Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit, but these observations have not been fundamentally understood. We explain and analytically prove all these observations by rigorously perturbatively showing the existence of certain algebraic structures that are exponentially stable in time. In particular, we show that many-body Bloch oscillations persist even at infinite temperature for exponentially long times using a type of dynamical algebra which we refer to as dynamical l-bits and provide a bound on the tilt strength for this nonergodic transition. We numerically confirm our results by studying the prototypical Stark MBL model of a tilted XXZ spin chain. Our work explains why thermalization was observed in a recent two-dimensional tilted experiment. As dynamical l-bits represent stable, localized, and quantum coherent excitations, our work opens possibilities for quantum information processing in Stark MBL systems even at high temperature.

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• Localization
• Many-body localization
• Density matrix renormalization group
• Mathematical physics methods
• Spin chains