We calculate the eigenmodes of the highly improved staggered quark 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 nonsinglet 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.

• Received 16 March 2023
• Accepted 26 September 2023

DOI:https://doi.org/10.1103/PhysRevD.108.094501

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Published by the American Physical Society