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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.15167 |
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| _version_ | 1866929259082153984 |
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| author | Ye, Haotian Li, Ruichen Gu, Yuntian Lu, Yiping He, Di Wang, Liwei |
| author_facet | Ye, Haotian Li, Ruichen Gu, Yuntian Lu, Yiping He, Di Wang, Liwei |
| contents | In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge by presenting an ${\widetilde O}(N^2)$ ansatz based on permutation-equivariant functions. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter [14], solving the proposed open problems that ${O}(N)$ Slater determinants are sufficient to provide universal representation of AS continuous functions. Together, we offer a generalizable and efficient approach to representing AS continuous functions, shedding light on designing neural networks to learn wave functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function Ye, Haotian Li, Ruichen Gu, Yuntian Lu, Yiping He, Di Wang, Liwei Quantum Physics In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge by presenting an ${\widetilde O}(N^2)$ ansatz based on permutation-equivariant functions. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter [14], solving the proposed open problems that ${O}(N)$ Slater determinants are sufficient to provide universal representation of AS continuous functions. Together, we offer a generalizable and efficient approach to representing AS continuous functions, shedding light on designing neural networks to learn wave functions. |
| title | $\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.15167 |