Complex Langevin simulations of a finite density matrix model for QCD

TL;DR

This paper investigates complex Langevin simulations of a finite density QCD matrix model, analyzing convergence issues near the chiral limit and proposing potential solutions for accurate results.

Contribution

It identifies convergence problems in complex Langevin methods for finite density QCD models and discusses possible remedies near the chiral limit.

Findings

Convergence issues occur when quark mass is within the Dirac spectrum.

Algorithm's convergence depends on quark mass and chemical potential.

Potential solutions to improve convergence are discussed.

Abstract

We study a random matrix model for QCD at finite density via complex Langevin dynamics. This model has a phase transition to a phase with nonzero baryon density. We study the convergence of the algorithm as a function of the quark mass and the chemical potential and focus on two main observables: the baryon density and the chiral condensate. For simulations close to the chiral limit, the algorithm has wrong convergence properties when the quark mass is in the spectral domain of the Dirac operator. A possible solution of this problem is discussed.