Poisson statistics in the high temperature QCD Dirac spectrum

TL;DR

This study investigates the eigenvalue statistics of the Dirac operator in high-temperature QCD with physical quark masses, revealing a transition from Poisson to Random Matrix behavior linked to eigenmode localization.

Contribution

It demonstrates the Poisson to Random Matrix transition in the Dirac spectrum of dynamical QCD, extending previous quenched results to realistic quark masses.

Findings

Eigenmodes at the low end are localized and follow Poisson statistics.

Delocalized eigenmodes obey Random Matrix statistics.

Transition observed in the spectrum similar to quenched SU(2) theory.

Abstract

We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the Dirac spectrum with the predictions of Random Matrix Theory for this universality class and with Poisson statistics. We show that at the low end of the spectrum the eigenmodes are localized and obey Poisson statistics. Above a boundary region the eigenmodes become delocalized and obey Random Matrix statistics. Thus the QCD Dirac spectrum with physical dynamical quarks also has the Poisson to Random Matrix transition previously seen in the quenched SU(2) theory.