Emergent ergodicity at the transition between many-body localized phases

Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. Here, we conjecture that no direct transition between distinct MBL orders can occur; rather, a thermal phase always intervenes. Motivated by recent advances in Rydberg-atom-based quantum simulation, we propose an experimental protocol where the intervening thermal phase can be diagnosed via the dynamics of local observables.