  After Anderson's prediction of disorder-induced insulating behavior,
extensive work found no singularities in the density of states of localized
systems. However, Johri and Bhatt recently uncovered the existence of a
non-analyticity in the density of states near the band edge of non-interacting
systems with bounded disorder, in an energy range outside that captured by
previous work. Moreover, this feature marks the boundary of an energy range in
which the localization is sharply suppressed. Given strong current interest in
the effect of interactions on disordered systems, we explore here the effect of
a Hubbard $U$ interaction on this behavior. We find that in ensembles of small
systems a cusp in the density of states persists and continues to be associated
with a sharp suppression of the localization. We explore the origins of this
behavior and discuss its connection with many-body localization.
