Dirac eigenvalues and eigenvectors at finite temperature

TL;DR

This paper studies the spectral properties and localization of Dirac eigenvalues and eigenvectors near the chiral phase transition in quenched SU(3) lattice gauge theory, revealing phase-dependent behaviors and deviations from random matrix theory.

Contribution

It provides a detailed analysis of how Dirac eigenvalues and eigenvectors behave across the phase transition, including the dependence on the Polyakov loop's $Z_3$-phase and the breakdown of random matrix theory descriptions.

Findings

Bulk correlations follow random matrix theory in the chirally symmetric phase.

Low-lying eigenvalues depend on the $Z_3$-phase of the Polyakov loop.

Localization properties vary across different $Z_3$-phases.

Abstract

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.