Progress on Complex Langevin simulations of a finite density matrix model for QCD

TL;DR

This paper investigates the application of the Complex Langevin algorithm to a QCD-inspired random matrix model, revealing persistent convergence issues and limited success of proposed modifications in aligning results with theoretical expectations.

Contribution

It provides a detailed analysis of the failure modes of the Complex Langevin method in a finite density QCD model and evaluates various gauge cooling techniques and matrix shifts.

Findings

Naive Complex Langevin converges to incorrect theories.

Gauge cooling and matrix shifts do not significantly improve results.

Final outcomes still deviate from analytical predictions.

Abstract

We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.