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We analyze the propagation of correlations after a sudden interaction changein a strongly interacting quantum system in contact with an environment. Inparticular, we consider an interaction quench in the Bose-Hubbard model, deepwithin the Mott-insulating phase, under the effect of dephasing. We observethat dissipation effectively speeds up the propagation of single-particlecorrelations while reducing their coherence. In contrast, for two-point densitycorrelations, the initial ballistic propagation regime gives way to diffusionat intermediate times. Numerical simulations, based on a time-dependent matrixproduct state algorithm, are supplemented by a quantitatively accuratefermionic quasi-particle approach providing an intuitive description of theinitial dynamics in terms of holon and doublon excitations.

Light-cone and diffusive propagation of correlations in a many-body dissipative system