Application of the path optimization method to a discrete spin system
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866911763639828480 |
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| author | Kashiwa, Kouji Namekawa, Yusuke Ohnishi, Akira Takase, Hayato |
| author_facet | Kashiwa, Kouji Namekawa, Yusuke Ohnishi, Akira Takase, Hayato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06018 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Application of the path optimization method to a discrete spin system Kashiwa, Kouji Namekawa, Yusuke Ohnishi, Akira Takase, Hayato High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Phenomenology 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. |
| title | Application of the path optimization method to a discrete spin system |
| topic | High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2309.06018 |