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Entanglement front generated by an impurity travelling in an isolated many-body quantum system

We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front which never fades. We argue that these effects are valid for generic systems whose correlations propagate inside a light-cone. To assess the fully chaotic regime, we formulate a random circuit model which supports a moving impurity and a sharp lightcone. Although the qualitative behavior is similar to the integrable case, the endogenous regime is only visible at short times due to the onset of diffusive energy transport. Our predictions are supported by numerical simulations in the different regimes.