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Gauge invariant input to neural network for path optimization method

Yusuke Namekawa1,*, Kouji Kashiwa2, Akira Ohnishi1, and Hayato Takase

  • 1Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 2Fukuoka Institute of Technology, Wajiro, Fukuoka 811-0295, Japan

  • *namekawa@yukawa.kyoto-u.ac.jp
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Phys. Rev. D 105, 034502 – Published 4 February, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.034502

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 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.

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Phys. Rev. D 105, 034502– Published 4 February, 2022
  • Received 30 September 2021
  • Accepted 3 January 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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