Emergent ergodicity at the transition between many-body localized phases

Due to their failure to thermalize, systems in the many-body localized (MBL) phase can support non-trivial order ( e.g. order characterized by spontaneously broken symmetries or symmetry-protected topological order) even in highly excited, many-body eigenstates. However, the stability of MBL as a system transitions between different ordered phases remains a mystery. In particular, it is unknown whether the competition between two orders near a phase boundary inevitably destabilizes the MBL and restores ergodicity to the system. Here, we present evidence that, indeed, a direct transition between different MBL phases cannot occur, and between any two MBL phases, an intervening finite-width thermalizing phase emerges. We probe the emergence of this thermalizing phase by numerically studying the level statistics of a variety of different models exhibiting either symmetry broken order or symmetry-protected topological order, both in the static and driven case. We complement our numerical analysis by providing an analytic picture for the instability of MBL around the phase transition.