  We propose a spatio-temporal characterization of the entanglement dynamics in
many-body localized (MBL) systems, which exhibits a striking resemblance with
dynamical heterogeneity in classical glasses. Specifically, we find that the
relaxation times of local entanglement, as measured by the concurrence, are
spatially correlated yielding a dynamical length scale for quantum
entanglement. As a consequence of this spatio-temporal analysis, we observe
that the considered MBL system is made up of dynamically correlated clusters
with a size set by this entanglement length scale. The system decomposes into
compartments of different activity such as active regions with fast quantum
entanglement dynamics and inactive regions where the dynamics is slow. We
further find that the relaxation times of the on-site concurrence become
broader distributed and more spatially correlated, as disorder increases or the
energy of the initial state decreases. Through this spatio-temporal
characterization of entanglement, our work unravels a previously unrecognized
connection between the behavior of classical glasses and the genuine quantum
dynamics of MBL systems.
