renormalization in the Hamiltonian truncation

    NASA Astrophysics Data System (ADS)

    Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

    2017-09-01

    Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

  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. REVIEWS OF TOPICAL PROBLEMS: Particle kinetics in highly turbulent plasmas (renormalization and self-consistent field methods)

    NASA Astrophysics Data System (ADS)

    Bykov, Andrei M.; Toptygin, Igor'N.

    1993-11-01

    This review presents methods available for calculating transport coefficients for impurity particles in plasmas with strong long-wave MHD-type velocity and magnetic-field fluctuations, and random ensembles of strong shock fronts. The renormalization of the coefficients of the mean-field equation of turbulent dynamo theory is also considered. Particular attention is devoted to the renormalization method developed by the authors in which the renormalized transport coefficients are calculated from a nonlinear transcendental equation (or a set of such equations) and are expressed in the form of explicit functions of pair correlation tensors describing turbulence. Numerical calculations are reproduced for different turbulence spectra. Spatial transport in a magnetic field and particle acceleration by strong turbulence are investigated. The theory can be used in a wide range of practical problems in plasma physics, atmospheric physics, ocean physics, astrophysics, cosmic-ray physics, and so on.

  14. Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

    DOE PAGES

    An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

    2016-03-14

    The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

  15. Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

    The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

  16. 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.

  17. 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.

  18. The QCD running coupling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

    Here, we review present knowledge onmore » $$\\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\\alpha_s(Q^2)$$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $$\\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $$\\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\\alpha_s$$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less

  19. The QCD running coupling

    DOE PAGES

    Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.

    2016-05-09

    Here, we review present knowledge onmore » $$\\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\\alpha_s(Q^2)$$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $$\\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $$\\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\\alpha_s$$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less

  20. Renormalization group, normal form theory and the Ising model

    NASA Astrophysics Data System (ADS)

    Raju, Archishman; Hayden, Lorien; Clement, Colin; Liarte, Danilo; Sethna, James

    The results of the renormalization group are commonly advertised as the existence of power law singularities at critical points. Logarithmic and exponential corrections are seen as special cases and dealt with on a case-by-case basis. We propose to systematize computing the singularities in the renormalization group using perturbative normal form theory. This gives us a way to classify all such singularities in a unified framework and to generate a systematic machinery to do scaling collapses. We show that this procedure leads to some new results even in classic cases like the Ising model and has general applicability.

  1. Optical phonon effect in quasi-one-dimensional semiconductor quantum wires: Band-gap renormalization

    NASA Astrophysics Data System (ADS)

    Dan, Nguyen Trung; Bechstedt, F.

    1996-02-01

    We present theoretical studies of dynamical screening in quasi-one-dimensional semiconductor quantum wires including electron-electron and electron-LO-phonon interactions. Within the random-phase approximation we obtain analytical expressions for screened interaction potentials. These expressions can be used to calculate the band-gap renormalization of quantum wires, which depends on the free-carrier density and temperature. We find that the optical phonon interaction effect plays a significant role in band-gap renormalization of quantum wires. The numerical results are compared with some recent experiment measurements as well as available theories.

  2. Renormalization scheme dependence of high-order perturbative QCD predictions

    NASA Astrophysics Data System (ADS)

    Ma, Yang; Wu, Xing-Gang

    2018-02-01

    Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

  3. Renormalization of Supersymmetric QCD on the Lattice

    NASA Astrophysics Data System (ADS)

    Costa, Marios; Panagopoulos, Haralambos

    2018-03-01

    We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

  4. Topics in elementary particle physics

    NASA Astrophysics Data System (ADS)

    Jin, Xiang

    The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

  5. Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.

    PubMed

    Andreev, Oleg

    2009-05-29

    We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.

  6. Convergence behavior of the random phase approximation renormalized correlation energy

    NASA Astrophysics Data System (ADS)

    Bates, Jefferson E.; Sensenig, Jonathon; Ruzsinszky, Adrienn

    2017-05-01

    Based on the random phase approximation (RPA), RPA renormalization [J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013), 10.1063/1.4827254] is a robust many-body perturbation theory that works for molecules and materials because it does not diverge as the Kohn-Sham gap approaches zero. Additionally, RPA renormalization enables the simultaneous calculation of RPA and beyond-RPA correlation energies since the total correlation energy is the sum of a series of independent contributions. The first-order approximation (RPAr1) yields the dominant beyond-RPA contribution to the correlation energy for a given exchange-correlation kernel, but systematically underestimates the total beyond-RPA correction. For both the homogeneous electron gas model and real systems, we demonstrate numerically that RPA renormalization beyond first order converges monotonically to the infinite-order beyond-RPA correlation energy for several model exchange-correlation kernels and that the rate of convergence is principally determined by the choice of the kernel and spin polarization of the ground state. The monotonic convergence is rationalized from an analysis of the RPA renormalized correlation energy corrections, assuming the exchange-correlation kernel and response functions satisfy some reasonable conditions. For spin-unpolarized atoms, molecules, and bulk solids, we find that RPA renormalization is typically converged to 1 meV error or less by fourth order regardless of the band gap or dimensionality. Most spin-polarized systems converge at a slightly slower rate, with errors on the order of 10 meV at fourth order and typically requiring up to sixth order to reach 1 meV error or less. Slowest to converge, however, open-shell atoms present the most challenging case and require many higher orders to converge.

  7. CP violation in heavy MSSM Higgs scenarios

    DOE PAGES

    Carena, M.; Ellis, J.; Lee, J. S.; ...

    2016-02-18

    We introduce and explore new heavy Higgs scenarios in the Minimal Supersymmetric Standard Model (MSSM) with explicit CP violation, which have important phenomenological implications that may be testable at the LHC. For soft supersymmetry-breaking scales M S above a few TeV and a charged Higgs boson mass M H+ above a few hundred GeV, new physics effects including those from explicit CP violation decouple from the light Higgs boson sector. However, such effects can significantly alter the phenomenology of the heavy Higgs bosons while still being consistent with constraints from low-energy observables, for instance electric dipole moments. To consider scenariosmore » with a charged Higgs boson much heavier than the Standard Model (SM) particles but much lighter than the supersymmetric particles, we revisit previous calculations of the MSSM Higgs sector. We compute the Higgs boson masses in the presence of CP violating phases, implementing improved matching and renormalization-group (RG) effects, as well as two-loop RG effects from the effective two-Higgs Doublet Model (2HDM) scale M H± to the scale M S. Here, we illustrate the possibility of non-decoupling CP-violating effects in the heavy Higgs sector using new benchmark scenarios named.« less

  8. Swelling of biological and semiflexible polyelectrolytes.

    PubMed

    Dobrynin, Andrey V; Carrillo, Jan-Michael Y

    2009-10-21

    We have developed a theoretical model of swelling of semiflexible (biological) polyelectrolytes in salt solutions. Our approach is based on separation of length scales which allowed us to split a chain's electrostatic energy into two parts that describe local and remote electrostatic interactions along the polymer backbone. The local part takes into account interactions between charged monomers that are separated by distances along the polymer backbone shorter than the chain's persistence length. These electrostatic interactions renormalize chain persistence length. The second part includes electrostatic interactions between remote charged pairs along the polymer backbone located at distances larger than the chain persistence length. These interactions are responsible for chain swelling. In the framework of this approach we calculated effective chain persistence length and chain size as a function of the Debye screening length, chain degree of ionization, bare persistence length and chain degree of polymerization. Our crossover expression for the effective chain's persistence length is in good quantitative agreement with the experimental data on DNA. We have been able to fit experimental datasets by using two adjustable parameters: DNA ionization degree (α = 0.15-0.17) and a bare persistence length (l(p) = 40-44 nm).

  9. CP violation in heavy MSSM Higgs scenarios

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Carena, M.; Ellis, J.; Lee, J. S.

    We introduce and explore new heavy Higgs scenarios in the Minimal Supersymmetric Standard Model (MSSM) with explicit CP violation, which have important phenomenological implications that may be testable at the LHC. For soft supersymmetry-breaking scales M S above a few TeV and a charged Higgs boson mass M H+ above a few hundred GeV, new physics effects including those from explicit CP violation decouple from the light Higgs boson sector. However, such effects can significantly alter the phenomenology of the heavy Higgs bosons while still being consistent with constraints from low-energy observables, for instance electric dipole moments. To consider scenariosmore » with a charged Higgs boson much heavier than the Standard Model (SM) particles but much lighter than the supersymmetric particles, we revisit previous calculations of the MSSM Higgs sector. We compute the Higgs boson masses in the presence of CP violating phases, implementing improved matching and renormalization-group (RG) effects, as well as two-loop RG effects from the effective two-Higgs Doublet Model (2HDM) scale M H± to the scale M S. Here, we illustrate the possibility of non-decoupling CP-violating effects in the heavy Higgs sector using new benchmark scenarios named.« less

  10. Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter /κ

    NASA Astrophysics Data System (ADS)

    Kleinert, Hagen; Nogueira, Flavio S.

    2003-02-01

    We present a semi-perturbative approach which yields an infrared-stable fixed point in the Ginzburg-Landau for N=2, where N/2 is the number of complex components. The calculations are done in d=3 dimensions and below Tc, where the renormalization group functions can be expressed directly as functions of the Ginzburg parameter κ which is the ratio between the two fundamental scales of the problem, the penetration depth λ and the correlation length ξ. We find a charged fixed point for κ>1/ 2, that is, in the type II regime, where Δκ≡κ-1/ 2 is shown to be a natural expansion parameter. This parameter controls a momentum space instability in the two-point correlation function of the order field. This instability appears at a non-zero wave-vector p0 whose magnitude scales like ˜ Δκ β¯, with a critical exponent β¯=1/2 in the one-loop approximation, a behavior known from magnetic systems with a Lifshitz point in the phase diagram. This momentum space instability is argued to be the origin of the negative η-exponent of the order field.

  11. Instabilities of coupled Cu2O5 ladders

    NASA Astrophysics Data System (ADS)

    Schuetz, Florian; Marston, Brad

    2008-03-01

    The spin-ladder compound Sr14-xCaxCu24O41 has a complex phase diagram including charge-density-wave order as well as unconventional superconductivity under high pressure. Due to its quasi-one-dimensional natureootnotetextS. Lee, J. B. Marston, J. O. Fjaerestad, Phys. Rev. B 72, 075126. fundamental questions about the high-Tc cuprates might be more easily addressed in this context. However, due to the spatial proximity of neighboring ladders inter-ladder Coulomb repulsion as well as hopping between ladders might still be important. Using the functional renormalization groupootnotetextM. Salmhofer and C. Honerkamp, Prog. Theor. Physics 105, 1 (2001). and an analysis of generalized susceptibilities ootnotetextD. Zanchi and H. J. Schulz, Phys. Rev. B 61, 13609 (2000); C. J. Halboth and W. Metzner, Phys. Rev. Lett. 85, 5162 (2000)., we study a model of coupled Cu2O5 ladders ootnotetextK. Wohlfeld, A. M. Oles, and G. A. Sawatzky, Phys. Rev. B 75, 180501(R) (2007).. We investigate instabilities towards charge, spin, and pairing order as a function of hole doping, inter-ladder hopping, and interaction strength starting from experimentally relevant hopping parametersootnotetextT. F. A. Müller, et al., Phys. Rev. B 57, R12655 (1998)..

  12. Simple on-shell renormalization framework for the Cabibbo-Kobayashi-Maskawa matrix

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kniehl, Bernd A.; Sirlin, Alberto

    2006-12-01

    We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust nondiagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the Hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W{yields}q{sub i}+q{sub j} reduces to that in the unmixed, single-generation case. Diagonalizationmore » of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.« less

  13. Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

    NASA Astrophysics Data System (ADS)

    Panagopoulos, Haralambos; Spanoudes, Gregoris

    2018-03-01

    In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].

  14. Nonlinear Gyro-Landau-Fluid Equations

    NASA Astrophysics Data System (ADS)

    Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

    1996-11-01

    We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

  15. Controlling sign problems in spin models using tensor renormalization

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

    We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds 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.

  16. The propagator of stochastic electrodynamics

    NASA Astrophysics Data System (ADS)

    Cavalleri, G.

    1981-01-01

    The "elementary propagator" for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density ~ω3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to ψψ* where ψ is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics.

  17. Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4-

    NASA Astrophysics Data System (ADS)

    Sharma, Prachi; Truhlar, Donald G.; Gagliardi, Laura

    2018-03-01

    The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

  18. Holographic heat engines

    NASA Astrophysics Data System (ADS)

    Johnson, Clifford V.

    2014-10-01

    It is shown that in theories of gravity where the cosmological constant is considered a thermodynamic variable, it is natural to use black holes as heat engines. Two examples are presented in detail using AdS charged black holes as the working substance. We notice that for static black holes, the maximally efficient traditional Carnot engine is also a Stirling engine. The case of negative cosmological constant supplies a natural realization of these engines in terms of the field theory description of the fluids to which they are holographically dual. We first propose a precise picture of how the traditional thermodynamic dictionary of holography is extended when the cosmological constant is dynamical and then conjecture that the engine cycles can be performed by using renormalization group flow. We speculate about the existence of a natural dual field theory counterpart to the gravitational thermodynamic volume.

  19. Complexity Induced Anisotropic Bimodal Intermittent Turbulence in Space Plasmas

    NASA Technical Reports Server (NTRS)

    Chang, Tom; Tam, Sunny W. Y.; Wu, Cheng-Chin

    2004-01-01

    The "physics of complexity" in space plasmas is the central theme of this exposition. It is demonstrated that the sporadic and localized interactions of magnetic coherent structures arising from the plasma resonances can be the source for the coexistence of nonpropagating spatiotemporal fluctuations and propagating modes. Non-Gaussian probability distribution functions of the intermittent fluctuations from direct numerical simulations are obtained and discussed. Power spectra and local intermittency measures using the wavelet analyses are presented to display the spottiness of the small-scale turbulent fluctuations and the non-uniformity of coarse-grained dissipation that can lead to magnetic topological reconfigurations. The technique of the dynamic renormalization group is applied to the study of the scaling properties of such type of multiscale fluctuations. Charged particle interactions with both the propagating and nonpropagating portions of the intermittent turbulence are also described.

  20. Many-body interactions in quasi-freestanding graphene

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu

    2011-06-03

    The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities tomore » marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.« less

  1. Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4.

    PubMed

    Sharma, Prachi; Truhlar, Donald G; Gagliardi, Laura

    2018-03-28

    The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

  2. Un-renormalized classical electromagnetism

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ibison, Michael

    2006-02-15

    This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. However, the direct-action approach ultimately failed in that respect because its initial exclusion of self-action was later found to be untenable in the relativistic domain. Pursing the same end, this paper examines instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinitemore » forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be self-sustaining and naturally quantized.« less

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

    PubMed

    Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

    2011-12-01

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

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ma, Hong -Hao; Wu, Xing -Gang; Ma, Yang

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

  5. Exact renormalization group equations: an introductory review

    NASA Astrophysics Data System (ADS)

    Bagnuls, C.; Bervillier, C.

    2001-07-01

    We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

  6. Coexistence of Velocity Renormalization and Ferrimagnetic Fluctuation in the Organic Dirac Electron System α-(BEDT-TTF)2I3

    NASA Astrophysics Data System (ADS)

    Matsuno, Genki; Kobayashi, Akito

    2018-05-01

    We evaluate the uniform spin susceptibility in an extended Hubbard model describing α-(BEDT-TTF)2I3. Employing the Fock-type self-energy with the long-range Coulomb interaction and the random phase approximation with the on-site Coulomb interaction, it is clarified that the characteristic energy scales at which ferrimagnetic fluctuation and velocity renormalization emerge are different. This is why these phenomena coexist while the ferrimagnetic fluctuation is disturbed by the velocity renormalization. In addition, it is found that screening effect to the self-energy is irrelevant in the presence of a strong on-site Coulomb interaction U.

  7. On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions

    NASA Astrophysics Data System (ADS)

    Punshon-Smith, Samuel; Smith, Scott

    2018-02-01

    This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in {{L}1}.

  8. Dimension-5 C P -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 γ 5.« less

  9. Effective Field Theory on Manifolds with Boundary

    NASA Astrophysics Data System (ADS)

    Albert, Benjamin I.

    In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

  10. Running with rugby balls: bulk renormalization of codimension-2 branes

    NASA Astrophysics Data System (ADS)

    Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

    2013-01-01

    We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

  11. Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization Ansatz

    NASA Astrophysics Data System (ADS)

    Hu, Q.; Vidal, G.

    2017-07-01

    The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013), 10.1103/PhysRevLett.110.100402], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |ΨΛ⟩ with finite UV cutoff Λ can capture the spacetime symmetries of the ground state |Ψ ⟩. For a free boson conformal field theory (CFT) in 1 +1 dimensions, as a concrete example, we build a quasilocal unitary transformation V that maps |Ψ ⟩ into |ΨΛ⟩ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ ⟩ is also mapped by V into a spacetime symmetry of the cMERA |ΨΛ⟩. However, while in the CFT, the stress-energy tensor Tμ ν(x ) (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor Tμν Λ(x )=V Tμ ν(x )V† is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators OαΛ(x ) characterized by the exact same scaling dimensions Δα, conformal spins sα, operator product expansion coefficients Cα β γ, and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories.

  12. 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.

  13. Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system II. Vacuum energy

    NASA Astrophysics Data System (ADS)

    Davydov, A.; Sveshnikov, K.; Voronina, Yu.

    2018-01-01

    Nonperturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with Z > Zcr,1 in 2+1D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. 1-3. Both the vacuum charge density ρV P(r→) and vacuum energy ℰV P are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I4 for ρV P, in the present part II, the evaluation of the vacuum energy ℰV P is investigated with emphasis on the renormalization and convergence of the partial expansion for ℰV P. It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially nonperturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region ℰV P turns out to be a rapidly decreasing function ˜-ηeffZ3/R with ηeff > 0 and R being the size of the external Coulomb source. To the end the similarity in calculations of ℰV P in 2+1 and 3+1D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for Z ≫ Zcr,1 in 3+1D.

  14. 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

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

    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.

  16. Cooper-pair-condensate fluctuations and plasmons in layered superconductors

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cote, R.; Griffin, A.

    1993-10-01

    Starting from a given attractive potential, we give a systematic analysis of the spin-singlet [ital s]-wave Cooper-pair-condensate fluctuations in a two-dimensional (2D) superconductor. These results are applied to a superlattice of superconducting sheets in which the 2D charge fluctuations are coupled via the Coulomb interaction. Our main interest is how the low-energy Anderson-Bogoliubov (AB) phonon mode in the pair-breaking gap [omega][lt]2[Delta] is modified by the Coulomb interaction. Our formal analysis is valid at arbitrary temperatures. It describes the weakly bound, large-Cooper-pair limit as well as the strongly bound, small-Cooper-pair limit and thus includes both the BCS and Bose-Einstein scenarios (asmore » discussed by Nozieres and Schmitt-Rink as well as Randeira [ital et] [ital al].). A comlete normal-mode analysis is given for a charged BCS superconductor, showing how the repulsive (Coulomb) interaction modifies the collective modes of a neutral superconductor. This complements the recent numerical study carried out by Fertig and Das Sarma. We show that the pair-response function shares the same spectrum as the charge-response function, given by the zero of the longitudinal dielectric function [epsilon]([bold q],[omega]). In 2D and layered superconductors, there is a low-frequency and high-frequency plasmon branch, separated by a relatively narrow particle-hole continuum at around 2[Delta]. The low-frequency ([omega][lt]2[Delta]) plasmon branch is a renormalized version of the AB phonon mode.« less

  17. Renormalization of Coulomb interactions in s-wave superconductor NaxCoO2

    NASA Astrophysics Data System (ADS)

    Yada, Keiji; Kontani, Hiroshi

    2007-03-01

    We study the renormalized Coulomb interactions due to retardation effect in NaxCoO2. Although the Morel Anderson's pseudo-potential for a1g orbital μa1g* is relatively large because the direct Coulomb repulsion U is large, that for interband transition between a1g and eg' orbitals μa1g,eg'* is very small since the renormalization factor for pair hopping J is square of that for U. Therefore, the s-wave superconductivity due to valence-band Suhl-Kondo mechanism will survive against strong Coulomb interactions. The interband hopping of Cooper pairs due to shear phonons is essential to understand the superconductivity in NaxCoO2.

  18. Quasiparticle renormalization in ABC graphene trilayers

    NASA Astrophysics Data System (ADS)

    Dou, Xu; Jaefari, Akbar; Barlas, Yafis; Uchoa, Bruno

    2015-03-01

    We investigate the effect of electron-electron interactions in ABC stacked graphene trilayers. In the gapless regime, we show that the self-energy corrections lead to the renormalization of the dynamical exponent z = 3 +α1 / N , with α1 ~ 0 . 52 and N is the number of fermionic species. Although the quasiparticle residue is suppressed near the neutrality point, the lifetime has a sublinear scaling with the energy and the quasiparticles are well defined even at zero energy. We calculate the renormalization of a variety of physical observables, which can be directly measured in experiments. X.D., A.J., and B.U. acknowledge University of Oklahoma for support. B.U. acknowledges NSF Career Grant No. DMR-1352604 for partial support.

  19. Calculational Schemes in GUTs

    NASA Astrophysics Data System (ADS)

    Kounnas, Costas

    The following sections are included: * Introduction * Mass Spectrum in a Spontaneously Broken-Theory SU(5) - Minimal Model * Renormalization and Renormalization Group Equation (R.G.E.) * Step Approximation and Decoupling Theorem * Notion of the Effective Coupling Constant * First Estimation of MX, α(MX) and sin2θ(MW) * Renormalization Properties and Photon-Z Mixing * β-Function Definitions * Threshold Functions and Decoupling Theorem * MX-Determination * Proton Lifetime * sin2θ(μ)-Determination * Quark-Lepton Mass Relations (mb/mτ) * Overview of the Conventional GUTs - Hierarchy Problem * Stability of Hierarchy - Supersymmetric GUTS * Cosmologically Acceptable SUSY GUT Models * Radiative Breaking of SU(2) × U(1) — MW/MX Hierarchy Generation * No Scale Supergravity Models^{56,57} Dynamical Determination of M_{B}-M_{F} * Conclusion * References

  20. Two formalisms, one renormalized stress-energy tensor

    NASA Astrophysics Data System (ADS)

    Barceló, C.; Carballo, R.; Garay, L. J.

    2012-04-01

    We explicitly compare the structure of the renormalized stress-energy tensor of a massless scalar field in a (1+1) curved spacetime as obtained by two different strategies: normal-mode construction of the field operator and one-loop effective action. We pay special attention to where and how the information related to the choice of vacuum state in both formalisms is encoded. By establishing a clear translation map between both procedures, we show that these two potentially different renormalized stress-energy tensors are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms.

  1. The Holographic F Theorem

    NASA Astrophysics Data System (ADS)

    Taylor, Marika; Woodhead, William

    2017-12-01

    The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

  2. Kenneth Wilson and Renormalization

    Science.gov Websites

    of the Renormalization Group (RG) into a central tool in physics. ... He received a doctorate from one of the most amazing experiences of my life," says Peskin. "He was saying, 'I see the big actually the data you need to move from one scale to another. ... RG theory implies that, with enough

  3. Two-loop renormalization of the quark propagator in the light-cone gauge

    NASA Astrophysics Data System (ADS)

    Williams, James Daniel

    The divergent parts of the five two-loop quark self- energy diagrams of quantum chromodynamics are evaluated in the noncovariant light-cone gauge. Most of the Feynman integrals are computed by means of the powerful matrix integration method, originally developed for the author's Master's thesis. From the results of the integrations, it is shown how to renormalize the quark mass and wave function in such a way that the effective quark propagator is rendered finite at two-loop order. The required counterterms turn out to be local functions of the quark momentum, due to cancellation of the nonlocal divergent parts of the two-loop integrals with equal and opposite contributions from one-loop counterterm subtraction diagrams. The final form of the counterterms is seen to be consistent with the renormalization framework proposed by Bassetto, Dalbosco, and Soldati, in which all noncovariant divergences are absorbed into the wave function normalizations. It also turns out that the mass renormalization d m is the same in the light-cone gauge as it is in a general covariant gauge, at least up to two-loop order.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Führer, Florian; Rigopoulos, Gerasimos, E-mail: fuhrer@thphys.uni-heidelberg.de, 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 ordermore » 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.« less

  5. Relativistic bound-state problem in the light-front Yukawa model

    NASA Astrophysics Data System (ADS)

    Głazek, Stanisław; Harindranath, Avaroth; Pinsky, Stephen; Shigemitsu, Junko; Wilson, Kenneth

    1993-02-01

    We study the renormalization problem on the light front for the two-fermion bound state in the (3+1)-dimensional Yukawa model, working within the lowest-order Tamm-Dancoff approximation. In addition to traditional mass and wave-function renormalization, new types of counterterms are required. These are nonlocal and involve arbitrary functions of the longitudinal momenta. Their appearance is consistent with general power-counting arguments on the light front. We estimate the ``arbitrary function'' in two ways: (1) by using perturbation theory as a guide and (2) by considering the asymptotic large transverse momentum behavior of the kernel in the bound-state equations. The latter method, as it is currently implemented, is applicable only to the helicity-zero sector of the theory. Because of triviality, in the Yukawa model one must retain a finite cutoff Λ in order to have a nonvanishing renormalized coupling. For the range of renormalized couplings (and cutoffs) allowed by triviality, one finds that the perturbative counterterm does a good job in eliminating cutoff dependence in the low-energy spectrum (masses <<Λ).

  6. Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

    NASA Astrophysics Data System (ADS)

    Rose, F.; Dupuis, N.

    2018-05-01

    We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

  7. Functional renormalization group analysis of tensorial group field theories on Rd

    NASA Astrophysics Data System (ADS)

    Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele

    2016-07-01

    Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

  8. Nonperturbative Quantum Nature of the Dislocation–Phonon Interaction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Li, Mingda; Ding, Zhiwei; Meng, Qingping

    Despite the long history of dislocation–phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and their capability of dealing with thermal transport phenomena for bulk material only. Here in this paper, by utilizing a fully quantized dislocation field, which we called a “dislon”, a phonon interacting with a dislocation is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime, which are reducible to classical results.more » A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. For instance, a renormalized phonon naturally resolves the decade-long debate between dynamic and static dislocation–phonon scattering approaches, as two limiting cases. In particular, at nanoscale, both the dynamic and static approaches break down, while the present renormalization approach remains valid by capturing the size effect, showing good agreement with lattice dynamics simulations.« less

  9. Precise MS light-quark masses from lattice QCD in the regularization invariant symmetric momentum-subtraction scheme

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gorbahn, Martin; Jaeger, Sebastian; Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH

    2010-12-01

    We compute the conversion factors needed to obtain the MS and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM{sub {gamma}{sub {mu}} }renormalization schemes. This is important for obtaining the MS masses with the best possible precision from numerical lattice QCD simulations, because the customary RI{sup (')}/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scalemore » dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM{sub {gamma}{sub {mu}} }scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.« less

  10. Renormalization group fixed points of foliated gravity-matter systems

    NASA Astrophysics Data System (ADS)

    Biemans, Jorn; Platania, Alessia; Saueressig, Frank

    2017-05-01

    We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

  11. Nonperturbative Quantum Nature of the Dislocation–Phonon Interaction

    DOE PAGES

    Li, Mingda; Ding, Zhiwei; Meng, Qingping; ...

    2017-01-31

    Despite the long history of dislocation–phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and their capability of dealing with thermal transport phenomena for bulk material only. Here in this paper, by utilizing a fully quantized dislocation field, which we called a “dislon”, a phonon interacting with a dislocation is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime, which are reducible to classical results.more » A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. For instance, a renormalized phonon naturally resolves the decade-long debate between dynamic and static dislocation–phonon scattering approaches, as two limiting cases. In particular, at nanoscale, both the dynamic and static approaches break down, while the present renormalization approach remains valid by capturing the size effect, showing good agreement with lattice dynamics simulations.« less

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Anton, Luis; MartI, Jose M; Ibanez, Jose M

    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, andmore » 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.« less

  13. Time-resolved nonlinear optics in strongly correlated insulators

    NASA Astrophysics Data System (ADS)

    Dodge, J. Steven

    2000-03-01

    Transition metal oxides form the basis for much of our understanding of Mott insulators, and have enjoyed a renaissance of interest since the discovery of high temperature superconductivity in the cuprates. They are characterized by complex interactions among spin, lattice, orbital and charge degrees of freedom, which lead to dynamical behavior on time scales ranging from femtoseconds to microseconds. We have applied time resolved nonlinear optical spectroscopy to probe these dynamics. In one well-studied antiferromagnetic insulator, Cr_2O_3, we observed spin-wave dynamics on a picosecond time scale by performing pump-probe spectroscopy of the exciton-magnon transition(J. S. Dodge, et al.), Phys. Rev. Lett. 83, 4650 (1999).. At excitation densities ~ 10-3/Cr, a lineshape associated with the exciton-magnon absorption appears in the pump-probe spectrum. We assign this nonlinearity to a time-dependent renormalization of the magnon band structure, which in turn modifies the lineshape of the exciton-magnon transition. At long time delays, this assignment agrees semiquantitatively with calculations based on spin-wave theory. However, the initial population at the zone-boundary induces surprisingly little renormalization effect, indicating that spin-wave theory is insufficient to describe our observations in this regime. The renormalization lineshape grows on a time scale of ~ 50 ps, which we associate with the decay of the photoexcited, nonequilibrium population of zone-boundary spin-waves into a thermalized population of zone-center spin-waves. We have also performed a study of the linear and nonlinear optical properties of Sr_2CuO_2Cl_2, an insulating, two-dimensional cuprate. In the nonlinear optical experiments, we have performed pump-probe spectroscopy over a 1 eV spectral range, varying both the pump and the probe energy. We observe a pump-probe lineshape which varies considerably as a function of pump energy and temperature, and which differs sharply from those typically observed in band insulators. At low-temperatures, in particular, we observe an overall increase of spectral weight in our probe range, indicating that states are shifting over an energy scale larger than 1 eV. We attribute this behavior to the strongly correlated nature of the electronic structure in this material. Studies of the elementary excitations in other magnetic oxides, currently in progress, will be discussed.

  14. 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: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

  15. 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 of initial scale is highly suppressed even for low-order predictions. Thus the PMC, based on the standard RGI, has a rigorous foundation; it eliminates an unnecessary systematic error for high precision pQCD predictions and can be widely applied to virtually all high-energy hadronic processes, including multi-scale problems.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  17. The ultraviolet behavior of quantum gravity

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano; Piva, Marco

    2018-05-01

    A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, √{-g}{R}_{μ ν }{R}^{μ ν } and √{-g}{R}^2 . In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge c of the matter fields coupled to gravity.

  18. Testing microscopically derived descriptions of nuclear collectivity: Coulomb excitation of 22Mg

    NASA Astrophysics Data System (ADS)

    Henderson, J.; Hackman, G.; Ruotsalainen, P.; Stroberg, S. R.; Launey, K. D.; Holt, J. D.; Ali, F. A.; Bernier, N.; Bentley, M. A.; Bowry, M.; Caballero-Folch, R.; Evitts, L. J.; Frederick, R.; Garnsworthy, A. B.; Garrett, P. E.; Jigmeddorj, B.; Kilic, A. I.; Lassen, J.; Measures, J.; Muecher, D.; Olaizola, B.; O'Sullivan, E.; Paetkau, O.; Park, J.; Smallcombe, J.; Svensson, C. E.; Wadsworth, R.; Wu, C. Y.

    2018-07-01

    Many-body nuclear theory utilizing microscopic or chiral potentials has developed to the point that collectivity might be studied within a microscopic or ab initio framework without the use of effective charges; for example with the proper evolution of the E2 operator, or alternatively, through the use of an appropriate and manageable subset of particle-hole excitations. We present a precise determination of E2 strength in 22Mg and its mirror 22Ne by Coulomb excitation, allowing for rigorous comparisons with theory. No-core symplectic shell-model calculations were performed and agree with the new B (E 2) values while in-medium similarity-renormalization-group calculations consistently underpredict the absolute strength, with the missing strength found to have both isoscalar and isovector components. The discrepancy between two microscopic models demonstrates the sensitivity of E2 strength to the choice of many-body approximation employed.

  19. Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

    NASA Astrophysics Data System (ADS)

    Nedelko, Sergei N.; Voronin, Vladimir V.

    2017-03-01

    An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(Nf) × SUR(Nf) and UA(1) symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal n-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.

  20. Graphene-induced band gap renormalization in polythiophene: a many-body perturbation study

    NASA Astrophysics Data System (ADS)

    Marsusi, F.; Fedorov, I. A.; Gerivani, S.

    2018-01-01

    Density functional theory and many-body perturbation theory at the G0W0 level are employed to study the electronic properties of polythiophene (PT) adsorbed on the graphene surface. Analysis of the charge density difference shows that substrate-adsorbate interaction leads to a strong physisorption and interfacial electric dipole moment formation. The electrostatic potential displays a  -0.19 eV shift in the graphene work function from its initial value of 4.53 eV, as the result of the interaction. The LDA band gap of the polymer does not show any change. However, the band structure exhibits weak orbital hybridizations resulting from slight overlapping between the polymer and graphene states wave functions. The interfacial polarization effects on the band gap and levels alignment are investigated at the G0W0 level and show a notable reduction of PT band gap compared to that of the isolated chain.

  1. Many-particle-effects in the theory of the extended X-ray absorption fine structure

    NASA Astrophysics Data System (ADS)

    Tran Thoai, D. B.; Ekardt, W.

    1981-10-01

    The Lee-Beni-procedure for the calculation of the extended X-ray absorption fine structure (EXAFS) is extended so as to include the effects of the electronic charge density outside the localized muffin-tin potentials. In our scheme EXAFS is caused by back-scattering of an elementary excitation of a homogeneous electron gas by localized energy dependent many-particle muffin-tin potentials. The difference between the two schemes is negligible at large k's, as expected from physical grounds. However, at small and intermediate k-values the difference is quite large. The effect of the outer electrons as compared to the Lee-Beni-model is twofold. First, they renormalize the scattered electron in the usual way. Second, they are missing within the scattering muffin-tins. Hence, we avoid to count some of the electrons twice. Results are presented for Cu as an example.

  2. On the idea of low-energy nuclear reactions in metallic lattices by producing neutrons from protons capturing "heavy" electrons

    NASA Astrophysics Data System (ADS)

    Tennfors, Einar

    2013-02-01

    The present article is a critical comment on Widom and Larsens speculations concerning low-energy nuclear reactions (LENR) based on spontaneous collective motion of protons in a room temperature metallic hydride lattice producing oscillating electric fields that renormalize the electron self-energy, adding significantly to the effective electron mass and enabling production of low-energy neutrons. The frequency and mean proton displacement estimated on the basis of neutron scattering from protons in palladium and applied to the Widom and Larsens model of the proton oscillations yield an electron mass enhancement less than one percent, far below the threshold for the proposed neutron production and even farther below the mass enhancement obtained by Widom and Larsen assuming a high charge density. Neutrons are not stopped by the Coulomb barrier, but the energy required for the neutron production is not low.

  3. Correlations and enlarged superconducting phase of t -J⊥ chains of ultracold molecules on optical lattices

    NASA Astrophysics Data System (ADS)

    Manmana, Salvatore R.; Möller, Marcel; Gezzi, Riccardo; Hazzard, Kaden R. A.

    2017-10-01

    We compute physical properties across the phase diagram of the t -J⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component Jz of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.

  4. Using nonequilibrium dynamics to probe competing orders in a Mott-Peierls system

    DOE PAGES

    Wang, Y.; Moritz, B.; Chen, C. -C.; ...

    2016-02-24

    Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softeningmore » due to a stronger coupling near k F. As a result, this behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.« less

  5. Quasiparticles and Fermi liquid behaviour in an organic metal

    PubMed Central

    Kiss, T.; Chainani, A.; Yamamoto, H.M.; Miyazaki, T.; Akimoto, T.; Shimojima, T.; Ishizaka, K.; Watanabe, S.; Chen, C.-T.; Fukaya, A.; Kato, R.; Shin, S.

    2012-01-01

    Many organic metals display exotic properties such as superconductivity, spin-charge separation and so on and have been described as quasi-one-dimensional Luttinger liquids. However, a genuine Fermi liquid behaviour with quasiparticles and Fermi surfaces have not been reported to date for any organic metal. Here, we report the experimental Fermi surface and band structure of an organic metal (BEDT-TTF)3Br(pBIB) obtained using angle-resolved photoelectron spectroscopy, and show its consistency with first-principles band structure calculations. Our results reveal a quasiparticle renormalization at low energy scales (effective mass m*=1.9 me) and ω2 dependence of the imaginary part of the self energy, limited by a kink at ~50 meV arising from coupling to molecular vibrations. The study unambiguously proves that (BEDT-TTF)3Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface consistent with Shubnikov-de Haas results. PMID:23011143

  6. Two-loop renormalization of gaugino masses in general supersymmetric gauge models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yamada, Y.

    1994-01-03

    We calculate the two-loop renormalization group equations for the running gaugino masses in general supersymmetry (SUSY) gauge models, improving our previous result. We also study its consequences on the unification of the gaugino masses in the SUSY SU(5) model. The two-loop correction to the one-loop relation [ital m][sub [ital i

  7. Galilean invariance and vertex renormalization in turbulence theory.

    PubMed

    McComb, W D

    2005-03-01

    The Navier-Stokes equation is invariant under Galilean transformation of the instantaneous velocity field. However, the total velocity transformation is effected by transformation of the mean velocity alone. For a constant mean velocity, the equation of motion for the fluctuating velocity is automatically Galilean invariant in the comoving frame, and vertex renormalization is not constrained by this symmetry.

  8. Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

    PubMed

    Saveliev, V L; Gorokhovski, M A

    2005-07-01

    On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

  9. Large-cell renormalisation and systems of dimensionality larger than the upper marginal dimension

    NASA Technical Reports Server (NTRS)

    Nakanishi, H.

    1984-01-01

    A recent argument dismissing the applicability of large-cell renormalization schemes to systems whose dimensionality is larger than the upper marginal dimension is critically discussed. In this connection, new large-cell renormalization results for the random walk for a dimensionality of 3 and 4 are presented which indicate convergence to the correct results.

  10. Rayleigh surface wave interaction with the 2D exciton Bose-Einstein condensate

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Boev, M. V.; Kovalev, V. M., E-mail: vadimkovalev@isp.nsc.ru

    We describe the interaction of a Rayleigh surface acoustic wave (SAW) traveling on the semiconductor substrate with the excitonic gas in a double quantum well located on the substrate surface. We study the SAW attenuation and its velocity renormalization due to the coupling to excitons. Both the deformation potential and piezoelectric mechanisms of the SAW-exciton interaction are considered. We focus on the frequency and excitonic density dependences of the SAW absorption coefficient and velocity renormalization at temperatures both above and well below the critical temperature of Bose-Einstein condensation of the excitonic gas. We demonstrate that the SAW attenuation and velocitymore » renormalization are strongly different below and above the critical temperature.« less

  11. Poissonian renormalizations, exponentials, and power laws.

    PubMed

    Eliazar, Iddo

    2013-05-01

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

  12. Functional renormalization group and Kohn-Sham scheme in density functional theory

    NASA Astrophysics Data System (ADS)

    Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

    2018-04-01

    Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

  13. 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.

  14. Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions

    NASA Astrophysics Data System (ADS)

    Katzav, Eytan

    2013-04-01

    In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.

  15. 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.

  16. Renormalization group flow of the Higgs potential

    NASA Astrophysics Data System (ADS)

    Gies, Holger; Sondenheimer, René

    2018-01-01

    We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.

  17. Loop optimization for tensor network renormalization

    NASA Astrophysics Data System (ADS)

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

    We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize 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. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

  18. E-cigarette marketing and older smokers: road to renormalization.

    PubMed

    Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

    2015-05-01

    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. 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. 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. 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.

  19. Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

    NASA Astrophysics Data System (ADS)

    Stauber, T.; Parida, P.; Trushin, M.; Ulybyshev, M. V.; Boyda, D. L.; Schliemann, J.

    2017-06-01

    We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

  20. Anomalous dimension in a two-species reaction-diffusion system

    NASA Astrophysics Data System (ADS)

    Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

    2018-01-01

    We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

  1. A functional renormalization method for wave propagation in random media

    NASA Astrophysics Data System (ADS)

    Lamagna, Federico; Calzetta, Esteban

    2017-08-01

    We develop the exact renormalization group approach as a way to evaluate the effective speed of the propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. A simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.

  2. Velocity renormalization in graphene: The role of trigonal warping and electron-phonon coupling effects

    NASA Astrophysics Data System (ADS)

    Kandemir, B. S.; Gökçek, N.

    2017-12-01

    We investigate the combined effects of trigonal warping and electron-phonon interactions on the renormalization of the Fermi velocity in graphene. We present an analytical solution to the associated Fröhlich Hamiltonian describing the interaction of doubly degenerate-optical phonon modes of graphene with electrons in the presence of trigonal warp within the framework of Lee-Low-Pines theory. On the basis of our model, it is analytically shown that in addition to its renormalization, Fermi velocity exhibits strong anisotropy due to the trigonal warping. It is also found that in the regime where the trigonal warp starts, distortion of energy bands emerges due to electron-phonon coupling, and the bands exhibit strong anisotropy.

  3. A holographic model of the Kondo effect

    NASA Astrophysics Data System (ADS)

    Erdmenger, Johanna; Hoyos, Carlos; O'Bannon, Andy; Wu, Jackson

    2013-12-01

    We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional CFT description, the Kondo effect is a renormalization group flow triggered by a marginally relevant (0+1)-dimensional operator between two fixed points with the same Kac-Moody current algebra. In the large- N limit, with spin SU( N) and charge U(1) symmetries, the Kondo effect appears as a (0+1)-dimensional second-order mean-field transition in which the U(1) charge symmetry is spontaneously broken. Our holographic model, which combines the CFT and large- N descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space, AdS 3, dual to the Kac-Moody current, coupled to a holographic superconductor along an AdS 2 sub-space. Our model exhibits several characteristic features of the Kondo effect, including a dynamically generated scale, a resistivity with power-law behavior in temperature at low temperatures, and a spectral flow producing a phase shift. Our holographic Kondo model may be useful for studying many open problems involving impurities, including for example the Kondo lattice problem.

  4. Transport coefficients of a hot QCD medium and their relative significance in heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Mitra, Sukanya; Chandra, Vinod

    2017-11-01

    The main focus of this article is to obtain various transport coefficients for a hot QCD medium that is likely to be produced while colliding two heavy nuclei ultra-relativistically. The technical approach adopted here is the semiclassical transport theory. The away-from-equilibrium linearized transport equation has been set up by employing the Chapman-Enskog technique from the kinetic theory of a many-particle system with a collision term that includes the binary collisions of quarks/antiquarks and gluons. In order to include the effects of a strongly interacting, thermal medium, a quasi-particle description of a realistic hot QCD equation of state has been employed through the equilibrium modeling of the momentum distributions of gluons and quarks with nontrivial dispersion relations while extending the model for finite but small quark chemical potential. The effective coupling for strong interaction has been redefined following the charge renormalization under the scheme of the quasi-particle model. The consolidated effects on transport coefficients are seen to have a significant impact on their temperature dependence. Finally, the relative significances of momentum and heat transfer, as well as the charge diffusion processes in hot QCD, have been investigated by studying the ratios of the respective transport coefficients indicating different physical laws.

  5. Tadpole renormalization and relativistic corrections in lattice NRQCD

    NASA Astrophysics Data System (ADS)

    Shakespeare, Norman H.; Trottier, Howard D.

    1998-08-01

    We make a detailed comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. We renormalize improved gauge-field and NRQCD actions using the mean-link u0,L in the Landau gauge, and using the fourth root of the average plaquette u0,P. Simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed both at leading [O(MQv4)] and at next-to-leading [O(MQv6)] order in the relativistic expansion, where MQ is the renormalized quark mass, and v2 is the mean-squared velocity. Results are obtained at a large number of lattice spacings, in the range of about 0.14-0.38 fm. A number of features emerge, all of which favor tadpole renormalization using u0,L. This includes a much better scaling behavior of the hyperfine splittings in the three quarkonium systems when u0,L is used. We also find that relativistic corrections to the spin splittings are smaller when u0,L is used, particularly for the cc¯ and bc¯ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about 1 in lattice units. Simulations with u0,L also appear to be better behaved in this context: the bare quark masses turn out to be larger when u0,L is used, compared to when u0,P is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.

  6. Features and flaws of a contact interaction treatment of the kaon

    NASA Astrophysics Data System (ADS)

    Chen, Chen; Chang, Lei; Roberts, Craig D.; Schmidt, Sebastian M.; Wan, Shaolong; Wilson, David J.

    2013-04-01

    Elastic and semileptonic transition form factors for the kaon and pion are calculated using the leading order in a global-symmetry-preserving truncation of the Dyson-Schwinger equations and a momentum-independent form for the associated kernels in the gap and Bethe-Salpeter equations. The computed form factors are compared both with those obtained using the same truncation but an interaction that preserves the one-loop renormalization-group behavior of QCD and with data. The comparisons show that in connection with observables revealed by probes with |Q2|≲M2, where M≈0.4GeV is an infrared value of the dressed-quark mass, results obtained using a symmetry-preserving regularization of the contact interaction are not realistically distinguishable from those produced by more sophisticated kernels, and available data on kaon form factors do not extend into the domain whereupon one could distinguish among the interactions. The situation differs if one includes the domain Q2>M2. Thereupon, a fully consistent treatment of the contact interaction produces form factors that are typically harder than those obtained with QCD renormalization-group-improved kernels. Among other things also described are a Ward identity for the inhomogeneous scalar vertex, similarity between the charge distribution of a dressed u quark in the K+ and that of the dressed u quark in the π+, and reflections upon the point whereat one might begin to see perturbative behavior in the pion form factor. Interpolations of the form factors are provided, which should assist in working to chart the interaction between light quarks by explicating the impact on hadron properties of differing assumptions about the behavior of the Bethe-Salpeter kernel.

  7. Ghost busting: PT-symmetric interpretation of the Lee model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bender, Carl M.; Brandt, Sebastian F.; Chen, J.-H.

    2005-01-15

    The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g{sup 2}, the square of the renormalized coupling constant, above which g{sub 0}{sup 2}, the square of the unrenormalized coupling constant, is negative. Thus, for g{sup 2} larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative.more » This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V/N{theta} sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g{sup 2}.« less

  8. Vacuum polarization and classical self-action near higher-dimensional defects

    NASA Astrophysics Data System (ADS)

    Grats, Yuri V.; Spirin, Pavel

    2017-02-01

    We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of (d-n)-dimensional Minkowski space and n-dimensional spherically/cylindrically symmetric space with a solid/planar angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole (if n≥slant 3) or cosmic string (if n=2) with (d-n-1) flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms of the angular-deficit value, we derive the perturbative expression for the scalar Green function, valid for any d≥slant 3 and 2≤slant n≤slant d-1, and compute it to the leading order. With the use of this Green function we compute the renormalized vacuum expectation value of the field square {< φ {2}(x)rangle }_{ren} and the renormalized vacuum averaged of the scalar-field energy-momentum tensor {< T_{M N}(x)rangle }_{ren} for arbitrary d and n from the interval mentioned above and arbitrary coupling constant to the curvature ξ . In particular, we revisit the computation of the vacuum polarization effects for a non-minimally coupled massless scalar field in the spacetime of a straight cosmic string. The same Green function enables to consider the old purely classical problem of the gravity-induced self-action of a classical point-like scalar or electric charge, placed at rest at some fixed point of the space under consideration. To deal with divergences, which appear in consideration of the two problems, we apply the dimensional-regularization technique, widely used in quantum field theory. The explicit dependence of the results upon the dimensionalities of both the bulk and conical submanifold is discussed.

  9. External electric field driving the ultra-low thermal conductivity of silicene.

    PubMed

    Qin, Guangzhao; Qin, Zhenzhen; Yue, Sheng-Ying; Yan, Qing-Bo; Hu, Ming

    2017-06-01

    The manipulation of thermal transport is in increasing demand as heat transfer plays a critical role in a wide range of practical applications, such as efficient heat dissipation in nanoelectronics and heat conduction hindering in solid-state thermoelectrics. It is well established that the thermal transport in semiconductors and insulators (phonons) can be effectively modulated by structure engineering or materials processing. However, almost all the existing approaches involve altering the original atomic structure of materials, which would be hindered due to either irreversible structure change or limited tunability of thermal conductivity. Motivated by the inherent relationship between phonon behavior and interatomic electrostatic interaction, we comprehensively investigate the effect of external electric field, a widely used gating technique in modern electronics, on the lattice thermal conductivity (κ). Taking two-dimensional silicon (silicene) as a model, we demonstrate that by applying an electric field (E z = 0.5 V Å -1 ) the κ of silicene can be reduced to a record low value of 0.091 W m -1 K -1 , which is more than two orders of magnitude lower than that without an electric field (19.21 W m -1 K -1 ) and is even comparable to that of the best thermal insulation materials. Fundamental insights are gained from observing the electronic structures. With an electric field applied, due to the screened potential resulting from the redistributed charge density, the interactions between silicon atoms are renormalized, leading to phonon renormalization and the modulation of phonon anharmonicity through electron-phonon coupling. Our study paves the way for robustly tuning phonon transport in materials without altering the atomic structure, and would have significant impact on emerging applications, such as thermal management, nanoelectronics and thermoelectrics.

  10. Multifield Galileons and higher codimension branes

    DOE PAGES

    Hinterbichler, Kurt; Trodden, Mark; Wesley, Daniel

    2010-12-07

    We studied a multi-field generalizations of the galileon - a popular idea of how to modify gravity to account for the acceleration of the universe. We derived an extremely restrictive theory of multiple galileon fields, and explored some properties of this theory, including proving a general non-renormalization theorem: multi-field galileons are not renormalized quantum mechanically to any loop in perturbation theory.

  11. Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

    NASA Astrophysics Data System (ADS)

    Bufalo, R.; Cardoso, T. R.; Nogueira, A. A.; Pimentel, B. M.

    2018-05-01

    We establish the multiplicative renormalization procedure of generalized scalar Duffin-Kemmer-Petiau electrodynamics (GSDKP4 ) in the mass shell. We show an explicit calculation of the first radiative corrections (one-loop) associated with the photon propagator, meson propagator, vertex function, and photon-photon four-point function utilizing the dimensional regularization method, where the gauge symmetry is manifest. As we will see, one of the consequences of the study is that, from the complete photon propagator renormalization condition, imposing that it behaves as a massless field, an energy range where GSDKP4 is well defined is m2≪k2

  12. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Abolhasani, Ali Akbar; School of Physics, Institute for Research in Fundamental Sciences; Mirbabayi, Mehrdad

    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 showmore » 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.« less

  13. Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

    NASA Astrophysics Data System (ADS)

    Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

    2018-03-01

    The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

  14. New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

    NASA Astrophysics Data System (ADS)

    Kazantsev, A. E.; Shakhmanov, V. Yu.; Stepanyantz, K. V.

    2018-04-01

    We investigate a recently proposed new form of the exact NSVZ β-function, which relates the β-function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the chiral matter superfields. Namely, for the general renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives, the sum of all three-loop contributions to the β-function containing the Yukawa couplings is compared with the corresponding two-loop contributions to the anomalous dimensions of the quantum superfields. It is demonstrated that for the considered terms both new and original forms of the NSVZ relation are valid independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings. This result is obtained from the equality relating the loop integrals, which, in turn, follows from the factorization of the integrals for the β-function into integrals of double total derivatives. For the renormalization group functions defined in terms of the renormalized couplings we verify that the NSVZ scheme is obtained with the higher covariant derivative regularization supplemented by the subtraction scheme in which only powers of ln Λ /μ are included into the renormalization constants.

  15. How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

    NASA Astrophysics Data System (ADS)

    Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.

    2017-07-01

    We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions d →2 . Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, 2 αF=2 -d and 2 αG=d at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

  16. 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.

  17. Renormalization group analysis of dipolar Heisenberg model on square lattice

    NASA Astrophysics Data System (ADS)

    Keleş, Ahmet; Zhao, Erhai

    2018-06-01

    We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well-known J1-J2 model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here, we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phases. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range-ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

  18. 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.

  19. Poissonian renormalizations, exponentials, and power laws

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo

    2013-05-01

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

  20. Two-loop renormalization of quantum gravity simplified

    NASA Astrophysics Data System (ADS)

    Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

    2017-02-01

    The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

  1. Covariant Derivatives and the Renormalization Group Equation

    NASA Astrophysics Data System (ADS)

    Dolan, Brian P.

    The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

  2. Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

    NASA Astrophysics Data System (ADS)

    Bischoff, Jan-Moritz; Jeckelmann, Eric

    2017-11-01

    We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

  3. Renormalization group flow of the Higgs potential.

    PubMed

    Gies, Holger; Sondenheimer, René

    2018-03-06

    We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

  4. 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

  5. Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

    NASA Astrophysics Data System (ADS)

    Lahoche, Vincent; Oriti, Daniele

    2017-01-01

    We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d  =  4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.

  6. Nonperturbative renormalization of the axial current in Nf=3 lattice QCD with Wilson fermions and a tree-level improved gauge action

    NASA Astrophysics Data System (ADS)

    Bulava, John; Della Morte, Michele; Heitger, Jochen; Wittemeier, Christian

    2016-06-01

    We nonperturbatively determine the renormalization factor of the axial vector current in lattice QCD with Nf=3 flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity, and it is imposed among Schrödinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of ≈0.09 fm and below. An interpolation formula for ZA(g02) , smoothly connecting the nonperturbative values to the 1-loop expression, is provided together with our final results.

  7. Renormalization group procedure for potential -g/r2

    NASA Astrophysics Data System (ADS)

    Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.

    2018-02-01

    Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

  8. Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

    NASA Astrophysics Data System (ADS)

    Antenucci, F.; Crisanti, A.; Leuzzi, L.

    2014-07-01

    The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

  9. Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii-Moriya interaction using trance distance discord

    NASA Astrophysics Data System (ADS)

    Zhang, Ren-jie; Xu, Shuai; Shi, Jia-dong; Ma, Wen-chao; Ye, Liu

    2015-11-01

    In the paper, we researched the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group (QRG) method. The innovation point is that we adopt a new approach called trace distance discord to indicate the quantum correlation of the system. QPT after several iterations of renormalization in current system has been observed. Consequently, it opened the possibility of investigation of QPR in the geometric discord territory. While the anisotropy suppresses the correlation due to favoring of the alignment of spins, the DM interaction restores the spoiled correlation via creation of the quantum fluctuations. We also apply quantum renormalization group method to probe the thermodynamic limit of the model and emerging of nonanalytic behavior of the correlation.

  10. 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.

  11. Critical behavior of a chiral superfluid in a bipartite square lattice

    NASA Astrophysics Data System (ADS)

    Okamoto, Junichi; Huang, Wen-Min; Höppner, Robert; Mathey, Ludwig

    2018-01-01

    We study the critical behavior of Bose-Einstein condensation in the second band of a bipartite optical square lattice in a renormalization group framework at one-loop order. Within our field theoretical representation of the system, we approximate the system as a two-component Bose gas in three dimensions. We demonstrate that the system is in a different universality class than the previously studied condensation in a frustrated triangular lattice due to an additional Umklapp scattering term, which stabilizes the chiral superfluid order at low temperatures. We derive the renormalization group flow of the system and show that this order persists in the low energy limit. Furthermore, the renormalization flow suggests that the phase transition from the thermal phase to the chiral superfluid state is first order.

  12. Self-energy renormalization for inhomogeneous nonequilibrium systems and field expansion via complete set of time-dependent wavefunctions

    NASA Astrophysics Data System (ADS)

    Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.

    2018-04-01

    The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.

  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 N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.« less

  14. Including diverging electrostatic potential in 3D-RISM theory: The charged wall case.

    PubMed

    Vyalov, Ivan; Rocchia, Walter

    2018-03-21

    Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.

  15. Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons

    NASA Astrophysics Data System (ADS)

    Blas, H.; Zambrano, M.

    2016-03-01

    The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schrödinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potential V=η {I}^2-in /6{I}^3 and the saturable type potential satisfying [InlineEquation not available: see fulltext.], with a deformation parameter ɛ ∈ [InlineMediaObject not available: see fulltext.] and I = | ψ|2. The issue of the renormalization of the charges and anomalies, and their (quasi)conservation laws are properly addressed. The saturable NLS supports elastic scattering of two soliton solutions for a wide range of values of { η, ɛ, q}. Our results may find potential applications in several areas of non-linear science, such as the Bose-Einstein condensation.

  16. Including diverging electrostatic potential in 3D-RISM theory: The charged wall case

    NASA Astrophysics Data System (ADS)

    Vyalov, Ivan; Rocchia, Walter

    2018-03-01

    Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.

  17. Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

    NASA Astrophysics Data System (ADS)

    Aristov, D. N.; Wölfle, P.

    2018-05-01

    We develop the renormalization group theory of the conductances of N -lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group β functions are derived up to second order.

  18. Emergent supersymmetry in the marginal deformations of $$\\mathcal{N}=4$$ SYM

    DOE PAGES

    Jin, Qingjun

    2016-10-24

    Here, we study the one loop renormalization group flow of the marginal deformations ofmore » $$\\mathcal{N}=4$$ SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by the Leigh-Strassler theory. This means supersymmetry emerges as a result of renormalization group flow.« less

  19. Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ɛ-Expansion

    NASA Astrophysics Data System (ADS)

    Adzhemyan, L. Ts.; Vorob'eva, S. E.; Ivanova, E. V.; Kompaniets, M. V.

    2018-04-01

    Using the representation for renormalization group functions in terms of nonsingular integrals, we calculate the dynamical critical exponents in the model of critical dynamics of ferromagnets in the fourth order of the ɛ-expansion. We calculate the Feynman diagrams using the sector decomposition technique generalized to critical dynamics problems.

  20. Microscopic Theory of Supercapacitors

    NASA Astrophysics Data System (ADS)

    Skinner, Brian Joseph

    As new energy technologies are designed and implemented, there is a rising demand for improved energy storage devices. At present the most promising class of these devices is the electric double-layer capacitor (EDLC), also known as the supercapacitor. A number of recently created supercapacitors have been shown to produce remarkably large capacitance, but the microscopic mechanisms that underlie their operation remain largely mysterious. In this thesis we present an analytical, microscopic-level theory of supercapacitors, and we explain how such large capacitance can result. Specifically, we focus on four types of devices that have been shown to produce large capacitance. The first is a capacitor composed of a clean, low-temperature two-dimensional electron gas adjacent to a metal gate electrode. Recent experiments have shown that such a device can produce capacitance as much as 40% larger than that of a conventional plane capacitor. We show that this enhanced capacitance can be understood as the result of positional correlations between electrons and screening by the gate electrode in the form of image charges. Thus, the enhancement of the capacitance can be understood primarily as a classical, electrostatic phenomenon. Accounting for the quantum mechanical properties of the electron gas provides corrections to the classical theory, and these are discussed. We also present a detailed numerical calculation of the capacitance of the system based on a calculation of the system's ground state energy using the variational principle. The variational technique that we develop is broadly applicable, and we use it here to make an accurate comparison to experiment and to discuss quantitatively the behavior of the electrons' correlation function. The second device discussed in this thesis is a simple EDLC composed of an ionic liquid between two metal electrodes. We adopt a simple description of the ionic liquid and show that for realistic parameter values the capacitance can be as much as three times larger than that of a plane capacitor with thickness equal to the ion diameter. As in the previous system, this large capacitance is the result of image charge formation in the metal electrode and positional correlations between discrete ions that comprise the electric double-layer. We show that the maximum capacitance scales with the temperature to the power -1/3, and that at moderately large voltage the capacitance also decays as the inverse one third power of voltage. These results are confirmed by a Monte Carlo simulation. The third type of device we consider is that of a porous supercapacitor, where the electrode is made from a conducting material with a dense arrangement of narrow, planar pores into which ionic liquid can enter when a voltage is applied. In this case we show that when the electrode is metallic the narrow pores aggressively screen the interaction between neighboring ions in a pore, leading to an interaction energy between ions that decays exponentially. This exponential interaction between ions allows the capacitance to be nearly an order of magnitude larger than what is predicted by mean-field theories. This result is confirmed by a Monte Carlo simulation. We also present a theory for the capacitance when the electrode is not a perfect metal, but has a finite electronic screening radius. When this screening radius is larger than the distance between pores, ions begin to interact across multiple pores and the capacitance is determined by the Yukawa-like interaction of a three-dimensional, correlated arrangement of ions. Finally, we consider the case of supercapacitor electrodes made from a stack of graphene sheets with randomly-inserted "spacer" molecules. For such devices, experiments have produced very large capacitance despite the small density of states of the electrode material, which would seem to imply poor screening of the ionic charge. We show that these large capacitance values can be understood as the result of collective entrance of ions into the graphene stack (GS) and the renormalization of the ionic charge produced by nonlinear screening. The collective behavior of ions results from the strong elastic energy associated with intercalated ions deforming the GS, which creates an effective attraction between them. The result is the formation of "disks" of charge that enter the electrode collectively and have their charge renormalized by the strong, nonlinear screening of the surrounding graphene layers. This renormalization leads to a capacitance that at small voltages increases linearly with voltage and is enhanced over mean-field predictions by a large factor proportional to the number of ions within the disk to the power 9/4. At large voltages, the capacitance is dictated by the physics of graphite intercalation compounds and is proportional to the voltage raised to the power -4/5. We also examine theoretically the case where the effective fine structure constant of the GS is a small parameter, and we uncover a wealth of scaling regimes.

  1. 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.

  2. Emergence of Criticality in the Transportation Passenger Flow: Scaling and Renormalization in the Seoul Bus System

    PubMed Central

    Goh, Segun; Lee, Keumsook; Choi, MooYoung; Fortin, Jean-Yves

    2014-01-01

    Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221

  3. Two-loop renormalization of quantum gravity simplified

    DOE PAGES

    Bern, Zvi; Chi, Huan -Hang; Dixon, Lance; ...

    2017-02-22

    The coefficient of the dimensionally regularized two-loop R 3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple.more » As a result, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.« less

  4. 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.

  5. 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.

  6. Renormalization Group scale-setting in astrophysical systems

    NASA Astrophysics Data System (ADS)

    Domazet, Silvije; Štefančić, Hrvoje

    2011-09-01

    A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

  7. Higher-order quantum-chromodynamic corrections to the longitudinal coefficient function in deep-inelastic scattering

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sowell, G.A.

    1982-01-01

    A calculation of nonsinglet longitudinal coefficient function of deep-inelastic scattering through order-g/sup 4/ is presented, using the operator-product expansion and the renormalization group. Both ultraviolet and infrared divergences are regulated with dimensional regularization. The renormalization scheme dependence of the result is discussed along with its phenomenological application in the determination of R = sigma/sub L//sigma/sub T/.

  8. Remarks on the renormalization group in statistical fluid dynamics

    NASA Astrophysics Data System (ADS)

    Fournier, J.-D.; Frisch, U.

    1983-08-01

    A variant of the renormalization group is applied to the problem of randomly forced fluids studied by Forster, Nelson, and Stephen

    [Phys. Rev. A 16, 732 (1977)]
    and others. Amplitude factors (thought to be nonuniversal by some authors) are evaluated and shown to have universal values. Comparisons with closures are made. The possibility of a breakdown of self-similarity and/or universality due to intermittency effects is discussed.

  9. Fickian dispersion is anomalous

    DOE PAGES

    Cushman, John H.; O’Malley, Dan

    2015-06-22

    The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion wemore » illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Finally, power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.« less

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

    NASA Astrophysics Data System (ADS)

    Nakatani, Naoki; Chan, Garnet Kin-Lic

    2013-04-01

    We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

  11. Mode-sum regularization of ⟨ϕ2⟩ in the angular-splitting method

    NASA Astrophysics Data System (ADS)

    Levi, Adam; Ori, Amos

    2016-08-01

    The computation of the renormalized stress-energy tensor or ⟨ϕ2⟩ren in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute ⟨ϕ2⟩ren in a stationary spacetime using t splitting, namely splitting in the time-translation direction. Here we present the angular-splitting version of this approach, aimed for computing renormalized quantities in a general (possibly dynamical) spherically symmetric spacetime. To illustrate how the angular-splitting method works, we use it here to compute ⟨ϕ2⟩ren for a quantum massless scalar field in Schwarzschild background, in various quantum states (Boulware, Unruh, and Hartle-Hawking states). We find excellent agreement with the results obtained from the t -splitting variant and also with other methods. Our main goal in pursuing this new mode-sum approach was to enable the computation of the renormalized stress-energy tensor in a dynamical spherically symmetric background, e.g. an evaporating black hole. The angular-splitting variant presented here is most suitable to this purpose.

  12. Supersymmetric QCD on the lattice: An exploratory study

    NASA Astrophysics Data System (ADS)

    Costa, M.; Panagopoulos, H.

    2017-08-01

    We perform a pilot study of the perturbative renormalization of a supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider supersymmetric N =1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. The gauge group that we consider is S U (Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α , are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (Zψ), gluon (Zu), gluino (Zλ), squark (ZA ±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

  13. Renormalization group naturalness of GUT Higgs potentials

    NASA Astrophysics Data System (ADS)

    Allanach, B. C.; Amelino-Camelia, G.; Philipsen, O.; Pisanti, O.; Rosa, L.

    1999-01-01

    We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.

  14. The density-matrix renormalization group: a short introduction.

    PubMed

    Schollwöck, Ulrich

    2011-07-13

    The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

  15. Quenched results for light quark physics with overlap fermions

    NASA Astrophysics Data System (ADS)

    Giusti, L.; Hoelbling, C.; Rebbi, C.

    2002-03-01

    We present results of a quenched QCD simulation with overlap fermions on a lattice of volume V = 16 3 × 32 at β = 6.0, which corresponds to a lattice cutoff of ⋍ 2 GeV and an extension of ⋍ 1.4 fm. From the two-point correlation functions of bilinear operators we extract the pseudoscalar meson masses and the corresponding decay constants. From the GMOR relation we determine the chiral condensate and, by using the K-meson mass as experimental input, we compute the sum of the strange and average up-down quark masses ( m s + overlinem). The needed logarithmic divergent renormalization constant Z S is computed with the RI/MOM non-perturbative renormalization technique. Since the overlap preserves chiral symmetry at finite cutoff and volume, no divergent quark mass and chiral condensate additive renormalizations are required and the results are O( a) improved.

  16. Renormalizing Entanglement Distillation.

    PubMed

    Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens

    2016-01-15

    Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

  17. The Flynn effect and U.S. policies: the impact of rising IQ scores on American society via mental retardation diagnoses.

    PubMed

    Kanaya, Tomoe; Scullin, Matthew H; Ceci, Stephen J

    2003-10-01

    Over the last century, IQ scores have been steadily rising, a phenomenon dubbed the Flynn effect. Because of the Flynn effect, IQ tests are periodically renormed, making them harder. Given that eligibility for mental retardation (MR) services relies heavily on IQ scores, renormed tests could have a significant impact on MR placements. In longitudinal IQ records from 9 sites around the country, students in the borderline and mild MR range lost an average of 5.6 points when retested on a renormed test and were more likely to be classified MR compared with peers retested on the same test. The magnitude of the effect is large and affects national policies on education, social security, the death penalty, and the military. This paper reports the perceptions of professionals as they relate to IQ score fluctuations in normal, borderline, and/or MR populations.

  18. Renormalizing Entanglement Distillation

    NASA Astrophysics Data System (ADS)

    Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens

    2016-01-01

    Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

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

    PubMed

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

    2010-01-14

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

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cirac, J.I.; Pérez-García, D., E-mail: dperezga@ucm.es; ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid

    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 asmore » 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).« less

  1. 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.

  2. Alien calculus and a Schwinger-Dyson equation: two-point function with a nonperturbative mass scale

    NASA Astrophysics Data System (ADS)

    Bellon, Marc P.; Clavier, Pierre J.

    2018-02-01

    Starting from the Schwinger-Dyson equation and the renormalization group equation for the massless Wess-Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.

  3. Mass deformations of 5d SCFTs via holography

    NASA Astrophysics Data System (ADS)

    Gutperle, Michael; Kaidi, Justin; Raj, Himanshu

    2018-02-01

    Using six-dimensional Euclidean F (4) gauged supergravity we construct a holographic renormalization group flow for a CFT on S 5. Numerical solutions to the BPS equations are obtained and the free energy of the theory on S 5 is determined holographically by calculation of the renormalized on-shell supergravity action. In the process, we deal with subtle issues such as holographic renormalization and addition of finite counterterms. We then propose a candidate field theory dual to these solutions. This tentative dual is a supersymmetry-preserving deformation of the strongly-coupled non-Lagrangian SCFT derived from the D4-D8 system in string theory. In the IR, this theory is a mass deformation of a USp(2 N ) gauge theory. A localization calculation of the free energy is performed for this IR theory, which for reasonably small values of the deformation parameter is found to have the same qualitative behaviour as the holographic free energy.

  4. One-loop renormalization of Lee-Wick gauge theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Grinstein, Benjamin; O'Connell, Donal

    2008-11-15

    We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theorymore » than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.« less

  5. Baryon chiral perturbation theory extended beyond the low-energy region.

    PubMed

    Epelbaum, E; Gegelia, J; Meißner, Ulf-G; Yao, De-Liang

    We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

  6. Renormalization group analysis of B →π form factors with B -meson light-cone sum rules

    NASA Astrophysics Data System (ADS)

    Shen, Yue-Long; Wei, Yan-Bing; Lü, Cai-Dian

    2018-03-01

    Within the framework of the B -meson light-cone sum rules, we review the calculation of radiative corrections to the three B →π transition form factors at leading power in Λ /mb. To resum large logarithmic terms, we perform the complete renormalization group evolution of the correlation function. We employ the integral transformation which diagonalizes evolution equations of the jet function and the B -meson light-cone distribution amplitude to solve these evolution equations and obtain renormalization group improved sum rules for the B →π form factors. Results of the form factors are extrapolated to the whole physical q2 region and are compared with that of other approaches. The effect of B -meson three-particle light-cone distribution amplitudes, which will contribute to the form factors at next-to-leading power in Λ /mb at tree level, is not considered in this paper.

  7. Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

    2008-10-15

    The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

  8. Conformal Symmetry as a Template for QCD

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brodsky, S

    2004-08-04

    Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadronmore » phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized.« less

  9. Neutrino mass matrices with two vanishing cofactors and Fritzsch texture for charged lepton mass matrix

    NASA Astrophysics Data System (ADS)

    Wang, Weijian; Guo, Shu-Yuan; Wang, Zhi-Gang

    2016-04-01

    In this paper, we study the cofactor 2 zero neutrino mass matrices with the Fritzsch-type structure in charged lepton mass matrix (CLMM). In the numerical analysis, we perform a scan over the parameter space of all the 15 possible patterns to get a large sample of viable scattering points. Among the 15 possible patterns, three of them can accommodate the latest lepton mixing and neutrino mass data. We compare the predictions of the allowed patterns with their counterparts with diagonal CLMM. In this case, the severe cosmology bound on the neutrino mass set a strong constraint on the parameter space, rendering two patterns only marginally allowed. The Fritzsch-type CLMM will have impact on the viable parameter space and give rise to different phenomenological predictions. Each allowed pattern predicts the strong correlations between physical variables, which is essential for model selection and can be probed in future experiments. It is found that under the no-diagonal CLMM, the cofactor zeros structure in neutrino mass matrix is unstable as the running of renormalization group (RG) from seesaw scale to the electroweak scale. A way out of the problem is to propose the flavor symmetry under the models with a TeV seesaw scale. The inverse seesaw model and a loop-induced model are given as two examples.

  10. Electrons at the monkey saddle: A multicritical Lifshitz point

    NASA Astrophysics Data System (ADS)

    Shtyk, A.; Goldstein, G.; Chamon, C.

    2017-01-01

    We consider two-dimensional interacting electrons at a monkey saddle with dispersion ∝px3-3 pxpy2 . Such a dispersion naturally arises at the multicritical Lifshitz point when three Van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em∝(Bm ) 3 /2 and related oscillations in thermodynamic and transport properties, such as de Haas-Van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the noninteracting electron fixed point is unstable to interactions under the renormalization-group flow, developing either a superconducting instability or non-Fermi-liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K' points, exhibits an interplay of competing many-body instabilities, namely, s -wave superconductivity, ferromagnetism, and spin- and charge-density waves.

  11. Hierarchy of Modes in an Interacting One-Dimensional System

    NASA Astrophysics Data System (ADS)

    Tsyplyatyev, O.; Schofield, A. J.; Jin, Y.; Moreno, M.; Tan, W. K.; Ford, C. J. B.; Griffiths, J. P.; Farrer, I.; Jones, G. A. C.; Ritchie, D. A.

    2015-05-01

    Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R2/L2, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

  12. Optically adjustable valley Hall current in single-layer transition metal dichalcogenides

    NASA Astrophysics Data System (ADS)

    Sengupta, Parijat; Pavlidis, Dimitris; Shi, Junxia

    2018-02-01

    The illumination of a single-layer transition metal dichalcogenide with an elliptically polarized light beam is shown to give rise to a differential rate of inter-band carrier excitation between the valence and conduction states around the valley edges, K and K' . This rate with a linear dependence on the beam ellipticity and inverse of the optical gap manifests as an asymmetric Fermi distribution between the valleys or a non-equilibrium population which under an external field and a Berry curvature induced anomalous velocity, results in an externally tunable finite valley Hall current. Surface imperfections that influence the excitation rates are included through the self-consistent Born approximation. Further, we describe applications centered around circular dichroism, quantum computing, and spin torque via optically excited spin currents within the framework of the suggested formalism. A closing summary points to the possibility of extending the calculations to composite charged particles like trions. The role of the substrate in renormalizing the fundamental band gap and moderating the valley Hall current is also discussed.

  13. Chiral Tricritical Point: A New Universality Class in Dirac Systems

    NASA Astrophysics Data System (ADS)

    Yin, Shuai; Jian, Shao-Kai; Yao, Hong

    2018-05-01

    Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

  14. Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

    DOE PAGES

    Jiang, Hong -Chen; Devereaux, T.; Kivelson, S. A.

    2017-08-07

    We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t–J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ = 0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole permore » unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. In conclusion, our results may be relevant to kagome lattice herbertsmithite upon doping.« less

  15. Defects in Nematic Shells: A Γ-Convergence Discrete-to-Continuum Approach

    NASA Astrophysics Data System (ADS)

    Canevari, Giacomo; Segatti, Antonio

    2018-07-01

    In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment of the director field. To this end, we consider a discrete XY system on the shell M, described by a tangent vector field with unit norm sitting at the vertices of a triangulation of the shell. Defects emerge when we let the mesh size of the triangulation go to zero, namely in the discrete-to-continuum limit. In this paper we investigate the discrete-to-continuum limit in terms of Γ-convergence in two different asymptotic regimes. The first scaling promotes the appearance of a finite number of defects whose charges are in accordance with the topology of shell M, via the Poincaré-Hopf Theorem. The second scaling produces the so called Renormalized Energy that governs the equilibrium of the configurations with defects.

  16. Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn₅ revealed by precision microwave spectroscopy.

    PubMed

    Truncik, C J S; Huttema, W A; Turner, P J; Ozcan, S; Murphy, N C; Carrière, P R; Thewalt, E; Morse, K J; Koenig, A J; Sarrao, J L; Broun, D M

    2013-01-01

    CeCoIn₅ is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low-temperature microwave spectroscopy to study the charge dynamics of the CeCoIn₅ superconducting state. The similarities to cuprates, in particular to ultra-clean YBa₂Cu₃O(y), are striking: the frequency and temperature dependence of the quasiparticle conductivity are instantly recognizable, a consequence of rapid suppression of quasiparticle scattering below T(c); and penetration-depth data, when properly treated, reveal a clean, linear temperature dependence of the quasiparticle contribution to superfluid density. The measurements also expose key differences, including prominent multiband effects and a temperature-dependent renormalization of the quasiparticle mass.

  17. Development of a Renormalization Group Approach to Multi-Scale Plasma Physics Computation

    DTIC Science & Technology

    2012-03-28

    with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1...NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: a . REPORT...code) 29-12-2008 Final Technical Report From 29-12-2008 To 16-95-2011 (STTR PHASE II) DEVELOPMENT OF A RENORMALIZATION GROUP APPROACH TO MULTI-SCALE

  18. 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.

  19. Renormalization Group Theory for the Imbalanced Fermi Gas

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gubbels, K. B.; Stoof, H. T. C.

    2008-04-11

    We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)].

  20. 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.

  1. BPHZ renormalization in configuration space for the A4-model

    NASA Astrophysics Data System (ADS)

    Pottel, Steffen

    2018-02-01

    Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

  2. Functional renormalization group approach to SU(N ) Heisenberg models: Real-space renormalization group at arbitrary N

    NASA Astrophysics Data System (ADS)

    Buessen, Finn Lasse; Roscher, Dietrich; Diehl, Sebastian; Trebst, Simon

    2018-02-01

    The pseudofermion functional renormalization group (pf-FRG) is one of the few numerical approaches that has been demonstrated to quantitatively determine the ordering tendencies of frustrated quantum magnets in two and three spatial dimensions. The approach, however, relies on a number of presumptions and approximations, in particular the choice of pseudofermion decomposition and the truncation of an infinite number of flow equations to a finite set. Here we generalize the pf-FRG approach to SU (N )-spin systems with arbitrary N and demonstrate that the scheme becomes exact in the large-N limit. Numerically solving the generalized real-space renormalization group equations for arbitrary N , we can make a stringent connection between the physically most significant case of SU(2) spins and more accessible SU (N ) models. In a case study of the square-lattice SU (N ) Heisenberg antiferromagnet, we explicitly demonstrate that the generalized pf-FRG approach is capable of identifying the instability indicating the transition into a staggered flux spin liquid ground state in these models for large, but finite, values of N . In a companion paper [Roscher et al., Phys. Rev. B 97, 064416 (2018), 10.1103/PhysRevB.97.064416] we formulate a momentum-space pf-FRG approach for SU (N ) spin models that allows us to explicitly study the large-N limit and access the low-temperature spin liquid phase.

  3. Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts.

    PubMed

    Grzywacz, Piotr; Qin, Jian; Morse, David C

    2007-12-01

    Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor S(-1)(k) predicted by a "one-loop" approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to S(-1)(k) is shown to be the sum of (i) a k -independent contribution that arises from a renormalization of the effective chi parameter, (ii) a k-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to k(2) that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a k-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

  4. Renormalized Two-Fluid Hydrodynamics of Cosmic-Ray--modified Shocks

    NASA Astrophysics Data System (ADS)

    Malkov, M. A.; Voelk, H. J.

    1996-12-01

    A simple two-fluid model of diffusive shock acceleration, introduced by Axford, Leer, & Skadron and Drury & Völk, is revisited. This theory became a chief instrument in the studies of shock modification due to particle acceleration. Unfortunately its most intriguing steady state prediction about a significant enhancement of the shock compression and a corresponding increase of the cosmic-ray production violates assumptions which are critical for the derivation of this theory. In particular, for strong shocks the spectral flattening makes a cutoff-independent definition of pressure and energy density impossible and therefore causes an additional closure problem. Confining ourselves for simplicity to the case of plane shocks, assuming reacceleration of a preexisting cosmic-ray population, we argue that also under these circumstances the kinetic solution has a rather simple form. It can be characterized by only a few parameters, in the simplest case by the slope and the magnitude of the momentum distribution at the upper momentum cutoff. We relate these parameters to standard hydrodynamic quantities like the overall shock compression ratio and the downstream cosmic-ray pressure. The two-fluid theory produced in this way has the traditional form but renormalized closure parameters. By solving the renormalized Rankine-Hugoniot equations, we show that for the efficient stationary solution, most significant for cosmic-ray acceleration, the renormalization is needed in the whole parameter range of astrophysical interest.

  5. Renormalized Hamiltonian for a peptide chain: Digitalizing the protein folding problem

    NASA Astrophysics Data System (ADS)

    Fernández, Ariel; Colubri, Andrés

    2000-05-01

    A renormalized Hamiltonian for a flexible peptide chain is derived to generate the long-time limit dynamics compatible with a coarsening of torsional conformation space. The renormalization procedure is tailored taking into account the coarse graining imposed by the backbone torsional constraints due to the local steric hindrance and the local backbone-side-group interactions. Thus, the torsional degrees of freedom for each residue are resolved modulo basins of attraction in its so-called Ramachandran map. This Ramachandran renormalization (RR) procedure is implemented so that the chain is energetically driven to form contact patterns as their respective collective topological constraints are fulfilled within the coarse description. In this way, the torsional dynamics are digitalized and become codified as an evolving pattern in a binary matrix. Each accepted Monte Carlo step in a canonical ensemble simulation is correlated with the real mean first passage time it takes to reach the destination coarse topological state. This real-time correlation enables us to test the RR dynamics by comparison with experimentally probed kinetic bottlenecks along the dominant folding pathway. Such intermediates are scarcely populated at any given time, but they determine the kinetic funnel leading to the active structure. This landscape region is reached through kinetically controlled steps needed to overcome the conformational entropy of the random coil. The results are specialized for the bovine pancreatic trypsin inhibitor, corroborating the validity of our method.

  6. Impact of saturation on the polariton renormalization in III-nitride based planar microcavities

    NASA Astrophysics Data System (ADS)

    Rossbach, Georg; Levrat, Jacques; Feltin, Eric; Carlin, Jean-François; Butté, Raphaël; Grandjean, Nicolas

    2013-10-01

    It has been widely observed that an increasing carrier density in a strongly coupled semiconductor microcavity (MC) alters the dispersion of cavity polaritons, below and above the condensation threshold. The interacting nature of cavity polaritons stems from their excitonic fraction being intrinsically subject to Coulomb interactions and the Pauli-blocking principle at high carrier densities. By means of injection-dependent photoluminescence studies performed nonresonantly on a GaN-based MC at various temperatures, it is shown that already below the condensation threshold saturation effects generally dominate over any energy variation in the excitonic resonance. This observation is in sharp contrast to the usually assumed picture in strongly coupled semiconductor MCs, where the impact of saturation is widely neglected. These experimental findings are confirmed by tracking the exciton emission properties of the bare MC active medium and those of a high-quality single GaN quantum well up to the Mott density. The systematic investigation of renormalization up to the polariton condensation threshold as a function of lattice temperature and exciton-cavity photon detuning is strongly hampered by photonic disorder. However, when overcoming the latter by averaging over a larger spot size, a behavior in agreement with a saturation-dominated polariton renormalization is revealed. Finally, a comparison with other inorganic material systems suggests that for correctly reproducing polariton renormalization, exciton saturation effects should be taken into account systematically.

  7. Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

    NASA Astrophysics Data System (ADS)

    Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.

    2016-12-01

    We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

  8. Type 0 open string amplitudes and the tensionless limit

    NASA Astrophysics Data System (ADS)

    Rojas, Francisco

    2014-12-01

    The sum over planar multiloop diagrams in the NS + sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve nonperturbative issues of gauge theories in the large N limit. With S U (N ) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N →∞ with N gs2 held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Möbius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount p ≡∑ i n ki≠0 at the level of the integrands in the integrals over the moduli and analytically continuing them to p =0 at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary n -gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.

  9. Monte Carlo renormalization-group study of the Baxter-Wu model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Novotny, M.A.; Landau, D.P.; Swendsen, R.H.

    1982-07-01

    The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevent eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.

  10. FRACTAL DIMENSION OF SPIN-GLASSES INTERFACES IN DIMENSION d = 2 AND d = 3 VIA STRONG DISORDER RENORMALIZATION AT ZERO TEMPERATURE

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2015-09-01

    For Gaussian Spin-Glasses in low dimensions, we introduce a simple Strong Disorder renormalization at zero temperature in order to construct ground states for Periodic and Anti-Periodic boundary conditions. The numerical study in dimensions d = 2 (up to sizes 20482) and d = 3 (up to sizes 1283) yields that Domain Walls are fractal of dimensions ds(d = 2) ≃ 1.27 and ds(d = 3) ≃ 2.55, respectively.

  11. Chiral algebras in Landau-Ginzburg models

    NASA Astrophysics Data System (ADS)

    Dedushenko, Mykola

    2018-03-01

    Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.

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

    PubMed

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

    2011-07-13

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

  13. Multiloop Functional Renormalization Group That Sums Up All Parquet Diagrams

    NASA Astrophysics Data System (ADS)

    Kugler, Fabian B.; von Delft, Jan

    2018-02-01

    We present a multiloop flow equation for the four-point vertex in the functional renormalization group (FRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of FRG computations for the four-point vertex and, consequently, the self-energy. Using the x-ray-edge singularity as an example, we show that solving the multiloop FRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hill, Christopher T.

    We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.

  15. Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

    NASA Astrophysics Data System (ADS)

    An, Ok Song

    2017-12-01

    We present a systematic approach to supersymmetric holographic renormalization for a generic 5D N=2 gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities of a 4D superconformal field theory on a generic background, including the Weyl and super-Weyl anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor.

  16. On the soft supersymmetry-breaking parameters in gauge-mediated models

    NASA Astrophysics Data System (ADS)

    Wagner, C. E. M.

    1998-09-01

    Gauge mediation of supersymmetry breaking in the observable sector is an attractive idea, which naturally alleviates the flavor changing neutral current problem of supersymmetric theories. Quite generally, however, the number and quantum number of the messengers are not known; nor is their characteristic mass scale determined by the theory. Using the recently proposed method to extract supersymmetry-breaking parameters from wave-function renormalization, we derived general formulae for the soft supersymmetry-breaking parameters in the observable sector, valid in the small and moderate tan β regimes, for the case of split messengers. The full leading-order effects of top Yukawa and gauge couplings on the soft supersymmetry-breaking parameters are included. We give a simple interpretation of the general formulae in terms of the renormalization group evolution of the soft supersymmetry-breaking parameters. As a by-product of this analysis, the one-loop renormalization group evolution of the soft supersymmetry-breaking parameters is obtained for arbitrary boundary conditions of the scalar and gaugino mass parameters at high energies.

  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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Katanin, A. A., E-mail: katanin@mail.ru

    We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32].more » 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.« less

  18. Functional Integration

    NASA Astrophysics Data System (ADS)

    Cartier, Pierre; DeWitt-Morette, Cecile

    2006-11-01

    Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

  19. Functional Integration

    NASA Astrophysics Data System (ADS)

    Cartier, Pierre; DeWitt-Morette, Cecile

    2010-06-01

    Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

  20. Electrostatic contribution to the persistence length of a semiflexible dipolar chain.

    PubMed

    Podgornik, Rudi

    2004-09-01

    We investigate the electrostatic contribution to the persistence length of a semiflexible polymer chain whose segments interact via a screened Debye-Hückel dipolar interaction potential. We derive the expressions for the renormalized persistence length on the level of a 1/D-expansion method already successfully used in other contexts of polyelectrolye physics. We investigate different limiting forms of the renormalized persistence length of the dipolar chain and show that, in, general, it depends less strongly on the screening length than in the context of a monopolar chain. We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. This can be understood solely on the basis of a swifter decay of the dipolar interactions with separation compared to the monopolar electrostatic interactions. We comment also on the general contribution of higher multipoles to the electrostatic renormalization of the bending rigidity.

  1. Renormalization group study of the melting of a two-dimensional system of collapsing hard disks

    NASA Astrophysics Data System (ADS)

    Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu. D.; Tsiok, E. N.; Chumakov, E. S.

    2017-06-01

    We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.

  2. Renormalization group method based on the ionization energy theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Arulsamy, Andrew Das, E-mail: sadwerdna@gmail.com; School of Physics, University of Sydney, Sydney, New South Wales 2006

    2011-03-15

    Proofs are developed to explicitly show that the ionization energy theory is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for the ionization energy theory relies on the energy-level spacing, instead of lattice point spacing in k-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition,more » as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.« less

  3. Impact of topology in foliated quantum Einstein gravity.

    PubMed

    Houthoff, W B; Kurov, A; Saueressig, F

    2017-01-01

    We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

  4. Phase structure of NJL model with weak renormalization group

    NASA Astrophysics Data System (ADS)

    Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

    2018-06-01

    We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

  5. Effective field renormalization group approach for Ising lattice spin systems

    NASA Astrophysics Data System (ADS)

    Fittipaldi, Ivon P.

    1994-03-01

    A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

  6. Renormalization, conformal ward identities and the origin of a conformal anomaly pole

    NASA Astrophysics Data System (ADS)

    Corianò, Claudio; Maglio, Matteo Maria

    2018-06-01

    We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the TJJ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the F-basis), where only one of them requires renormalization (F13), extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the TJJ in momentum space, expressed in terms of a minimal set of 4 form factors (A-basis), with the properties of the F-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.

  7. Reconstructing source terms from atmospheric concentration measurements: Optimality analysis of an inversion technique

    NASA Astrophysics Data System (ADS)

    Turbelin, Grégory; Singh, Sarvesh Kumar; Issartel, Jean-Pierre

    2014-12-01

    In the event of an accidental or intentional contaminant release in the atmosphere, it is imperative, for managing emergency response, to diagnose the release parameters of the source from measured data. Reconstruction of the source information exploiting measured data is called an inverse problem. To solve such a problem, several techniques are currently being developed. The first part of this paper provides a detailed description of one of them, known as the renormalization method. This technique, proposed by Issartel (2005), has been derived using an approach different from that of standard inversion methods and gives a linear solution to the continuous Source Term Estimation (STE) problem. In the second part of this paper, the discrete counterpart of this method is presented. By using matrix notation, common in data assimilation and suitable for numerical computing, it is shown that the discrete renormalized solution belongs to a family of well-known inverse solutions (minimum weighted norm solutions), which can be computed by using the concept of generalized inverse operator. It is shown that, when the weight matrix satisfies the renormalization condition, this operator satisfies the criteria used in geophysics to define good inverses. Notably, by means of the Model Resolution Matrix (MRM) formalism, we demonstrate that the renormalized solution fulfils optimal properties for the localization of single point sources. Throughout the article, the main concepts are illustrated with data from a wind tunnel experiment conducted at the Environmental Flow Research Centre at the University of Surrey, UK.

  8. Restoration of dimensional reduction in the random-field Ising model at five dimensions

    NASA Astrophysics Data System (ADS)

    Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

    2017-04-01

    The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

  9. Restoration of dimensional reduction in the random-field Ising model at five dimensions.

    PubMed

    Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

    2017-04-01

    The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

  10. Quantum multicriticality in disordered Weyl semimetals

    NASA Astrophysics Data System (ADS)

    Luo, Xunlong; Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi

    2018-01-01

    In electronic band structure of solid-state material, two band-touching points with linear dispersion appear in pairs in the momentum space. When they annihilate each other, the system undergoes a quantum phase transition from a three-dimensional (3D) Weyl semimetal (WSM) phase to a band insulator phase such as a Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a "magnetic dipole"-like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases: a renormalized WSM phase, a CI phase, and a diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band-touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states, and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized WSM phase turns out to be a direct phase transition whose critical exponent ν =0.80 ±0.01 . We interpret these numerical results by a renormalization group analysis on the critical theory.

  11. 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.

  12. A bulk localized state and new holographic renormalization group flow in 3D spin-3 gravity

    NASA Astrophysics Data System (ADS)

    Nakayama, Ryuichi; Suzuki, Tomotaka

    2018-04-01

    We construct a localized state of a scalar field in 3D spin-3 gravity. 3D spin-3 gravity is thought to be holographically dual to W3-extended CFT on a boundary at infinity. It is known that while W3 algebra is a nonlinear algebra, in the limit of large central charge c a linear finite-dimensional subalgebra generated by Wn (n = 0,±1,±2) and Ln (n = 0,±1) is singled out. The localized state is constructed in terms of these generators. To write down an equation of motion for a scalar field which is satisfied by this localized state, it is necessary to introduce new variables for an internal space α±, β±, γ, in addition to ordinary coordinates x± and y. The higher-dimensional space, which combines the bulk space-time with the “internal space,” which is an analog of superspace in supersymmetric theory, is introduced. The “physical bulk space-time” is a 3D hypersurface with constant α±, β± and γ embedded in this space. We will work in Poincaré coordinates of AdS space and consider W-quasi-primary operators Φh(x+) with a conformal weight h in the boundary and study two and three point functions of W-quasi-primary operators transformed as eix+L‑1heβ+W‑1hΦh(0)e‑β+W‑1he‑ix+L‑1h. Here, Lnh and Wnh are sl(3,R) generators in the hyperbolic basis for Poincaré coordinates. It is shown that in the β+ →∞ limit, the conformal weight changes to a new value h‧ = h/2. This may be regarded as a Renormalization Group (RG) flow. It is argued that this RG flow will be triggered by terms ΔS ∝ β+W ‑1h + β‑W¯ ‑1h added to the action.

  13. One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for density-functional theory.

    PubMed

    Stoudenmire, E M; Wagner, Lucas O; White, Steven R; Burke, Kieron

    2012-08-03

    We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated artificial hydrogen atoms. The method can be used to simulate 1D cold atom systems and to study density-functional theory in an exact setting. To illustrate, we find an interacting, extended system which is an insulator but whose Kohn-Sham system is metallic.

  14. Weyl consistency conditions in non-relativistic quantum field theory

    DOE PAGES

    Pal, Sridip; Grinstein, Benjamín

    2016-12-05

    Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2 + 1 dimensions with anisotropic scaling exponent z = 2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. Here, we comment on possible candidates for a C-theorem in higher dimensions.

  15. Exact renormalization group equation for the Lifshitz critical point

    NASA Astrophysics Data System (ADS)

    Bervillier, C.

    2004-10-01

    An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

  16. Universality, twisted fans, and the Ising model. [Renormalization, two-loop calculations, scale

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dash, J.W.; Harrington, S.J.

    1975-06-24

    Critical exponents are evaluated for the Ising model using universality in the form of ''twisted fans'' previously introduced in Reggeon field theory. The universality is with respect to scales induced through renormalization. Exact twists are obtained at ..beta.. = 0 in one loop for D = 2,3 with ..nu.. = 0.75 and 0.60 respectively. In two loops one obtains ..nu.. approximately 1.32 and 0.68. No twists are obtained for eta, however. The results for the standard two loop calculations are also presented as functions of a scale.

  17. Node synchronization schemes for the Big Viterbi Decoder

    NASA Technical Reports Server (NTRS)

    Cheung, K.-M.; Swanson, L.; Arnold, S.

    1992-01-01

    The Big Viterbi Decoder (BVD), currently under development for the DSN, includes three separate algorithms to acquire and maintain node and frame synchronization. The first measures the number of decoded bits between two consecutive renormalization operations (renorm rate), the second detects the presence of the frame marker in the decoded bit stream (bit correlation), while the third searches for an encoded version of the frame marker in the encoded input stream (symbol correlation). A detailed account of the operation is given, as well as performance comparison, of the three methods.

  18. Invariant measure of the one-loop quantum gravitational backreaction on inflation

    NASA Astrophysics Data System (ADS)

    Miao, S. P.; Tsamis, N. C.; Woodard, R. P.

    2017-06-01

    We use dimensional regularization in pure quantum gravity on a de Sitter background to evaluate the one-loop expectation value of an invariant operator which gives the local expansion rate. We show that the renormalization of this nonlocal composite operator can be accomplished using the counterterms of a simple local theory of gravity plus matter, at least at one-loop order. This renormalization completely absorbs the one-loop correction, which accords with the prediction that the lowest secular backreaction should be a two-loop effect.

  19. 2PI effective theory at next-to-leading order using the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Carrington, M. E.; Friesen, S. A.; Meggison, B. A.; Phillips, C. D.; Pickering, D.; Sohrabi, K.

    2018-02-01

    We consider a symmetric scalar theory with quartic coupling in four dimensions. We show that the four-loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.

  20. Topological Luttinger liquids from decorated domain walls

    NASA Astrophysics Data System (ADS)

    Parker, Daniel E.; Scaffidi, Thomas; Vasseur, Romain

    2018-04-01

    We introduce a systematic construction of a gapless symmetry-protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids. The resulting strongly interacting phases provide a concrete example of a gapless symmetry-protected topological (gSPT) phase with robust symmetry-protected edge modes. Using boundary conformal field theory arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly coupled renormalization group fixed point. Our results are checked against extensive density matrix renormalization group calculations.

  1. Renormalization of Extended QCD2

    NASA Astrophysics Data System (ADS)

    Fukaya, Hidenori; Yamamura, Ryo

    2015-10-01

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

  2. Properties of resonance wave functions.

    NASA Technical Reports Server (NTRS)

    More, R. M.; Gerjuoy, E.

    1973-01-01

    Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.

  3. Entanglement renormalization, quantum error correction, and bulk causality

    NASA Astrophysics Data System (ADS)

    Kim, Isaac H.; Kastoryano, Michael J.

    2017-04-01

    Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progres-sively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

  4. Nonperturbative renormalization of quark bilinear operators and B{sub K} using domain wall fermions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Aoki, Y.; Dawson, C.; Brookhaven National Laboratory, Upton, New York 11973

    2008-09-01

    We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-K mixing parameter B{sub K}. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed nonperturbatively and then matched perturbatively to the MS scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16{sup 3}x32 lattice volume, the Iwasaki gauge action at {beta}=2.13 and domain wall fermions with L{sub s}=16.

  5. Exploring excited eigenstates of many-body systems using the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph

    2018-05-01

    We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.

  6. Directly Characterizing the Relative Strength and Momentum Dependence of Electron-Phonon Coupling Using Resonant Inelastic X-Ray Scattering

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Devereaux, T. P.; Shvaika, A. M.; Wu, K.

    The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge-density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and nonresonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom—the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usually through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong,more » impacting one’s ability to quantitatively characterize the coupling. Here, we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an eight-band model of copper oxides, we study the contributions from the lowest-order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross section, as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and nonresonant x-ray scattering, as well as Raman and infrared conductivity.« less

  7. Directly Characterizing the Relative Strength and Momentum Dependence of Electron-Phonon Coupling Using Resonant Inelastic X-Ray Scattering

    DOE PAGES

    Devereaux, T. P.; Shvaika, A. M.; Wu, K.; ...

    2016-10-25

    The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge-density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and nonresonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom—the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usually through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong,more » impacting one’s ability to quantitatively characterize the coupling. Here, we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an eight-band model of copper oxides, we study the contributions from the lowest-order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross section, as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and nonresonant x-ray scattering, as well as Raman and infrared conductivity.« less

  8. Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

    NASA Astrophysics Data System (ADS)

    Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

    2018-02-01

    The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

  9. Precision calculations for h → WW/ZZ → 4 fermions in the Two-Higgs-Doublet Model with Prophecy4f

    NASA Astrophysics Data System (ADS)

    Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi

    2018-03-01

    We have calculated the next-to-leading-order electroweak and QCD corrections to the decay processes h → WW/ZZ → 4 fermions of the light CP-even Higgs boson h of various types of Two-Higgs-Doublet Models (Types I and II, "lepton-specific" and "flipped" models). The input parameters are defined in four different renormalization schemes, where parameters that are not directly accessible by experiments are defined in the \\overline{MS} scheme. Numerical results are presented for the corrections to partial decay widths for various benchmark scenarios previously motivated in the literature, where we investigate the dependence on the \\overline{MS} renormalization scale and on the choice of the renormalization scheme in detail. We find that it is crucial to be precise with these issues in parameter analyses, since parameter conversions between different schemes can involve sizeable or large corrections, especially in scenarios that are close to experimental exclusion limits or theoretical bounds. It even turns out that some renormalization schemes are not applicable in specific regions of parameter space. Our investigation of differential distributions shows that corrections beyond the Standard Model are mostly constant offsets induced by the mixing between the light and heavy CP-even Higgs bosons, so that differential analyses of h→4 f decay observables do not help to identify Two-Higgs-Doublet Models. Moreover, the decay widths do not significantly depend on the specific type of those models. The calculations are implemented in the public Monte Carlo generator Prophecy4f and ready for application.

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

    NASA Astrophysics Data System (ADS)

    Connes, Alain; Kreimer, Dirk

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

  11. One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization

    NASA Astrophysics Data System (ADS)

    Zacharias, Marios; Giustino, Feliciano

    2016-08-01

    Recently, Zacharias et al. [Phys. Rev. Lett. 115, 177401 (2015), 10.1103/PhysRevLett.115.177401] developed an ab initio theory of temperature-dependent optical absorption spectra and band gaps in semiconductors and insulators. In that work, the zero-point renormalization and the temperature dependence were obtained by sampling the nuclear wave functions using a stochastic approach. In the present work, we show that the stochastic sampling of Zacharias et al. can be replaced by fully deterministic supercell calculations based on a single optimal configuration of the atomic positions. We demonstrate that a single calculation is able to capture the temperature-dependent band-gap renormalization including quantum nuclear effects in direct-gap and indirect-gap semiconductors, as well as phonon-assisted optical absorption in indirect-gap semiconductors. In order to demonstrate this methodology, we calculate from first principles the temperature-dependent optical absorption spectra and the renormalization of direct and indirect band gaps in silicon, diamond, and gallium arsenide, and we obtain good agreement with experiment and with previous calculations. In this work we also establish the formal connection between the Williams-Lax theory of optical transitions and the related theories of indirect absorption by Hall, Bardeen, and Blatt, and of temperature-dependent band structures by Allen and Heine. The present methodology enables systematic ab initio calculations of optical absorption spectra at finite temperature, including both direct and indirect transitions. This feature will be useful for high-throughput calculations of optical properties at finite temperature and for calculating temperature-dependent optical properties using high-level theories such as G W and Bethe-Salpeter approaches.

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

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna

    1998-03-01

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

  13. On the interface between perturbative and nonperturbative QCD

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.

    2016-04-04

    The QCD running couplingmore » $$\\alpha_s(Q^2)$$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $$\\alpha_s(Q^2)$$. The high-$Q^2$ dependence of the coupling $$\\alpha_s(Q^2)$$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $$\\alpha_s(Q^2)$$ then determines the scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $$Q_0$$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $$Q_0$$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $$\\bar{MS}$$, $$g_1$$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of $$\\alpha_s$$ at large distance seen in the literature can be explained by different choices of renormalization schemes. Lastly, we also provide the formulae to compute $$\\alpha_s(Q^2)$$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.« less

  14. Coarse-Graining of Polymer Dynamics via Energy Renormalization

    NASA Astrophysics Data System (ADS)

    Xia, Wenjie; Song, Jake; Phelan, Frederick; Douglas, Jack; Keten, Sinan

    The computational prediction of the properties of polymeric materials to serve the needs of materials design and prediction of their performance is a grand challenge due to the prohibitive computational times of all-atomistic (AA) simulations. Coarse-grained (CG) modeling is an essential strategy for making progress on this problem. While there has been intense activity in this area, effective methods of coarse-graining have been slow to develop. Our approach to this fundamental problem starts from the observation that integrating out degrees of freedom of the AA model leads to a strong modification of the configurational entropy and cohesive interaction. Based on this observation, we propose a temperature-dependent systematic renormalization of the cohesive interaction in the CG modeling to recover the thermodynamic modifications in the system and the dynamics of the AA model. Here, we show that this energy renormalization approach to CG can faithfully estimate the diffusive, segmental and glassy dynamics of the AA model over a large temperature range spanning from the Arrhenius melt to the non-equilibrium glassy states. Our proposed CG strategy offers a promising strategy for developing thermodynamically consistent CG models with temperature transferability.

  15. A measurement of energy correlations and a determination of αs( M2Z 0) e +e - annihilations at √ s=91 GeV

    NASA Astrophysics Data System (ADS)

    Akrawy, M. Z.; Alexander, G.; Allison, J.; Allport, P. P.; Anderson, K. J.; Armitage, J. C.; Arnison, G. T. J.; Ashton, P.; Azuelos, G.; Baines, J. T. M.; Ball, A. H.; Banks, J.; Barker, G. J.; Barlow, R. J.; Batley, J. R.; Beck, A.; Becker, J.; Behnke, T.; Bell, K. W.; Bella, G.; Bethke, S.; Biebel, O.; Binder, U.; Bloodworth, I. J.; Bock, P.; Breuker, H.; Brown, R. M.; Brun, R.; Buijs, A.; Burckhart, H. J.; Capiluppi, P.; Carnegie, R. K.; Carter, A. A.; Carter, J. R.; Chang, C. Y.; Charlton, D. G.; Chrin, J. T. M.; Clarke, P. E. L.; Cohen, I.; Collins, W. J.; Conboy, J. E.; Couch, M.; Coupland, M.; Cuffiani, M.; Dado, S.; Dallavalle, G. M.; Debu, P.; Deninno, M. M.; Dieckmann, A.; Dittmar, M.; Dixit, M. S.; Duchovni, E.; Duerdoth, I. P.; Dumas, D. J. P.; El Mamouni, H.; Elcombe, P. A.; Estabrooks, P. G.; Etzion, E.; Fabbri, F.; Farthouat, P.; Fischer, H. M.; Fong, D. G.; French, M. T.; Fukunaga, C.; Gaidot, A.; Ganel, O.; Gary, J. W.; Gascon, J.; Geddes, N. I.; Gee, C. N. P.; Geich-Gimbel, C.; Gensler, S. W.; Gentit, F. X.; Giacomelli, G.; Gibson, V.; Gibson, W. R.; Gillies, J. D.; Goldberg, J.; Goodrick, M. J.; Gorn, W.; Granite, D.; Gross, E.; Grunhaus, J.; Hagedorn, H.; Hagemann, J.; Hansroul, M.; Hargrove, C. K.; Harrus, I.; Hart, J.; Hattersley, P. M.; Hauschild, M.; Hawkes, C. M.; Heflin, E.; Hemingway, R. J.; Heuer, R. D.; Hill, J. C.; Hillier, S. J.; Ho, C.; Hobbs, J. D.; Hobson, P. R.; Hochman, D.; Holl, B.; Homer, R. J.; Hou, S. R.; Howarth, C. P.; Hughes-Jones, R. E.; Humbert, R.; Igo-Kemenes, P.; Ihssen, H.; Imrie, D. C.; Janissen, L.; Jawahery, A.; Jeffreys, P. W.; Jeremie, H.; Jimack, M.; Jobes, M.; Jones, R. W. L.; Jovanovic, P.; Karlen, D.; Kawagoe, K.; Kawamoto, T.; Kellogg, R. G.; Kennedy, B. W.; Kleinwort, C.; Klem, D. E.; Knop, G.; Kobayashi, T.; Kokott, T. P.; Köpke, L.; Kowalewski, R.; Kreutzmann, H.; Kroll, J.; Kuwano, M.; Kyberd, P.; Lafferty, G. D.; Lamarche, F.; Larson, W. J.; Layter, J. G.; Le Du, P.; Leblanc, P.; Lee, A. M.; Lehto, M. H.; Lellouch, D.; Lennert, P.; Lessard, L.; Levinson, L.; Lloyd, S. L.; Loebinger, F. K.; Lorah, J. M.; Lorazo, B.; Losty, M. J.; Ludwig, J.; Ma, J.; Macbeth, A. A.; Mannelli, M.; Marcellini, S.; Maringer, G.; Martin, A. J.; Martin, J. P.; Mashino, T.; Mättig, P.; Maur, U.; McMahon, T. J.; McNutt, J. R.; Meijers, F.; Menszner, D.; Merritt, F. S.; Mes, H.; Michelini, A.; Middleton, R. P.; Mikenberg, G.; Mildenberger, J.; Miller, D. J.; Milstene, C.; Minowa, M.; Mohr, W.; Montanari, A.; Mori, T.; Moss, M. W.; Murphy, P. G.; Murray, W. J.; Nellen, B.; Nguyen, H. H.; Nozaki, M.; O'Dowd, A. J. P.; O'Neale, S. W.; O'Neil, B. P.; Oakham, F. G.; Odorici, F.; Ogg, M.; Oh, H.; Oreglia, M. J.; Orito, S.; Pansart, J. P.; Patrick, G. N.; Pawley, S. J.; Pfister, P.; Pilcher, J. E.; Pinfold, J. L.; Plane, D. E.; Poli, B.; Pouladdej, A.; Prebys, E.; Pritchard, T. W.; Quast, G.; Raab, J.; Redmond, M. W.; Rees, D. L.; Regimbald, M.; Riles, K.; Roach, C. M.; Robins, S. A.; Rollnik, A.; Roney, J. M.; Rossberg, S.; Rossi, A. M.; Routenburg, P.; Runge, K.; Runolfsson, O.; Sanghera, S.; Sansum, R. A.; Sasaki, M.; Saunders, B. J.; Schaile, A. D.; Schaile, O.; Schappert, W.; Scharff-Hansen, P.; Schreiber, S.; Schwarz, J.; Shapira, A.; Shen, B. C.; Sherwood, P.; Simon, A.; Singh, P.; Siroli, G. P.; Skuja, A.; Smith, A. M.; Smith, T. J.; Snow, G. A.; Springer, R. W.; Sproston, M.; Stephens, K.; Stier, H. E.; Stroehmer, R.; Strom, D.; Takeda, H.; Takeshita, T.; Thackray, N. J.; Tsukamoto, T.; Turner, M. F.; Tysarczyk-Niemeyer, G.; van den plas, D.; VanDalen, G. J.; Vasseur, G.; Virtue, C. J.; von der Schmitt, H.; von Krogh, J.; Wagner, A.; Wahl, C.; Walker, J. P.; Ward, C. P.; Ward, D. R.; Watkins, P. M.; Watson, A. T.; Watson, N. K.; Weber, M.; Weisz, S.; Wells, P. S.; Wermes, N.; Weymann, M.; Wilson, G. W.; Wilson, J. A.; Wingerter, I.; Winterer, V.-H.; Wood, N. C.; Wotton, S.; Wuensch, B.; Wyatt, T. R.; Yaari, R.; Yang, Y.; Yekutieli, G.; Yoshida, T.; Zeuner, W.; Zorn, G. T.; OPAL Collaboration

    1990-12-01

    From an analysis of multi-hadron events from Z 0 decays, values of the strong coupling constant αs( M2Z 0)=0.131±0.006 (exp)±0.002(theor.) and αs( Mz02) = -0.009+0.007(exp.) -0.002+0.006(theor.) are derived from the energy-energy correlation distribution and its asymmetry, respectively, assuming the QCD renormalization scale μ= MZ0. The theoretical error accounts for differences between O( α2s) calculations. A two parameter fit Λ overlineMS and the renormalization scale μ leads to Λ overlineMS=216±85 MeV and {μ 2}/{s}=0.027±0.013 or to αs( M2Z 0)=0.117 +0.006-0.008(exp.) for the energy-energy correlation distribution. The energy-energy correlation asymmetry distribution is insensitive to a scale change: thus the α s value quoted above for this variable includes the theoretical uncertainty associated with the renormalization scale.

  16. Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kampf, Karol; Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, 18000 Prague; Novotny, Jiri

    2010-06-01

    We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1{sup --} meson self-energy within the resonance chiral theory in the chiral limit using different methods for the description of spin-1 particles, namely, the Proca field, antisymmetric tensor field, and the first-order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent tomore » the power-counting nonrenormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.« less

  17. Renormalizable group field theory beyond melonic diagrams: An example in rank four

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Lahoche, Vincent; Oriti, Daniele

    2017-09-01

    We prove the renormalizability of a gauge-invariant, four-dimensional group field theory (GFT) model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the nonperturbative level, using functional renormalization group methods, and identify a nontrivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4D quantum gravity, thus paving the way to more detailed investigations on them.

  18. A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

    NASA Astrophysics Data System (ADS)

    de Albuquerque, Douglas F.; Fittipaldi, I. P.

    1994-05-01

    A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

  19. Non-Hookean statistical mechanics of clamped graphene ribbons

    NASA Astrophysics Data System (ADS)

    Bowick, Mark J.; Košmrlj, Andrej; Nelson, David R.; Sknepnek, Rastko

    2017-03-01

    Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: Large distance elastic parameters are in fact not constant but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions W ×L (with L ≥W ), the macroscopic bending rigidity κR determined from cantilever deformations is independent of the width when W <ℓth , where ℓth is a thermal length scale, as expected. When W >ℓth , however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on W . When the ribbon length L >ℓp , where ℓp is the W -dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.

  20. 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.

  1. The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

    NASA Astrophysics Data System (ADS)

    Teodorovich, E. V.

    2018-03-01

    In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

  2. Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

    2018-05-01

    We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

  3. 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.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jiao, Yipeng; Liu, Zengyuan; Victora, R. H., E-mail: victora@umn.edu

    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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna; Nihat Berker, A.

    1997-02-01

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

  7. Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

    NASA Astrophysics Data System (ADS)

    Schmitteckert, Peter

    2018-04-01

    We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

  8. Mesons in strong magnetic fields: (I) General analyses

    DOE PAGES

    Hattori, Koichi; Kojo, Toru; Su, Nan

    2016-03-21

    Here, we study properties of neutral and charged mesons in strong magnetic fields |eB| >> Λ 2 QCD with Λ QCD being the QCD renormalization scale. Assuming long-range interactions, we examine magnetic-field dependences of various quantities such as the constituent quark mass, chiral condensate, meson spectra, and meson wavefunctions by analyzing the Schwinger–Dyson and Bethe–Salpeter equations. Based on the density of states obtained from these analyses, we extend the hadron resonance gas (HRG) model to investigate thermodynamics at large B. As B increases the meson energy behaves as a slowly growing function of the meson's transverse momenta, and thus amore » large number of meson states is accommodated in the low energy domain; the density of states at low temperature is proportional to B 2. This extended transverse phase space in the infrared regime significantly enhances the HRG pressure at finite temperature, so that the system reaches the percolation or chiral restoration regime at lower temperature compared to the case without a magnetic field; this simple picture would offer a gauge invariant and intuitive explanation of the inverse magnetic catalysis.« less

  9. Electrons at the monkey saddle: a multicritical Lifshitz point

    NASA Astrophysics Data System (ADS)

    Shtyk, Alex; Goldstein, Garry; Chamon, Claudio

    We consider 2D interacting electrons at a monkey saddle with dispersion px3 - 3pxpy2 . Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em (Bm) 3 / 2 and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K' points, exhibits an interplay of competing many-body instabilities, namely s-wave superconductivity, ferromagnetism, and spin- and charge-density wave. DOE DE-FG02-06ER46316.

  10. Latent instabilities in metallic LaNiO₃ films by strain control of Fermi-surface topology

    DOE PAGES

    Yoo, Hyang Keun; Hyun, Seung Ill; Moreschini, Luca; ...

    2015-03-04

    Strain control is one of the most promising avenues to search for new emergent phenomena in transition metal-oxide films. Here, we investigate the strain-induced changes of electronic structures in strongly correlated LaNiO₃ (LNO) films, using angle-resolved photoemission spectroscopy and the dynamical mean-field theory. The strongly renormalized e g-orbital bands are systematically rearranged by misfit strain to change its fermiology. As tensile strain increases, the hole pocket centered at the A point elongates along the k z-axis and seems to become open, thus changing Fermi-surface (FS) topology from three- to quasi-two-dimensional. Concomitantly, the FS shape becomes flattened to enhance FS nesting.more » A FS superstructure withQ₁ = (1/2,1/2,1/2) appears in all LNO films, while a tensile-strained LNO film has an additional Q₂ = (1/4,1/4,1/4) modulation, indicating that some instabilities are present in metallic LNO films. Charge disproportionation and spin-density-wave fluctuations observed in other nickelates might be their most probable origins« less

  11. 0{nu}{beta}{beta}-decay nuclear matrix elements with self-consistent short-range correlations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Simkovic, Fedor; Bogoliubov Laboratory of Theoretical Physics, JINR, RU-141 980 Dubna, Moscow region; Department of Nuclear Physics, Comenius University, Mlynska dolina F1, SK-842 15 Bratislava

    A self-consistent calculation of nuclear matrix elements of the neutrinoless double-beta decays (0{nu}{beta}{beta}) of {sup 76}Ge, {sup 82}Se, {sup 96}Zr, {sup 100}Mo, {sup 116}Cd, {sup 128}Te, {sup 130}Te, and {sup 136}Xe is presented in the framework of the renormalized quasiparticle random phase approximation (RQRPA) and the standard QRPA. The pairing and residual interactions as well as the two-nucleon short-range correlations are for the first time derived from the same modern realistic nucleon-nucleon potentials, namely, from the charge-dependent Bonn potential (CD-Bonn) and the Argonne V18 potential. In a comparison with the traditional approach of using the Miller-Spencer Jastrow correlations, matrix elementsmore » for the 0{nu}{beta}{beta} decay are obtained that are larger in magnitude. We analyze the differences among various two-nucleon correlations including those of the unitary correlation operator method (UCOM) and quantify the uncertainties in the calculated 0{nu}{beta}{beta}-decay matrix elements.« less

  12. Effects of correlated hybridization in the single-impurity Anderson model

    NASA Astrophysics Data System (ADS)

    Líbero, Valter; Veiga, Rodrigo

    2013-03-01

    The development of new materials often dependents on the theoretical foundations which study the microscopic matter, i.e., the way atoms interact and create distinct configurations. Among the interesting materials, those with partially filled d or f orbitals immersed in nonmagnetic metals have been described by the Anderson model, which takes into account Coulomb correlation (U) when a local level (energy Ed) is doubled occupied, and an electronic hybridization between local levels and conduction band states. In addition, here we include a correlated hybridization term, which depends on the local-level occupation number involved. This term breaks particle-hole symmetry (even when U + 2Ed = 0), enhances charge fluctuations on local levels and as a consequence strongly modifies the crossover between the Hamiltonian fixed-points, even suppressing one or other. We exemplify these behaviors showing data obtained from the Numerical Renormalization Group (NRG) computation for the impurity temperature-dependent specific heat, entropy and magnetic susceptibility. The interleaving procedure is used to recover the continuum spectrum after the NRG-logarithmic discretization of the conduction band. Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP.

  13. Ionic effects on the temperature-force phase diagram of DNA.

    PubMed

    Amnuanpol, Sitichoke

    2017-12-01

    Double-stranded DNA (dsDNA) undergoes a structural transition to single-stranded DNA (ssDNA) in many biologically important processes such as replication and transcription. This strand separation arises in response either to thermal fluctuations or to external forces. The roles of ions are twofold, shortening the range of the interstrand potential and renormalizing the DNA elastic modulus. The dsDNA-to-ssDNA transition is studied on the basis that dsDNA is regarded as a bound state while ssDNA is regarded as an unbound state. The ground state energy of DNA is obtained by mapping the statistical mechanics problem to the imaginary time quantum mechanics problem. In the temperature-force phase diagram the critical force F c (T) increases logarithmically with the Na + concentration in the range from 32 to 110 mM. Discussing this logarithmic dependence of F c (T) within the framework of polyelectrolyte theory, it inevitably suggests a constraint on the difference between the interstrand separation and the length per unit charge during the dsDNA-to-ssDNA transition.

  14. Universal dual amplitudes and asymptotic expansions for gg→ H and H→ γ γ in four dimensions

    NASA Astrophysics Data System (ADS)

    Driencourt-Mangin, Félix; Rodrigo, Germán; Sborlini, Germán F. R.

    2018-03-01

    Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.

  15. Fast-timing study of the l -forbidden 1 /2+→3 /2+ M 1 transition in 129Sn

    NASA Astrophysics Data System (ADS)

    Licǎ, R.; Mach, H.; Fraile, L. M.; Gargano, A.; Borge, M. J. G.; Mǎrginean, N.; Sotty, C. O.; Vedia, V.; Andreyev, A. N.; Benzoni, G.; Bomans, P.; Borcea, R.; Coraggio, L.; Costache, C.; De Witte, H.; Flavigny, F.; Fynbo, H.; Gaffney, L. P.; Greenlees, P. T.; Harkness-Brennan, L. J.; Huyse, M.; Ibáñez, P.; Judson, D. S.; Konki, J.; Korgul, A.; Kröll, T.; Kurcewicz, J.; Lalkovski, S.; Lazarus, I.; Lund, M. V.; Madurga, M.; Mǎrginean, R.; Marroquín, I.; Mihai, C.; Mihai, R. E.; Morales, A. I.; Nácher, E.; Negret, A.; Page, R. D.; Pakarinen, J.; Pascu, S.; Paziy, V.; Perea, A.; Pérez-Liva, M.; Picado, E.; Pucknell, V.; Rapisarda, E.; Rahkila, P.; Rotaru, F.; Swartz, J. A.; Tengblad, O.; Van Duppen, P.; Vidal, M.; Wadsworth, R.; Walters, W. B.; Warr, N.; IDS Collaboration

    2016-04-01

    The levels in 129Sn populated from the β- decay of 129In isomers were investigated at the ISOLDE facility of CERN using the newly commissioned ISOLDE Decay Station (IDS). The lowest 1 /2+ state and the 3 /2+ ground state in 129Sn are expected to have configurations dominated by the neutron s1 /2 (l =0 ) and d3 /2 (l =2 ) single-particle states, respectively. Consequently, these states should be connected by a somewhat slow l -forbidden M 1 transition. Using fast-timing spectroscopy we have measured the half-life of the 1 /2+ 315.3-keV state, T1 /2= 19(10) ps, which corresponds to a moderately fast M 1 transition. Shell-model calculations using the CD-Bonn effective interaction, with standard effective charges and g factors, predict a 4-ns half-life for this level. We can reconcile the shell-model calculations to the measured T1 /2 value by the renormalization of the M 1 effective operator for neutron holes.

  16. Reply to "Comment on `Conductance scaling in Kondo-correlated quantum dots: Role of level asymmetry and charging energy'"

    NASA Astrophysics Data System (ADS)

    Merker, L.; Kirchner, S.; Muñoz, E.; Costi, T. A.

    2014-08-01

    The Comment of A. A. Aligia claims that the superperturbation theory (SPT) approach [E. Muñoz, C. J. Bolech, and S. Kirchner, Phys. Rev. Lett. 110, 016601 (2013), 10.1103/PhysRevLett.110.016601] formulated using dual fermions [A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77, 033101 (2008), 10.1103/PhysRevB.77.033101] and used by us to compare with numerical renormalization group (NRG) results for the conductance [L. Merker, S. Kirchner, E. Muñoz, and T. A. Costi, Phys. Rev. B 87, 165132 (2013), 10.1103/PhysRevB.87.165132], fails to correctly extend the results of the symmetric Anderson impurity model (SIAM) for general values of the local level Ed in the Kondo regime. We answer this criticism. We also compare new NRG results for cB, with cB calculated directly from the low-field conductance, with new higher-order SPT calculations for this quantity, finding excellent agreement for all Ed and for U /πΔ extending into the strong coupling regime.

  17. Optical conductivity of an interacting Weyl liquid in the collisionless regime

    NASA Astrophysics Data System (ADS)

    Roy, Bitan; Juričić, Vladimir

    2017-10-01

    Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed-matter systems. We show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal σ (Ω ) =σ0(Ω ) [1 +1/N +1 ] , where σ0(Ω ) =N e02Ω /(12 h v ) is the OC in the noninteracting system, with v as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency Ω , and e0 is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes near the Fermi level (N ), is a remarkable consequence of an intriguing conspiracy among the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction, and violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl as well as Dirac materials. By contrast, a local density-density interaction produces a nonuniversal correction to the OC, stemming from the nonrenormalizable nature of the corresponding interacting field theory.

  18. Transverse Densities of Octet Baryons from Chiral Effective Field Theory

    DOE PAGES

    Alarcón, Jose Manuel; Hiller Blin, Astrid N.; Weiss, Christian

    2017-03-24

    Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. In this paper, we calculate the transverse densities of the octet baryons at peripheral distances b=O(M π -1) in an approach that combines chiral effective field theory (χχEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t>4Mmore » $$2\\atop{π}$$ are computed using relativistic χEFT with octet and decuplet baryons in the extended on-mass-shell renormalization scheme. The calculations are extended into the ρ-meson mass region using a dispersive method that incorporates the timelike pion form-factor data. The approach allows us to construct densities at distances b>1 fm with controlled uncertainties. Finally, our results provide insight into the peripheral structure of nucleons and hyperons and can be compared with empirical densities and lattice-QCD calculations.« less

  19. Baby de Sitter black holes and dS3/CFT2

    NASA Astrophysics Data System (ADS)

    de Buyl, Sophie; Detournay, Stéphane; Giribet, Gaston; Ng, Gim Seng

    2014-02-01

    Unlike three-dimensional Einstein gravity, three-dimensional massive gravity admits asymptotically de Sitter space (dS) black hole solutions. These black holes present interesting features and provide us with toy models to study the dS/CFT correspondence. A remarkable property of these black holes is that they are always in thermal equilibrium with the cosmological horizon of the space that hosts them. This invites us to study the thermodynamics of these solutions within the context of dS/CFT. We study the asymptotic symmetry group of the theory and find that it indeed coincides with the local two-dimensional conformal algebra. The charge algebra associated to the asymptotic Killing vectors consists of two copies of the Virasoro algebra with non-vanishing central extension. We compute the mass and angular momentum of the dS black holes and verify that a naive application of Cardy's formula exactly reproduces the entropy of both the black hole and the cosmological horizon. By adapting the holographic renormalization techniques to the case of dS space, we define the boundary stress tensor of the dual Euclidean conformal field theory.

  20. Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions.

    PubMed

    Rançon, A; Kodio, O; Dupuis, N; Lecheminant, P

    2013-07-01

    We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T(3)/c(2))F(N)(Δ/T), where c is the velocity of the excitations at the QCP and |Δ| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F(N). For small values of N (N/~1) regimes, but fails to describe the nonmonotonic behavior of F(N) in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T(BKT)/ρ(s)(0) is very close to π/2, implying that the stiffness ρ(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ρ(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.

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