Evading the model sign problem in the PNJL model with repulsive vector-type interaction via path optimization

TL;DR

This paper applies the path optimization method with neural networks to address the sign problem in the PNJL model with vector interactions, enabling more accurate Monte Carlo simulations.

Contribution

It introduces a neural network-based path optimization technique to mitigate the sign problem in the PNJL model with vector interactions, validating assumptions and deriving the optimal path equations.

Findings

The assumptions $ ext{Re}\,A_8 \, ext{and}\, ext{Re}\,\omega$ are justified by sampled configurations.

The optimized paths from different methods agree in high-weight regions.

The Euler-Lagrange equation for the optimal path is derived and satisfied.

Abstract

We discuss the sign problem in the Polyakov loop extended Nambu--Jona-Lasinio model with repulsive vector-type interaction by using the path optimization method. In this model, both of the Polyakov loop and the vector-type interaction cause the model sign problem, and several prescriptions have been utilized even in the mean field treatment. In the path optimization method, integration variables are complexified and the integration path (manifold) is optimized to evade the sign problem, or equivalently to enhance the average phase factor. Within the homogeneous field ansatz, the path is optimized by using the feedforward neural network. We find that the assumptions adopted in previous works, $\mathrm{Re}\,A_8 \simeq 0$ and $\mathrm{Re}\,\omega \simeq 0$, can be justified from the Monte-Carlo configurations sampled on the optimized path. We also derive the Euler-Lagrange equation for the optimal path to satisfy. The two optimized paths, the solution of the Euler-Lagrange equation and the variationally optimized path, agree with each other in the region with large statistical weight.