Effects of dynamical quarks on the spectrum of the Wilson Dirac operator

TL;DR

This paper investigates how dynamical quarks influence the microscopic spectral properties of the Wilson Dirac operator using effective field theory, revealing a mild sign problem and spectral density behavior.

Contribution

It provides a detailed analysis of the spectral distributions of the Wilson Dirac operator with dynamical quarks, including the case of one flavor, highlighting differences from the quenched approximation.

Findings

Dynamical quarks induce a mild sign problem.

Spectral density becomes non-positive as the gap closes.

Detailed spectral distribution for one flavor case.

Abstract

Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real modes of the Wilson Dirac operator as well as the spectrum of the Hermitian Wilson Dirac operator, and work out the case of one flavor in all detail. In contrast to the quenched case, the theory has a mild sign problem that manifests itself by giving a spectral density that is not positive definite as the spectral gap closes.