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

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.

7 pages, 9 figures

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• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Observation of Lee-Yang zeros
• Deep Learning Beyond Lefschetz Thimbles
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction