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

Understand

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').