Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

TL;DR

This paper investigates many-body localization in fermionic systems with single-particle mobility edges, revealing an intermediate nonergodic extended phase and critical scaling behaviors at the localization transition.

Contribution

It introduces the concept of a nonergodic extended phase in many-body localization with mobility edges and analyzes its properties and implications for interacting systems.

Findings

Identification of a nonergodic extended phase with volume law entanglement but large fluctuations

Discontinuous jumps in entanglement entropy and particle fluctuations at the localization transition

Single parameter scaling near the transition point

Abstract

We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of non-interacting fermions where the entanglement entropy manifests a volume law (`extended'), but there are large fluctuations in the subsystem particle numbers (`nonergodic'). We argue such an intermediate phase scenario may continue holding even for the many-body localization in the presence of interactions as well. We find for many-body states in non-interacting 1d Aubry-Andre and 3d Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is sub-thermal but obeys the "volume law". In the vicinity of the localization transition we find that both the entanglement entropy and the particle number fluctuations obey a single parameter scaling. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition eventually to the usual ergodic many-body extended phase.