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Dynamics of the impurity screening cloud following quantum quenches of the Resonant Level Model

We present a detailed analysis of the evolution of impurity screening cloud in the Resonant Level Model (RLM) followed by quenches of system parameters. The considered quenches are either local or found to be effectively local. The screening cloud is characterized by impurity-bath correlators and by the entanglement of a block centered around the impurity with the rest of the system. We consider several local quench protocols, such as, quenches from initially decoupled to coupled impurity, quenches between different finite couplings of the impurity, and `detuning quenches' involving changing the onsite impurity potential away from or to the chemical potential of the bath. The relevant correlators and the entanglement display versions of the `light-cone' effect, since the information about the quench travels through the bath at finite speed. At long times (`inside' the light cone), the impurity screening cloud relaxes exponentially to the final equilibrium structure, with the relaxation rate given by the emergent energy scale of impurity screening. Also, snaphots of the time-evolving spatial profile of impurity-bath correlators show exponential dependences on space, with the length scale given by the screening length.