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arXiv · 2411.11605

Fermionic Neural Networks through the lens of Group Theory

J. Rozalén Sarmiento·A. Rios
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Abstract

We present an overview of the method of Neural Quantum States applied to the many-body problem of atomic nuclei. Through the lens of group representation theory, we focus on the problem of constructing neural-network ans\"atze that respect physical symmetries. We explicitly prove that determinants, which are among the most common methods to build antisymmetric neural-network wave functions, can be understood as the result of a group convolution. We also identify the reason why this construction is so efficient in practice compared to other group convolutional operations. We conclude that group representation theory is a promising avenue to incorporate explicitly symmetries in Neural Quantum States.

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J. Rozalén Sarmiento, A. Rios. 2024-11-18. Fermionic Neural Networks through the lens of Group Theory. https://arxiv.org/abs/2411.11605

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