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When a generic quantum system is prepared in a simple initial condition, ittypically equilibrates toward a state that can be described by a thermalensemble. A known exception are localized systems which are non-ergodic and donot thermalize, however local observables are still believed to becomestationary. Here we demonstrate that this general picture is incomplete byconstructing product states which feature periodic high-fidelity revivals ofthe full wavefunction and local observables that oscillate indefinitely. Thesystem neither equilibrates nor thermalizes. This is analogous to thephenomenon of weak ergodicity breaking due to many-body scars and challengesaspects of the current MBL phenomenology, such as the logarithmic growth of theentanglement entropy. To support our claim, we combine analytic arguments withlarge-scale tensor network numerics for the disordered Heisenberg chain. Ourresults hold for arbitrarily long times in chains of 160 sites up to machineprecision.

Reviving product states in the disordered Heisenberg chain