Many-body mobility edges in a one-dimensional system of interacting fermions

We study many-body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold potential h < h(c), the noninteracting system has single particle mobility edges (MEs) at +/- E-c while for h > h(c) all the single particle states are localized. We demonstrate that even in the presence of single particle MEs, interactions do not always delocalize the system and the interacting system can have MBL. Our numerical calculation of energy level spacing statistics, participation ratio in the Fock space, and Shannon entropy shows that for some regime of particle densities, even for h < h(c), many-body states at the top (with E > E-2) and the bottom of the spectrum (with E < E-1) remain localized, though states in the middle of the spectrum are delocalized. Variance of entanglement entropy (EE) also diverges at E-1,E-2, indicating a transition from MBL to a delocalized regime, though transitions from volume to area law scaling for EE and from thermal to nonthermal behavior occur inside the MBL regime much below E-1 and above E-2.