Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases

We investigate the number entropy S_N—which characterizes particle-number fluctuations between subsystems—following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to show many-body localization and where the entanglement entropy grows as S ∼ln t as function of time t , the number entropy grows as S_N∼ln ln t , indicating continuing subdiffusive particle transport at a very slow rate. We demonstrate that this growth is consistent with a relation between entanglement and number entropy recently established for noninteracting systems.