  We perform variational studies of the interaction-localization problem to
describe the interaction-induced renormalizations of the effective (screened)
random potential seen by quasiparticles. Here we present results of careful
finite-size scaling studies for the conductance of disordered Hubbard chains at
half-filling and zero temperature. While our results indicate that
quasiparticle wave functions remain exponentially localized even in the
presence of moderate to strong repulsive interactions, we show that
interactions produce a strong decrease of the characteristic conductance scale
g* signaling the crossover to strong localization. This effect, which cannot be
captured by a simple renormalization of the disorder strength, instead reflects
a peculiar non-Gaussian form of the spatial correlations of the screened
disordered potential, a hitherto neglected mechanism to dramatically reduce the
impact of Anderson localization (interference) effects.
