Correlated Dirac eigenvalues around the transition temperature on $N_{\tau }=8$ lattices

Abstract

We investigate the criticality of chiral phase transition manifested in the first and second order derivatives of Dirac eigenvalue spectrum with respect to light quark mass in (2+1)-flavor lattice QCD. Simulations are performed at temperatures from about 137 MeV to 176 MeV on $N_{\tau }=8$ lattices using the highly improved staggered quarks and the tree-level improved Symanzik gauge action. The strange quark mass is fixed to its physical value $m_s^{\text{phy}}$ and the light quark mass is set to $m_s^{\text{phy}}/40$ which corresponds to a Goldstone pion mass $m_{\pi }=110$ MeV. We find that in contrast to the case at $T\simeq 205$ MeV $m_l^{-1}\partial \rho (\lambda ,m_l)/\partial m_l$ is no longer equal to ${\partial }^2\rho (\lambda ,m_l)/\partial m_l^2$ and ${\partial }^2\rho (\lambda ,m_l)/\partial m_l^2$ even becomes negative at certain low temperatures. This means that as temperature getting closer to $T_c$ $\rho (\lambda ,m_l)$ is no longer proportional to $m_l^2$ and thus dilute instanton gas approximation is not valid for these temperatures. We demonstrate the temperature dependence can be factored out in $\partial \rho (\lambda ,m_l)/\partial m_l$ and ${\partial }^2\rho (\lambda ,m_l)/\partial m_l^2$ at $T\in [137,153]$ MeV, and then we propose a feasible method to estimate the power $c$ given $\rho \propto m_l^c$.

arXiv commentTalk presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021, 26th-30th, July, 2021, Zoom/Gather@Massachusetts Institute of Technology

References in corpus (6)

• Chiral crossover in QCD at zero and non-zero chemical potentials
• The QCD crossover at finite chemical potential from lattice simulations
• Chiral phase transition temperature in (2+1)-Flavor QCD
• On the magnetic equation of state in (2+1)-flavor QCD
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD

Cited by in corpus (3)

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• Microscopic Encoding of Macroscopic Universality in QCD Chiral Phase Transition