Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory

TL;DR

This study confirms the correspondence between the low-lying eigenvalues of the QCD Dirac operator and chiral Random Matrix Theory in the epsilon-regime using two-flavor lattice QCD with overlap fermions, and extracts the chiral condensate.

Contribution

First lattice QCD simulation including sea quarks in the epsilon-regime that confirms the Dirac spectrum's agreement with ChRMT and extracts the chiral condensate.

Findings

Good agreement between lattice eigenvalues and ChRMT predictions.

Extracted chiral condensate value consistent with epsilon-regime estimates.

Reasonable spectral agreement even for heavier sea quarks without epsilon expansion.

Abstract

The low-lying eigenvalue spectrum of the QCD Dirac operator in the epsilon-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 \sim 3 MeV on a 16^3\times 32 lattice at a lattice spacing a \simeq 0.11 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, \Sigma(2 GeV)[MSbar] = [251(7)(11) MeV]^3, where errors represent statistical and higher order effects in the epsilon expansion. We also calculate the eigenvalue distributions on the lattices with heavier sea quarks at two lattice spacings. Although the epsilon expansion is not applied for those sea quarks, we find a reasonable agreement of the Dirac operator spectrum with ChRMT. The value of Sigma, after extrapolating to the chiral limit, is consistent with the estimate in the epsilon-regime.