Is attention all you need to solve the correlated electron problem?

• URL: http://arxiv.org/abs/2502.05383v1
• Date: Fri, 07 Feb 2025 23:41:41 GMT
• Title: Is attention all you need to solve the correlated electron problem?
• Authors: Max Geier, Khachatur Nazaryan, Timothy Zaklama, Liang Fu,
• Abstract summary: We show that a self-attention ansatz can be used to solve the interacting electron problem in solids. By a systematic neural-network variational Monte Carlo study on a moir'e quantum material, we demonstrate that the self-attention ansatz provides an accurate, efficient, and unbiased solution.
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• Abstract: The attention mechanism has transformed artificial intelligence research by its ability to learn relations between objects. In this work, we explore how a many-body wavefunction ansatz constructed from a large-parameter self-attention neural network can be used to solve the interacting electron problem in solids. By a systematic neural-network variational Monte Carlo study on a moir\'e quantum material, we demonstrate that the self-attention ansatz provides an accurate, efficient, and unbiased solution. Moreover, our numerical study finds that the required number of variational parameters scales roughly as $N^2$ with the number of electrons, which opens a path towards efficient large-scale simulations.

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