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

We investigate the effect on the entanglement dynamics of an impurity moving at a 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 light cone. 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.