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

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.

v2: Version to be published in Phys. Rev. D

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Cited by in corpus (5)

• The chiral phase transition and the axial anomaly
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature