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We investigate many body localization in the presence of a single particlemobility edge. By considering an interacting deterministic model with anincommensurate potential in one dimension we find that the single particlemobility edge in the noninteracting system leads to a many body mobility edgein the corresponding interacting system for certain parameter regimes. Usingexact diagonalization, we probe the mobility edge via energy resolvedentanglement entropy (EE) and study the energy resolved applicability (orfailure) of the eigenstate thermalization hypothesis (ETH). Our numericalresults indicate that the transition separating area and volume law scaling ofthe EE does not coincide with the non-thermal to thermal transition.Consequently, there exists an extended non-ergodic phase for an intermediateenergy window where the many body eigenstates violate the ETH while manifestingvolume law EE scaling. We also establish that the model possesses an infinitetemperature many body localization transition despite the existence of a singleparticle mobility edge. We propose a practical scheme to test our predictionsin atomic optical lattice experiments which can directly probe the effects ofthe mobility edge.

Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge