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Main Authors: Ye, Haotian, Li, Ruichen, Gu, Yuntian, Lu, Yiping, He, Di, Wang, Liwei
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.15167
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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