Path optimization method for the sign problem caused by fermion determinant

TL;DR

This paper applies a machine learning-based path optimization method to the one-dimensional massive lattice Thirring model, effectively reducing the sign problem caused by the fermion determinant and reproducing analytic results.

Contribution

It demonstrates the effectiveness of the path optimization method in mitigating the sign problem in fermionic lattice models, including an approximation of the Jacobian calculation.

Findings

Reduces statistical errors in the sign problem.

Reproduces analytic results accurately.

Approximate Jacobian calculation yields consistent results.

Abstract

The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization method works for the sign problem. We show that the path optimization method successfully reduces statistical errors and reproduces the analytic results. We also examine an approximation of the Jacobian calculation in the learning process and show that it gives consistent results with those without an approximation.