#### QuICS Special Seminar

We describe a novel dynamical phase in which thermalization breaks down even on the level of the many-body eigenstates. This “trapped” phase is found in spin glass models of particular relevance for quantum computing applications. After briefly discussing the use of eigenstates & eigenstate phases to understand isolated many-body quantum systems, we contrast this trapped phase to the better-known many-body localized (MBL) phase. Whereas MBL arises from the detuning of energy levels, the trapped phase arises from macroscopic energy barriers which suppress tunneling amplitudes to below the scale of the level spacing. We calculate the trapped-thermal phase boundary in a family of tractable toy models. We then discuss the relevance for using quantum fluctuations to solve “matching” problems, a type of hard computational task which might be amenable to adiabatic quantum computation.