Eigenvalue Distributions of the QCD Dirac Operator

TL;DR

This paper uses Monte Carlo simulations to analyze the distributions of the smallest eigenvalues of the QCD Dirac operator, confirming analytical predictions with high precision for both massless and massive quarks in SU(3) gauge theory.

Contribution

It provides the first detailed numerical verification of analytical eigenvalue distribution predictions for the QCD Dirac operator in SU(3) gauge theory with dynamical fermions.

Findings

Excellent agreement between Monte Carlo results and analytical predictions

Precise extraction of microscopic spectral density for SU(3) with dynamical fermions

Validation of spectral density formulas for different quark masses

Abstract

We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge theory with staggered fermions. Very precise agreement is found in all cases. As a simple by-product we also extract the microscopic spectral density of the Dirac operator in SU(3) gauge theory with dynamical massive fermions for $N_f=1$ and 2, and obtain high-accuracy agreement with analytical expressions.