Correlated Dirac eigenvalues around the transition temperature on $N_{\ddot{I}}„=8$ 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 $N_{\ddot{I}}„=8$ 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 $m_{\ddot{I}}€=110$ MeV. We find that in contrast to the case at $T\simeq 205$ MeV $m_l^{-1}\partial \ddot{I}(\hat{I}»,m_l)/\partial m_l$ is no longer equal to ${\partial }^2\ddot{I}(\hat{I}»,m_l)/\partial m_l^2$ and ${\partial }^2\ddot{I}(\hat{I}»,m_l)/\partial m_l^2$ even becomes negative at certain low temperatures. This means that as temperature getting closer to $T_c$ $\ddot{I}(\hat{I}»,m_l)$ 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 $\partial \ddot{I}(\hat{I}»,m_l)/\partial m_l$ and ${\partial }^2\ddot{I}(\hat{I}»,m_l)/\partial m_l^2$ at $T\in [137,153]$ MeV, and then we propose a feasible method to estimate the power $c$ given $\ddot{I}\propto m_l^c$.

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