Stability of lattice QCD simulations and the thermodynamic limit

TL;DR

This paper investigates how the spectral gap of the Wilson--Dirac operator in two-flavour lattice QCD depends on lattice parameters, showing that simulations are safe from zero modes in large volumes.

Contribution

It provides a detailed analysis of the spectral gap's dependence on lattice spacing, volume, and quark mass, ensuring the stability of lattice QCD simulations.

Findings

Spectral gap median scales with quark mass m

Width of the gap distribution is proportional to a/√V

Simulations are safe from zero modes at large volume

Abstract

We study the spectral gap of the Wilson--Dirac operator in two-flavour lattice QCD as a function of the lattice spacing $a$, the space-time volume $V$ and the current-quark mass $m$. It turns out that the median of the probability distribution of the gap scales proportionally to $m$ and that its width is practically equal to $a/\sqrt{V}$. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD.