Non-ergodic extended phase of the Quantum Random Energy model
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.
Keywords
Cite
@article{arxiv.1812.06016,
title = {Non-ergodic extended phase of the Quantum Random Energy model},
author = {Lara Faoro and Mikhail Feigel'man and Lev Ioffe},
journal= {arXiv preprint arXiv:1812.06016},
year = {2019}
}
Comments
Changes with respect to the first version (Dec. 2018): titles is slightly changed, abstract is extended, discussion of previous papers on similar subject is considerably augmented