We propose a spatio-temporal characterization of the entanglement dynamics in many-body localized (MBL) systems, which exhibits a striking resemblance with dynamical heterogeneities in classical glasses. Specifically, we find that the relaxation times of local entanglement, as measured by the concurrence, are spatially correlated giving rise to a dynamical correlation length for quantum entanglement. Our work provides a yet unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.
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