  We investigate many-body localization of interacting spinless fermions in a
one-dimensional disordered and tilted lattice. The fermions undergo
energy-dependent transitions from ergodic to Stark many-body localization
driven by the tilted potential, which are manifested by the appearance of
mobility edges between delocalized states and Stark many-body localized states
even when the disorder is weak. We can concretely diagnose these transitions
rather than crossovers by finite-size scaling of energy-level statistics.
Moreover, in the Stark many-body localization, the entanglement entropy obeys
the area law scaling, in analogy to that in the conventional many-body
localization.
