Machine Learning Enable the Large Scale Kinetic Monte Carlo for Falicov-Kimball Model

The Falicov-Kimball (FK) model was initially introduced as a statistical model for metal-insulator transition in correlated electron systems. It can be exactly solved by combining the classical Monte Carlo method for the lattice gas and exact diagonalization (ED) for the itinerant electrons. However, direct ED calculation, which is required in each time-step of dynamical simulations of the FK model, is very time-consuming. Here we apply the modern machine learning (ML) technique to enable the first-ever large-scale kinetic Monte Carlo (kMC) simulations of FK model. Using our neural-network model on a system of unprecedented 10^5 lattice sites, we uncover an intriguing hidden sub-lattice symmetry breaking in the phase separation dynamics of FK model.