Anomalous phase separation in a correlated electron system: Machine-learning–enabled large-scale kinetic Monte Carlo simulations

Phase separation plays a central role in the emergence of unusual functionalities of correlated electron materials. The structure of the mixed-phase states depends strongly on the nonequilibrium phase-separation dynamics, which have so far yet to be systematically investigated, especially on the theoretical side. With the aid of modern machine-learning methods, we demonstrate large-scale kinetic Monte Carlo simulations of the phase-ordering process for the Falicov–Kimball model, which is one of the canonical strongly correlated electron systems. We uncover unusual relaxation dynamics with domain growth occurring simultaneously at two different length scales. At a smaller scale, the phase-separation instability leads to the growth of insulating checkerboard clusters in a metallic background. Interestingly, a hidden dynamical breaking of the sublattice symmetry gives rise to the emergence and coarsening of superclusters, which are aggregates of the checkerboard clusters whose f electrons reside on the same sublattice, at a larger scale. Arrested growth of the checkerboard patterns and of the superclusters is shown to result from a correlation-induced self-trapping mechanism. Glassy behaviors similar to the one reported in this work could be generic for other correlated electron systems.