Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit

TL;DR

This study investigates the eigenvalues of the QCD Dirac matrix with improved staggered quarks near the chiral transition, revealing persistent spectral features and partial symmetry restoration in the continuum limit.

Contribution

It provides the first continuum extrapolation of the eigenvalue spectrum of the HISQ Dirac operator near the QCD transition, highlighting the behavior of the $U_A(1)$ symmetry.

Findings

No gap opens in the infrared eigenvalue density after continuum extrapolation.

A peak persists in the eigenvalue spectrum, linked to instanton effects.

Partial restoration of the $U_A(1)$ symmetry is observed, not simultaneous with non-singlet chiral symmetry.

Abstract

We calculate the eigenmodes of the Highly Improved Staggered Quark (HISQ) matrix near the chiral crossover transition in QCD with $2+1$ flavors with the aim to gain more insights into its temperature dependence. On performing the continuum extrapolation, we do not observe any gap opening up in the infrared part of the eigenvalue density of the QCD Dirac operator; instead we observe a peak. The existence of the peak and oscillations of the infrared eigenmodes can be understood in terms of an interacting ensemble of instantons. From the properties of the continuum extrapolated eigenspectrum we further show that the anomalous $U_A(1)$ part of the chiral symmetry is not effectively restored simultaneously along with its non-singlet counterpart. We provide an explanation for this observation, further showing interesting connections between the anomalous $U_A(1)$ restoration and the change in the infrared part of the eigenvalue distribution.