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Quantum Kibble-Zurek physics in the presence of spatially-correlated dissipation

We study how universal properties of quantum quenches across critical points are modified by a weak coupling to thermal dissipation, focusing on the paradigmatic case of the transverse field Ising model. Beyond the standard quench-induced Kibble-Zurek defect production in the absence of the bath, the bath contributes extra thermal defects. We show that spatial correlations in the noise produced by the bath can play a crucial role: one obtains quantitatively different scaling regimes depending on whether the correlation length of the noise is smaller or larger than the Kibble-Zurek length associated with the quench speed, and the thermal length set by temperature. For the case of spatially-correlated bath noise, additional thermal defect generation is restricted to a window that is both quantum critical and excluded from the non-equilibrium regime surrounding the critical point. We map the dissipative quench problem to a set of effectively independent dissipative Landau-Zener problems. Using this mapping along with both analytic and numerical calculations allows us to find the scaling of the excess defect density produced in the quench, and suggests a generic picture for such dissipative quenches.