  We consider spinless fermions on a finite one-dimensional lattice,
interacting via nearest-neighbor repulsion and subject to a strong electric
field. In the non-interacting case, due to Wannier-Stark localization, the
single-particle wave functions are exponentially localized even though the
model has no quenched disorder. We show that this system remains localized in
the presence of interactions and exhibits physics analogous to models of
conventional many-body localization (MBL). In particular, the entanglement
entropy grows logarithmically with time after a quench, albeit with a slightly
different functional form from the MBL case, and the level statistics of the
many-body energy spectrum are Poissonian. We moreover predict that a quench
experiment starting from a charge-density wave state would show results similar
to those of Schreiber et al. [Science 349, 842 (2015)].
