Gauge invariant input to neural network for path optimization method

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.

7 pages, 8 figures; published version

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Cited by in corpus (5)

• Exploring QCD matter in extreme conditions with Machine Learning
• Fourier-Flow model generating Feynman paths
• Improving efficiency of the path optimization method for a gauge theory
• Application of the path optimization method to a discrete spin system
• Path optimization method for the sign problem caused by fermion determinant