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  • Open Access

Path optimization method for the sign problem caused by the fermion determinant

Kazuki Hisayoshi1, Kouji Kashiwa1,*, Yusuke Namekawa2, and Hayato Takase

  • 1Department of Computer Science and Engineering, Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan
  • 2Education and Research Center for Artificial Intelligence and Data Innovation, Hiroshima University, Hiroshima 730-0053, Japan

  • *Contact author: kashiwa@fit.ac.jp
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Phys. Rev. D 111, 094503 – Published 6 May, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.094503

Abstract

The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization method works for the sign problem. We show that the path optimization method successfully reduces statistical errors and reproduces the analytic results. We also examine an approximation of the Jacobian calculation in the learning process and show that it gives consistent results with those without an approximation.

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Phys. Rev. D 111, 094503– Published 6 May, 2025
  • Received 5 February 2025
  • Accepted 9 April 2025
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