# 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.
Reference: Xiaopeng Li, J. H. Pixley, Dong-Ling Deng, S. Ganeshan, S. Das Sarma, Phys. Rev. B 93, 184204 (Editors' Suggestion)(2016); Phys. Rev. Lett 115, 186601 (2015)
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