Random Matrix Theory and the Spectra of Overlap Fermions

TL;DR

This paper applies Random Matrix Theory to predict the eigenvalue distributions of the Dirac operator in QCD and confirms these predictions through lattice simulations with overlap fermions, especially for the smallest eigenvalues in sufficiently large volumes.

Contribution

It demonstrates the agreement between Random Matrix Theory predictions and lattice QCD measurements of Dirac spectra using overlap fermions for various topological charges.

Findings

Predicted eigenvalue distributions match measured spectra for large volumes.

Agreement observed primarily for the first non-zero eigenvalue.

Results support the universality of spectral properties in QCD.

Abstract

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at topological charge \nu = 0, +- 1 and +- 2, and found agreement with those predictions - at least for the first non-zero eigenvalue - if the volume exceeds about (1.2 fm)^4.