Non-ergodic extended phase of the Quantum Random Energy model
Lara Faoro, Mikhail Feigel'man, Lev Ioffe
备注：
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
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.
Probing the ergodicity breaking transition via violations of random matrix theoretic predictions for local observables
Center for Quantum Technologies, Department of Physics, St. Kliment Ohridski University of Sofia（索非亚圣克利门特奥赫里德斯基大学量子技术中心和物理系）；Institute of Fundamental Physics IFF-CSIC（CSIC基础物理研究所）；Department of Physics and Astronomy, University of Exeter（埃克塞特大学物理与天文学系）
