Many-Body Localization: Non-Ergodic Metal from Interacting Localized and Extended Orbitals
We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We establish a nonergodic metallic state as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the 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). Based on our numerical results, 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 that the nonergodic metal phase is extended is real space but localized in the many-body Hilbert space. As a phenomenological description, we propose a subset of local integral of motion for the nonergodic metal phase, which is consistent with existing numerical results.
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