  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.
