# Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction

## TL;DR

This paper demonstrates how the path optimization method can effectively mitigate the sign problem in a QCD effective model with a repulsive vector interaction, enabling more accurate finite-temperature and density simulations.

## Contribution

It introduces the first successful application of path optimization to treat the vector interaction in a Polyakov-loop QCD model using Monte Carlo methods.

## Key findings

- Increased average phase factor with path optimization
- Effective control of the sign problem in the model
- Necessity of complexifying gluon and auxiliary fields

## Abstract

The path optimization method is applied to a QCD effective model with the Polyakov loop and the repulsive vector-type interaction at finite temperature and density to circumvent the model sign problem. We show how the path optimization method can increase the average phase factor and control the model sign problem. This is the first study which correctly treats the repulsive vector-type interaction in the QCD effective model with the Polyakov-loop via the Markov-chain Monte-Carlo approach. It is shown that the complexification of the temporal component of the gluon field and also the vector-type auxiliary field are necessary to evade the model sign problem within the standard path-integral formulation.