Internal Clock for Many-Body Delocalization

Explore the concept of many-body delocalization in disordered quantum wires through this comprehensive lecture. Delve into the growing consensus that generic disordered quantum systems, such as the XXZ-Heisenberg chain, may not exhibit strict many-body localization (MBL) within reasonable disorder values. Examine computational studies of short wires that reveal an extremely slow but unmistakable flow of physical observables over time and with increasing system size, consistently moving away from strict localization. Gain fresh insights into delocalization physics, including the absence of a generic time scale due to strong sample-to-sample fluctuations. Investigate the concept of an "internal clock" that survives in an ensemble sense. Analyze the relaxation of charge imbalance and entanglement entropy in a 1D system of interacting disordered fermions. Discover how the average entropy models the ensemble-averaged internal clock and reduces fluctuations. Consider the implications of faster-than-logarithmic growth of entanglement and smooth dependency on disorder for all observables within the simulation window, supporting a cross-over scenario and challenging the notion of an MBL transition within traditional computational study parameters.