Out-of-equilibrium phase diagram of the quantum random energy model

The quantum version of Derrida's Random Energy model is the simplest model of a quantum glass. Here, the authors study its dynamical phase diagram, revealing the existence of three distinct dynamical phases: a many-body fully localized phase at low energy, an ergodic phase at high energy, and a multifractal ``bad metal'' phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space.