Two-flavor lattice QCD in theϵregime and chiral random matrix theory

The low-lying eigenvalue spectrum of the QCD Dirac operator in the $ϵ$ regime is expected to match with that of chiral random matrix theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor QCD simulations on the lattice. Using the overlap fermion formulation, which preserves exact chiral symmetry at finite lattice spacings, we push the sea quark mass down to ~3 MeV on a 16³×32 lattice at a lattice spacing a0.11 fm. We compare the low-lying eigenvalue distributions and find a good agreement with the analytical predictions of ChRMT. By matching the lowest-lying eigenvalue we extract the chiral condensate, ΣMS̄(2 GeV)=(251±7±11 MeV)³, where errors represent statistical and higher order effects in the $ϵ$ expansion. We also calculate the eigenvalue distributions on the lattices with heavier sea quarks at two lattice spacings. Although the $ϵ$ expansion is not applied for those sea quarks, we find a reasonable agreement of the Dirac operator spectrum with ChRMT. The value of Σ, after extrapolating to the chiral limit, is consistent with the estimate in the $ϵ$ regime.