Fighting the sign problem in a chiral random matrix model with contour deformations

TL;DR

This paper explores contour deformation techniques in chiral random matrix theory to significantly reduce the finite-density sign problem, demonstrating exponential improvements through parameter optimization and comparisons with holomorphic flow methods.

Contribution

It introduces optimized contour deformations in chiral random matrix models, achieving exponential mitigation of the sign problem and comparing different deformation strategies.

Findings

Optimization of a single parameter greatly reduces the sign problem.

The improvement scales exponentially with matrix size.

Contour deformations from holomorphic flow are also effective.

Abstract

We studied integration contour deformations in the chiral random matrix theory of Stephanov with the goal of alleviating the finite-density sign problem. We considered simple ans\"atze for the deformed integration contours, and optimized their parameters. We find that optimization of a single parameter manages to considerably improve on the severity of the sign problem. We show numerical evidence that the improvement achieved is exponential in the degrees of freedom of the system, i.e., the size of the random matrix. We also compare the optimization method with contour deformations coming from the holomorphic flow equations.