Spectral Properties of the Overlap Dirac Operator in QCD

TL;DR

This paper investigates the eigenvalue distribution of the overlap Dirac operator in quenched QCD, comparing results with random matrix theory predictions and analyzing topological sectors across different lattice sizes and couplings.

Contribution

It provides a detailed comparison of the spectral properties of the overlap Dirac operator with random matrix theory, highlighting volume and topological effects in quenched QCD.

Findings

Eigenvalue distributions agree with random matrix theory for volumes > (1.2 fm)^4

Unfolded level spacing distribution matches the random matrix conjecture across all volumes studied

Topological sector distinctions are evident in eigenvalue distributions

Abstract

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.