Machine learning enabled large-scale quantum kinetic Monte Carlo simulations of the Falicov-Kimball model

We show that the celebrated Falicov-Kimball model exhibits rich and intriguing phase-ordering dynamics. With the aid of modern machine learning methods, we demonstrate the first-ever large-scale kinetic Monte Carlo simulations on the Falicov-Kimball model. We uncover an unusual phase-separation scenario where domain coarsening occurs simultaneously at two different scales: the growth of checkerboard clusters at smaller length scales and the expansion of super-clusters, which are aggregates of the checkerboard patterns of the same sign, at a larger scale. We show that the emergence of super-clusters is due to a hidden dynamical breaking of the sublattice symmetry. A self-trapping mechanism related to the super-clusters gives rise to the arrested growth of the checkerboard patterns and of the super-clusters themselves. Glassy behaviors similar to the one reported in this work could be generic for other correlated electron systems.