Eigenvalue Density of the non-Hermitian Wilson Dirac Operator

TL;DR

This paper analyzes how the eigenvalue density of the non-Hermitian Wilson Dirac operator varies with lattice spacing using random matrix theory, providing detailed spectral densities and counts of real modes.

Contribution

It introduces an analytical framework for the eigenvalue density dependence on lattice spacing, including densities of complex and real eigenvalues and counts of real modes.

Findings

Eigenvalue density depends on lattice spacing.

Explicit formulas for real and complex eigenvalue densities.

Analytical expression for the number of real modes.

Abstract

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.