Related papers: $\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function

$\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function

URL: http://arxiv.org/abs/2402.15167v2
Date: Thu, 29 Feb 2024 11:05:58 GMT
Title: $\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function
Authors: Haotian Ye, Ruichen Li, Yuntian Gu, Yiping Lu, Di He, Liwei Wang
Abstract summary: In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric and continuous. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter.
Score: 41.1983944775617
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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