Many-body localization with quasiperiodic driving

Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by D incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for D = 2, but not for D >= 3. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For D >= 3, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.