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. arXiv:1812.06016v2 [cond-mat.dis-nn]

Out-of-equilibrium phase diagram of the quantum random energy model

“…[34] the authors derive an estimate of the transition to NEE eigenstates in agreement with Ref. [28] and argue that the NEE phase is layered in an alternating sequence of two distinct subphases. The dynamical population transfer protocol on the QREM was further analyzed in Ref.…”

“…Also in experiments it is challenging to access the very long timescales, and possibly also long length scales, on which the critical behavior develops. Another frontier of the field is directed towards understanding the existence of MBL in higher dimensions [22][23][24] and its relationship with other form of ergodicity breaking such as quantum glassiness [25][26][27][28].…”

“…The quantum model's equilibrium phase diagram has been studied before [30,31] and a glassy phase was identified at low temperature and small transverse magnetic field. The MBL transition of the quantum random energy model (QREM) was also investigated previously [25,26,28,[32][33][34]. In Refs.…”

“…In particular, in Ref. [28] the MBL phase was identified with a hyperglass where the dynamics is practically absent while the entire phase above T MBL with a dynamical glass phase (or bad metal) is characterized by nonergodic extended (NEE) eigenstates. In Ref.…”

Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems

“…Multifractal statistics appears at the Anderson localization transition for single-particle lattice systems [17,[65][66][67][68][69][70][71]. In addition, recent examples have reported (multi)fractal phases extend-ing over a whole range of parameters [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]. Multifractal wavefunctions have been found for some quantum maps [68,70,87,88].…”