Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks

TL;DR

This paper investigates the relationship between chiral symmetry breaking and the Dirac operator spectrum in lattice QCD with Wilson quarks, demonstrating that low quark modes condense as expected and enabling calculation of the chiral condensate.

Contribution

It shows that the Banks--Casher relation holds in Wilson lattice QCD and introduces a method to compute the chiral condensate by counting low modes.

Findings

Low quark modes condense in two-flavour QCD.

The chiral condensate can be accurately computed from low mode counting.

Spectral observables are renormalizable and useful in Wilson lattice QCD.

Abstract

The Banks--Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in a given energy interval are renormalizable and can therefore be computed using the Wilson formulation of lattice QCD even though the latter violates chiral symmetry at energies on the order of the inverse lattice spacing. Using numerical simulations, we find (in two-flavour QCD) that the low quark modes do condense in the expected way. In particular, the chiral condensate can be accurately calculated simply by counting the low modes on large lattices. Other spectral observables can be considered as well and have a potentially wide range of uses.