  We have studied the effects of interactions on persistent currents in
half-filled and quarter-filled Hubbard models with weak and intermediate
strength disorder. Calculations are performed using a variational Gutzwiller
ansatz that describes short range correlations near the Mott transition. We
apply an Aharonov-Bohm magnetic flux, which generates a persistent current that
can be related to the Thouless conductance. The magnitude of the current
depends on both the strength of the screened disorder potential and the
strength of electron-electron correlations, and the Anderson localization
length can be extracted from the scaling of the current with system size. At
half filling, the persistent current is reduced by strong correlations when the
interaction strength is large. Surprisingly, we find that the disorder
potential is strongly screened in the large interaction limit, so that the
localization length grows with increasing interaction strength even as the
magnitude of the current is suppressed. This supports earlier dynamical mean
field theory predictions that the elastic scattering rate is suppressed near
the Mott transition.
