From single-particle to many-body mobility edges and the fate of overlapped spectra in coupled disorder models

Abstract: Mobility edge (ME) has played an essential role in disordered models. However, while this concept has been well established in disordered single-particle models, its existence in disordered many-body models is still under controversy. Here, a general approach based on coupling between extended and localized states in their overlapped spectra for ME is presented. We show that in the one-dimensional (1d) disordered single-particle models, all states are localized by direct coupling between them. However, in $d \ge 2$ disordered single-particle and 1d disordered many-body models, the resonant hybridization between these states in their overlapped spectra makes all states be extended, while these in the un-overlapped spectra are unchanged, leading to tunable MEs. We propose several models, including two disordered many-body spin models, to verify this mechanism. Our results establish a unified mechanism for MEs and demonstrate its universality in single-particle and many-body models, which opens an intriguing avenue for the realization and verification of MEs in many-body localization.