Application of the path optimization method to a discrete spin system

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 var...

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Bibliographic Details
Published inarXiv.org
Main Authors Kashiwa, Kouji, Namekawa, Yusuke, Ohnishi, Akira, Takase, Hayato
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.11.2023
Subjects
Degrees of freedom
Ising model
Machine learning
Optimization
Physics - High Energy Physics - Lattice
Physics - High Energy Physics - Phenomenology
Physics - Statistical Mechanics
Quantum theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2309.06018