Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory

TL;DR

This paper investigates the spectral properties of the SU(3) Dirac operator on the lattice, demonstrating a transition from random matrix theory predictions to chiral perturbation theory at a specific energy scale, and analyzing volume dependence.

Contribution

It provides a comprehensive spectral analysis of the lattice Dirac operator, connecting random matrix theory with chiral perturbation theory and exploring the Thouless energy scale.

Findings

Agreement with chiral random matrix theory up to the Thouless energy

Identification of anomalous volume dependence in connected susceptibility

Development of a model describing data beyond the Thouless energy

Abstract

We calculate complete spectra of the Kogut-Susskind Dirac operator on the lattice in quenched SU(3) gauge theory for various values of coupling constant and lattice size. From these spectra we compute the connected and disconnected scalar susceptibilities and find agreement with chiral random matrix theory up to a certain energy scale, the Thouless energy. The dependence of this scale on the lattice volume is analyzed. In the case of the connected susceptibility this dependence is anomalous, and we explain the reason for this. We present a model of chiral perturbation theory that is capable of describing the data beyond the Thouless energy and that has a common range of applicability with chiral random matrix theory.