Evading the sign problem in random matrix simulations

TL;DR

This paper introduces a subset method for random matrix simulations at nonzero chemical potential that eliminates the sign problem, enabling efficient Monte Carlo sampling and stable measurements of the chiral condensate.

Contribution

The authors develop a subset approach that ensures positive sums of fermionic determinants, avoiding the sign problem in dynamical random matrix simulations at nonzero chemical potential.

Findings

Sign problem is avoided using subset sums of matrices.

Statistical error remains stable across chemical potentials.

Error grows linearly with matrix dimension, not exponentially.

Abstract

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. For each subset the sum of fermionic determinants is real and positive 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.