Path optimization for $U(1)$ gauge theory with complexified parameters

TL;DR

This paper applies the path optimization method to complexified parameters in 1+1D U(1) gauge theory, enabling exploration of Lee-Yang zeros and phase structure while addressing gauge fixing and sign problem challenges.

Contribution

It introduces the use of path optimization with gauge fixing for complex parameters in lattice gauge theory, advancing Lee-Yang zero analysis.

Findings

Successfully handled complexified parameters in U(1) gauge theory

Clarified gauge fixing in path optimization

Controlled sign problem with gauge fixing

Abstract

In this article, we apply the path optimization method to handle the complexified parameters in the 1+1 dimensional pure $U(1)$ gauge theory on the lattice. Complexified parameters make it possible to explore the Lee-Yang zeros which helps us to understand the phase structure and thus we consider the complex coupling constant with the path optimization method in the theory. We clarify the gauge fixing issue in the path optimization method; the gauge fixing helps to optimize the integration path effectively. With the gauge fixing, the path optimization method can treat the complex parameter and control the sign problem. It is the first step to directly tackle the Lee-Yang zero analysis of the gauge theory by using the path optimization method.