Machine learning predictions for local electronic properties of disordered correlated electron systems

TL;DR

This paper introduces a scalable machine learning model that predicts local electronic properties in disordered correlated electron systems by leveraging the locality principle, demonstrated on the Anderson-Hubbard model with promising accuracy.

Contribution

The paper develops a novel ML approach based on a group-theoretical lattice descriptor and neural networks to predict local electronic properties, extending the application of ML to complex disordered correlated systems.

Findings

ML predictions agree well with variational Monte Carlo data

The approach effectively captures local electronic behavior in disordered systems

Demonstrates potential for multi-scale modeling of correlated electrons

Abstract

We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multi-layer fully connected neural network, which is trained from datasets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multi-scale modeling of correlated electron systems.