Eigenmodes of the Dirac Operator and Chiral Properties of QCD with Sea Quarks

Abstract

I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the eigenvalues $λ_i$ should behave as $z(i)/V$ for large volume $V$, where $z(i)$ is the i-th zero of the Bessel function. With neither chiral nor $λ$ extrapolation, one can precisely calculate the chiral condensate using only a small set of eigenvalues. Therefore, it is economical and free of systematic uncertainties. I present the first QCD data to support this mechanism and encourage the lattice community to test and use it.