# Non-ergodic extended phase of the Quantum Random Energy model

## TL;DR

This paper investigates the non-ergodic extended phase in the Quantum Random Energy Model, revealing a delocalized yet non-ergodic regime with power-law scaling of correlations, and discusses its implications for quantum information.

## Contribution

It identifies and characterizes a non-ergodic delocalized phase in the Quantum Random Energy Model, linking it to glassy behavior and contrasting it with many-body localization.

## Key findings

- Spin-spin correlators decay with power-law time scaling.
- Long-time correlator values scale as a power of Hilbert space volume.
- The non-ergodic phase is associated with a glassy state.

## Abstract

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. We identify this phase with the glass phase whilst the many body localized phase corresponds to a 'hyperglass' in which dynamics is practically absent. We discuss the implications of these finding to quantum information problems.