Speaker
Summary
We utilize eigenvalue filtering technique combined with the stochastic estimate of the mode number to determine the low-lying eigenvalue spectrum of the Dirac operator. Simulations are performed with (2 + 1)-flavor QCD using the Highly Improved Staggered Quarks (HISQ/tree) action on $N_{\tau}$ = 8 and 12 lattices with aspect ratios $N_{\sigma}/N_{\tau}$ ranging from 5 to 7. In our simulations the strange quark mass is fixed to its physical value $m_{s}^{phy}$, and the light quark masses $m_{l}$ are varied from $m_{s}^{phy}/40$ to $m_{s}^{phy}/160$ which correspond to pion mass $m_{\pi}$ ranging from 110 MeV to 55 MeV in the continuum limit. We calculate the chiral condensate, the disconnected chiral susceptibility, and $\chi_{\pi} - \chi_{\delta}$ from the eigenvalue spectrum via Banks-Casher relations. We compare these results with those obtained from a direct calculation of the observables which involves inversions of the fermion matrix using the stochastic "noise vector" method. We find that these approaches yield consistent results. Furthermore, we also investigate the quark mass and temperature dependences of the Dirac eigenvalue density at zero eigenvalue.
