Machine learning electron correlation in a disordered medium

TL;DR

This paper demonstrates that a neural network can learn and predict complex electron behaviors in disordered, strongly correlated systems, specifically the Anderson-Hubbard model, bypassing traditional computationally intensive methods.

Contribution

It introduces a neural network approach that accurately models electron correlations in disordered systems, combining many-body physics with deep learning.

Findings

Neural network accurately predicts local double occupation probabilities.

Model successfully estimates quasiparticle weights.

Approach effectively captures electron correlation effects in disordered media.

Abstract

Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-body techniques with a deep learning approach, we demonstrate that a fully-connected neural network is able to learn the complex collective behavior of electrons in strongly correlated systems. Specifically, we consider the Anderson-Hubbard (AH) model, which is a canonical system for studying the interplay between electron correlation and strong localization. The ground states of the AH model on a square lattice are obtained using the real-space Gutzwiller method. The obtained solutions are used to train a multi-task multi-layer neural network, which subsequently can accurately predict quantities such as the local probability of double occupation and the quasiparticle weight, given the disorder potential in the neighborhood as the input.