A constructive theory of the numerically and experimentally accessible many-body localized phase

The many-body localised (MBL) to thermal crossover observed in cold atom experiments and in numerical studies remains poorly understood, despite nearly a decade of intensive study. I will develop a model for the crossover in which the MBL chain is destabilised by many-body resonances. The model reproduces several observed properties of the crossover, identifies a large region of the observed phase diagram as only "apparent" or pre-thermal MBL, and makes new predictions for the scaling of thermalization time scales and eigenstate entropy in this apparent MBL region.