Machine learning predictions for local electronic properties of disordered correlated electron systems
This work addresses the challenge of multi-scale modeling for correlated electron systems, which is important for condensed matter physics, but it is incremental as it applies existing ML methods to a specific domain.
The authors tackled the problem of predicting local electronic properties in disordered correlated electron systems by developing a scalable machine learning model based on the locality principle, achieving predictions that agree reasonably well with variational Monte Carlo data.
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.