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arXiv:2402.15167

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

Haotian Ye, Ruichen Li, Yuntian Gu, Yiping Lu, Di He, Liwei Wang

Published Feb 23, 2024• 1 citation
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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.

DOI
10.48550/arxiv.2402.15167

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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 O~(N2){\widetilde O}(N^2)O(N2) 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){O}(N)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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O(N2)O(N^2)O(N2) Universal Antisymmetry in Fermionic Neural Networks
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