Critical Dynamics at the Many-Body-Localized Phase Transition

When an isolated quantum system is prepared far from equilibrium, transport of its constituent particles allows it to relax by energy exchange throughout the remaining system. However, the addition of strong disorder in these interacting systems breaks down transport at a critical disorder strength as a consequence of many-body localization (MBL). Here, we study many-body localization in a 1-D system of interacting bosons with quasi-periodic disorder. Through the site-resolved, correlated density fluctuations, we extract a dynamic transport length and observe exceptionally slow transport near this critical disorder strength. We additionally verify the critical nature of the system's dynamics by tuning the total system size. Finally, we identify a microscopic mechanism of the interaction-driven delocalization via a sparse-resonant structure. This sparse structure persists into higher-order correlation functions and additionally identifies the many-body critical nature. These results and observed mechanism lay a foundation for characterizing dynamic many-body phases and studying other proposed microscopic mechanisms in interacting, disordered systems.