Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

TL;DR

This study investigates how the low-lying Dirac eigenvalues and chiral condensate behave near the confinement-deconfinement transition in quenched SU(2) lattice gauge theory at finite temperature, revealing universal and non-universal spectral features.

Contribution

It provides the first detailed analysis of the Dirac spectrum and chiral condensate behavior across the phase transition in quenched SU(2) lattice gauge theory, highlighting the change from universal to non-universal eigenvalue distributions.

Findings

Chiral condensate drops rapidly at T=Tc but does not vanish.

Eigenvalue distributions are universal below Tc, described by chiral orthogonal ensemble.

Above Tc, eigenvalue spectra are better modeled by a dilute instanton-anti-instanton gas.

Abstract

The spectrum of low-lying eigenvalues of overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T = Tc, though not going to zero. At Tc' = 1.5 Tc = 480 MeV the chiral condensate decreases rapidly one again and becomes either very small or zero. At T < Tc the distributions of small eigenvalues are universal and are well described by chiral orthogonal ensemble of random matrices. In the temperature range above Tc where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton - anti-instanton gas.