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 wave-function 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 moiré quantum material, we demonstrate that the self-attention Ansatz provides an accurate and efficient solution without human bias. 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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• Strongly correlated systems
• Wigner crystal
• Artificial neural networks
• Exact diagonalization
• Hartree-Fock methods
• Neural network simulations
• Quantum Monte Carlo