Non-ergodic extended phase of the Quantum Random Energy model

Understand

The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators.

• In the former approach the non-ergodic delocalized states is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space.
• In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin-spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume.
• The long time limit of this correlator also scales as a power of the full Hilbert space volume.