Overlap Dirac operator at nonzero chemical potential and random matrix theory

TL;DR

This paper introduces a way to incorporate chemical potential into the overlap Dirac operator, preserving key properties and matching predictions from nonhermitian chiral random matrix theory.

Contribution

It presents a novel formulation of the overlap Dirac operator at nonzero chemical potential that maintains zero modes and aligns with random matrix theory predictions.

Findings

Spectral density matches analytical predictions for small eigenvalues.

Operator satisfies Ginsparg-Wilson relation with exact zero modes.

Eigenvalues occur in pairs despite loss of gamma_5-hermiticity.

Abstract

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of nonhermitian chiral random matrix theory for both trivial and nontrivial topology.