Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin

TL;DR

This paper demonstrates that the complex Langevin method can effectively simulate chiral random matrix theory at non-zero chemical potential, matching analytic predictions and controlling phase fluctuations.

Contribution

It introduces a novel simulation approach using complex Langevin with variable shifts and polar representation, improving the handling of phase fluctuations in non-zero chemical potential scenarios.

Findings

Successful match with analytic predictions for chiral condensate

Effective control of fermion determinant phase fluctuations

Validation of complex Langevin method for this context

Abstract

It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.