Poisson to Random Matrix Transition in the QCD Dirac Spectrum

Abstract

At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes drastically when the system is driven through the finite temperature cross-over. The lowest Dirac modes that are delocalized at low temperature become localized on the scale of the inverse temperature. At the same time the spectral statistics changes from random matrix to Poisson statistics. We demonstrate this with lattice QCD simulations using 2+1 flavors of light dynamical quarks with physical masses. Drawing an analogy with Anderson transitions we also examine the mobility edge separating localized and delocalized modes in the spectrum. We show that it scales in the continuum limit and increases sharply with the temperature.

10 pages, 9 eps figures, a few references added and typos corrected

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Cited by in corpus (27)

• Universality and the QCD Anderson Transition
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• The localization transition in SU(3) gauge theory
• An Ising-Anderson model of localisation in high-temperature QCD
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Anderson Metal-to-Critical Transition in QCD
• Localization with overlap fermions
• Anderson localization in QCD-like theories
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Features of a 2d Gauge Theory with Vanishing Chiral Condensate
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Quark localization in QCD above $T_c$
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition
• Chiral transition, eigenmode localisation and Anderson-like models
• Landau Levels in Lattice QCD