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The random energy model (REM) provides a solvable mean-field description ofthe equilibrium spin glass transition. Its quantum sibling (the QREM), obtainedby adding a transverse field to the REM, has similar properties and shows aspin glass phase for sufficiently small transverse field and temperature. In arecent work, some of us have shown that the QREM further exhibits a many-bodylocalization - delocalization (MBLD) transition when viewed as a closed quantumsystem, evolving according to the quantum dynamics. This phase encloses thefamiliar equilibrium spin-glass phase. In this paper we study in detail theMBLD transition within the forward-scattering approximation and replicatechniques. The predictions for the transition line are in good agreement withthe exact diagonalization numerics. We also observe that the structure of theeigenstates at the MBLD critical point changes continuously with the energydensity, raising the possibility of a family of critical theories for the MBLDtransition.

The many-body localized phase of the quantum random energy model