Emergence of Inhomogeneities after Interaction Quenches in the Hubbard Model

Understanding how correlated electrons evolve after a sudden change in interaction strength remains a central challenge in nonequilibrium physics. Although many approaches have been used to study quench dynamics in the Hubbard model, most treat the system as spatially uniform and miss the role of real-space fluctuations. Using the Gutzwiller von Neumann dynamics (GvND) method, a real-space extension of the time-dependent Gutzwiller approach, we directly track the evolution of local quantities across the lattice. Our simulations reveal that even tiny initial inhomogeneities grow rapidly after the quench, leading to a breakdown of synchronized oscillations seen in homogeneous mean-field descriptions. At longer times, the system evolves into quasi-stationary states whose spatial structures and distributions of physical quantities after the collapsed oscillation depend strongly on the quench strength, with strong quenches giving rise to pronounced phase separation. These results demonstrate that spatial fluctuations play a crucial role in shaping the nonequilibrium behavior of strongly correlated systems.