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High Energy Physics - Lattice

arXiv:2309.06018 (hep-lat)
[Submitted on 12 Sep 2023 (v1), last revised 4 Nov 2023 (this version, v2)]

Title:Application of the path optimization method to a discrete spin system

Authors:Kouji Kashiwa, Yusuke Namekawa, Akira Ohnishi, Hayato Takase
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Abstract:The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors.
Comments: 8 pages, 5 figures, version accepted for publication in Phys. Rev. D
Subjects: High Energy Physics - Lattice (hep-lat); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:2309.06018 [hep-lat]
  (or arXiv:2309.06018v2 [hep-lat] for this version)
  https://doi.org/10.48550/arXiv.2309.06018
Journal reference: Phys. Rev. D 108, 094504 (2023)
Related DOI: https://doi.org/10.1103/PhysRevD.108.094504

Submission history

From: Kouji Kashiwa [view email]
[v1] Tue, 12 Sep 2023 07:34:08 UTC (183 KB)
[v2] Sat, 4 Nov 2023 05:24:43 UTC (183 KB)
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