Simulating real-time dynamics with projected entangled-pair state for quantum lattice models

Simulating real-time dynamics of two-dimensional quantum systems poses a significant challenge in modern physics. Here we develop a time-dependent variational approach based on projected entangled pair states (PEPS) combined with variational Monte Carlo (VMC) techniques to study non-equilibrium dynamics in two-dimensional lattice models. We apply the method to both global quenches, where a sudden parameter change drives the entire system out of equilibrium, and local quenches, where a localized perturbation generates spreading correlations. Our results show that this PEPS–VMC framework captures essential dynamical features beyond the reach of conventional approaches, offering a powerful tool for exploring quantum dynamics in two dimensions.