Evading the sign problem in random matrix simulations

TL;DR

This paper presents a method to circumvent the sign problem in random matrix simulations at nonzero chemical potential by creating subsets of matrices with positive weights, enabling efficient importance sampling.

Contribution

It introduces a subset construction technique that ensures positive weights, allowing Monte Carlo simulations without the sign problem in random matrix models.

Findings

Statistical error is independent of chemical potential.

Error grows linearly with matrix dimension.

Method outperforms reweighting in handling the sign problem.

Abstract

In this talk we show how the sign problem, occurring in dynamical simulations of random matrices at nonzero chemical potential, can be avoided by judiciously combining matrices into subsets. One can prove that these subsets have real and positive weights such that importance sampling can be used in Monte Carlo simulations. The number of matrices per subset is proportional to the matrix dimension. We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.