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Prethermalization and glassiness in the bosonic Hubbard model

We investigate the non-equilibrium dynamics of the bosonic Hubbard model starting from inhomogeneous superfluid or Mott insulator initial states using the truncated Wigner approximation (TWA). We find that the relaxation of the system develops in two steps for sufficiently large interaction strengths: after a fast relaxation the system gets caught in metastable prethermalized states that precede the true equilibrium state. We find that the lifetime of these prethermalized states increases by several orders of magnitude as we increase the on-site interaction strength beyond a threshold value. We show that the emergence of long-lived metastable states in the quantum dynamics is associated with an ergodic (active) to non-ergodic (inactive) dynamical phase transition in the ensemble of classical trajectories that contribute to the semiclassical limit. This dynamic phase transition, which is very similar to that found in different classical models of glasses, is closely related to the dynamic heterogeneity of the classical relaxation.