Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature

TL;DR

This study investigates the spectral properties of the staggered Dirac operator in finite-temperature QCD, revealing a phase transition characterized by a gap opening and localization phenomena of eigenstates.

Contribution

It provides new insights into the behavior of eigenvalues and eigenvectors across the QCD phase transition, especially regarding localization mechanisms and finite-volume effects.

Findings

A spectral gap opens at the phase transition.

Eigenvectors are extended at low temperature and localized at high temperature.

Localization occurs via Mott's mechanism, but the gap scales to zero with increasing volume.

Abstract

We examine the eigenvalues and eigenvectors of the staggered Dirac operator on thermal ensembles created in QCD with two flavours of staggered quarks. We see that across the phase transition a gap opens in the spectrum. For finite volume lattices in the low-temperature phase the eigenvectors are extended, but generic field configurations in the high temperature phase give rise to localized eigenstates. We examine measures of the stability of such localization and find that at finite volumes localization occurs through Mott's mechanism of the formation of mobility edges. However, the band gap between the localized and extended states seem to scale to zero in the limit of large volume.