Non-ergodic phase of purely quantum random energy model
Random energy model can be viewed as the toy model of a glass. The thermodynamics of this model display the transition from glassy low temperature phase where it is dominated by a single low energy state to the paramagnetic high temperature phase. The dynamical properties quantum version of this model is much less trivial, especially in the absence of any contact with the bath. Furthermore, recently it was realized that quantum dynamics of random energy model is relevant for the problem of the efficient quantum searches which revived the interest to the purely quantum version of this problem. In this work we show that at low temperatures the dynamics of this model is equivalent to that of Porter Thomas random matrix model and show all properties associated with non-ergodic states, including anomalous power-law dependences on the system size and display non-ergodic to fully localized transition.