Gauge invariant input to neural network for path optimization method

TL;DR

This paper explores the use of gauge invariant inputs, like plaquettes, in neural networks for path optimization to better address the sign problem in gauge theories, showing promising results in 2D U(1) models.

Contribution

It introduces a gauge invariant input approach for neural network-based path optimization, improving sign problem control in gauge theories.

Findings

Gauge invariant inputs significantly improve phase factor enhancement.

Path optimization with plaquette inputs effectively controls the sign problem.

Potential applicability to complex gauge theories like QCD.

Abstract

We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method. While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple gauge theory, the optimization does not work well when the gauge degrees of freedom remain. We propose to employ a gauge invariant input, such as plaquette, to overcome this problem. The efficiency of the gauge invariant input to the neural network is evaluated for the 2-dimensional $U(1)$ gauge theory with a complex coupling. The average phase factor is significantly enhanced by the path optimization with the plaquette input, indicating good control of the sign problem. It opens a possibility that the path optimization is available to complicated gauge theories, including Quantum Chromodynamics, in a realistic setup.