Absence of correlations in the QCD Dirac spectrum at high temperature

TL;DR

This paper introduces a simple model for the distribution of small eigenvalues of the QCD Dirac operator at high temperature, showing that spectral correlations are negligible when chiral symmetry is restored, with results matching lattice data.

Contribution

It presents an analytic model assuming no correlations in the low-lying spectrum of the QCD Dirac operator at high temperature, validated by lattice simulation data.

Findings

Good agreement between the model and lattice data

Spectral correlations are negligible in the high-temperature phase

Spectral properties are determined solely by the spectral density

Abstract

I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the absence of correlations between different regions of the low lying spectrum I derive analytic formulas for the distribution of the first two eigenvalues. I find good agreement with data obtained using the overlap Dirac operator in quenched SU(2) lattice simulations. This suggests that if chiral symmetry is restored spectral correlations are not important and all the statistical properties of the spectrum are encoded in the spectral density.