Dirac Eigenvalue spectrum of $N_f$=2+1 QCD towards the chiral limit using HISQ fermions

Abstract

We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number to determine the eigenvalue spectrum. Simulations of (2 + 1)-flavor QCD are performed using the Highly Improved Staggered Quarks (HISQ/tree) action on $N_{\tau }$ = 8 lattices with aspect ratios $N_{\sigma }/N_{\tau }$ ranging from 5 to 7. The strange quark mass is fixed to its physical value $m_s^{\mathrm{phy}}$, and the light quark masses $m_l$ are varied from $m_s^{\mathrm{phy}}/40$ to $m_s^{\mathrm{phy}}/160$ which correspond to pion mass $m_{\pi }$ ranging from 110 MeV to 55 MeV in the continuum limit. We compute the chiral condensate and ${\chi }_{\pi }-{\chi }_{\delta }$ through the eigenvalue spectrum obtained from the the eigenvalue filtering method. 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 eigenvalues to gain more insights about the $U_A(1)$ symmetry breaking in QCD.

arXiv comment7 pages, 4 figures. Contribution to the 37th International Symposium on Lattice Field Theory - Lattice2019, 16-22 June 2019, Wuhan, China

References in corpus (5)

• The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions
• Meson Screening Masses in (2+1)-Flavor QCD
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• New approach to the Dirac spectral density in lattice gauge theory applications
• Stochastic calculation of the QCD Dirac operator spectrum with Mobius domain-wall fermion