Graph neural network models for predicting local electronic properties of disordered correlated electron systems

The rapid development of machine learning (ML) methods has opened up many new avenues of research in the field of condensed matter physics that would be difficult, if not impossible, to explore using conventional approaches. In particular, ML methods can bridge the tradeoff between efficiency and accuracy that is inherent to many numerical methods used for multiscale simulations. Here, we present a scalable ML model that can predict local and short-range electronic and spin properties such as on-site electron number, double occupation, local magnetic moment, and spin-spin correlations for disordered correlated electron systems. A novel feature of our model is the use of a graph neural network (GNN). A GNN works with data structured as graphs by passing and aggregating information between connected nodes to learn representations that capture the structure and relationships of the data. While GNNs have achieved considerable success in a number of fields including quantum chemistry and materials science, their applications in condensed matter physics remain largely unexplored. We tested the model by training on small-system-size determinant quantum Monte Carlo (DQMC) simulations of the square-lattice Anderson-Hubbard model, a paradigmatic system for studying the interplay between disorder and correlations. We find that the model is able to reasonably predict the local and short-range electronic and spin properties of the system. Our results demonstrate the potential and effectiveness of using GNNs for multiscale modeling of disordered correlated electron and other condensed matter systems.