Random matrix analysis of the QCD sign problem

TL;DR

This paper uses random matrix theory to analyze the severity of the QCD sign problem, revealing that higher topological charge reduces the problem's severity, with analytical results confirmed by simulations.

Contribution

It provides a novel analytical approach to quantify the sign problem in QCD using random matrix theory, especially its dependence on topology.

Findings

Sign problem becomes milder with increasing topological charge.

Analytic predictions match numerical simulations.

Provides insights into the sign problem's behavior at nonzero baryon density.

Abstract

The severity of the sign problem in lattice QCD at nonzero baryon density is measured by the average phase of the fermion determinant. Motivated by the equivalence of chiral random matrix theory and QCD to leading order in the epsilon regime, we compute the phase of the fermion determinant for general topology in random matrix theory as a function of the quark chemical potential and the quark mass. We find that the sign problem becomes milder with increasing topological charge. The analytic predictions are verified by detailed numerical random matrix simulations.