Two-Flavor Lattice-QCD Simulation in theϵRegime with Exact Chiral Symmetry

Abstract

We perform lattice simulations of two-flavor QCD using Neuberger's overlap fermion, with which the exact chiral symmetry is realized at finite lattice spacings. The $ϵ$ regime is reached by decreasing the light quark mass down to 3 MeV on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice with a lattice spacing $\ensuremath{\sim}0.11\text{ }\text{ }\mathrm{fm}$. We find a good agreement of the low-lying Dirac eigenvalue spectrum with the analytical predictions of the chiral random matrix theory, which reduces to the chiral perturbation theory in the $ϵ$ regime. The chiral condensate is extracted as ${\ensuremath{\Sigma}}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=(251\ifmmode\pm\else\textpm\fi{}7\ifmmode\pm\else\textpm\fi{}11\text{ }\text{ }\mathrm{MeV}{)}^{3}$, where the errors are statistical and an estimate of the higher order effects in the $ϵ$ expansion.