Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD

Abstract

The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors, concerning the density of low modes and their localization properties, are qualitatively reproduced by a toy-model random Hamiltonian, based on an Ising-type spin model mimicking the dynamics of the Polyakov lines. Here we study the low modes of this toy model in the vicinity of the ordering transition of the spin model, and show that at the critical point the spectral density at the origin has a singularity, and the localization properties of the lowest modes change. This provides further evidence of the close relation between deconfinement, chiral transition and localization of the low modes.

arXiv comment11 pages, 7 figures

References in corpus (28)

• The QCD equation of state with dynamical quarks
• Random Matrix Theory and Chiral Symmetry in QCD
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• Ising Universality in Three Dimensions: A Monte Carlo Study
• The equation of state in lattice QCD: with physical quark masses towards the continuum limit
• Constrained Curve Fitting
• Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory with Adjoint Fermions
• The Chiral Critical Point in 3-Flavour QCD
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Evidence of effective axial U(1) symmetry restoration at high temperature QCD
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• Universality and the QCD Anderson Transition
• Absence of correlations in the QCD Dirac spectrum at high temperature
• Microscopic universality with dynamical fermions
• Anderson localization through Polyakov loops: lattice evidence and Random matrix model
• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Calorons and localization of quark eigenvectors in lattice QCD
• An Ising-Anderson model of localisation in high-temperature QCD
• Anderson Localization in high temperature QCD: background configuration properties and Dirac eigenmodes
• Deconfinement, chiral transition and localisation in a QCD-like model
• Localization properties of fermions and bosons
• An Anderson-like model of the QCD chiral transition
• Anderson localization in QCD-like theories
• Quark localization in QCD above $T_c$

Cited by in corpus (8)

• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition