Gauge invariant input to neural network for path optimization method

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 a plaquette, to overcome this problem. The efficiency of the gauge invariant input to the neural network is evaluated for the two-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.

Automated summary

This paper investigates the efficiency of a gauge invariant input for neural network path optimization. By using a gauge invariant input, such as a plaquette, the sign problem is successfully tamed in a two-dimensional U(1) gauge theory with a complex coupling. This opens up the possibility of applying path optimization to complex gauge theories, including quantum chromodynamics, in a realistic setup.