  The quantum random energy model provides a mean-field description of the
equilibrium spin glass transition. We show that it further exhibits a many-body
localization - delocalization (MBLD) transition when viewed as a closed quantum
system. The mean-field structure of the model allows an analytically tractable
description of the MBLD transition using the forward-scattering approximation
and replica techniques. The predictions are in good agreement with the
numerics. The MBLD lies at energy density significantly above the equilibrium
spin glass transition, indicating that the closed system dynamics freezes well
outside of the traditional glass phase. We also observe that the structure of
the eigenstates at the MBLD critical point changes continuously with the energy
density, raising the possibility of a family of critical theories for the MBLD
transition.
