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

We investigate the number entropy SN-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∼lnt as function of time t, the number entropy grows as SN∼lnlnt, 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.