Is attention all you need to solve the correlated electron problem?
This work provides a solution to the correlated electron problem, which is significant for researchers and scientists in the field of quantum materials and condensed matter physics, particularly those relying on large-scale simulations.
This work tackles the correlated electron problem by using a self-attention neural network, achieving an accurate and efficient solution with the number of variational parameters scaling roughly as $N^2$ with the number of electrons. The result enables a path towards efficient large-scale simulations.
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 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.