Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop

TL;DR

This paper introduces a path optimization method with complexified fields to effectively mitigate the sign problem in finite-density QCD effective models, enabling more accurate Monte Carlo simulations.

Contribution

It demonstrates that complexifying temporal gluon fields within the path optimization framework can significantly improve the average phase factor in QCD models.

Findings

Improved average phase factor with path optimization

Effective control of the sign problem in QCD models

Potential applicability to finite-density QCD simulations

Abstract

We apply the path optimization method to a QCD effective model with the Polyakov loop at finite density to circumvent the model sign problem. The Polyakov-loop extended Nambu--Jona-Lasinio model is employed as the typical QCD effective model and then the hybrid Monte-Carlo method is used to perform the path integration. To control the sign problem, the path optimization method is used with complexification of temporal gluon fields to modify the integral path in the complex space. We show that the average phase factor is well improved on the modified integral-path compared with that on the original one. This indicates that the complexification of temporal gluon fields may be enough to control the sign problem of QCD in the path optimization method.