Low-lying Dirac operator eigenvalues, lattice effects and random matrix theory

TL;DR

This paper compares lattice QCD eigenvalue data for Wilson and staggered fermions with extended random matrix theory predictions, showing Wilson data aligns well and taste breaking effects vanish in the continuum limit for staggered fermions.

Contribution

It provides the first detailed comparison of lattice eigenvalues with RMT predictions including lattice effects for both Wilson and staggered fermions.

Findings

Wilson RMT describes Wilson data well

Taste breaking effects diminish in the continuum limit for staggered fermions

Eigenvalue distributions match RMT predictions with lattice effects included

Abstract

Recently, random matrix theory predictions for the distribution of low-lying Dirac operator eigenvalues have been extended to include lattice effects for both staggered and Wilson fermions. We computed low-lying eigenvalues for the Hermitian Wilson-Dirac operator and for improved staggered fermions on several quenched ensembles with size $\approx 1.5$ fm. Comparisons to the expectations from RMT with lattice effects included are made. Wilson RMT describes our Wilson data nicely. For improved staggered fermions we find strong indications that taste breaking effects on the low-lying spectrum disappear in the continuum limit, as expected from staggered RMT.