  We study the delocalization effect of a short-range repulsive interaction on
the ground state of a finite density of spinless fermions in strongly
disordered one dimensional lattices. The density matrix renormalization group
method is used to explore the charge density and the sensitivity of the ground
state energy with respect to the boundary condition (the persistent current)
for a wide range of parameters (carrier density, interaction and disorder).
Analytical approaches are developed and allow to understand some mechanisms and
limiting conditions. For weak interaction strength, one has a Fermi glass of
Anderson localized states, while in the opposite limit of strong interaction,
one has a correlated array of charges (Mott insulator). In the two cases, the
system is strongly insulating and the ground state energy is essentially
invariant under a twist of the boundary conditions. Reducing the interaction
strength from large to intermediate values, the quantum melting of the solid
array gives rise to a more homogeneous distribution of charges, and the ground
state energy changes when the boundary conditions are twisted. In individual
chains, this melting occurs by abrupt steps located at sample-dependent values
of the interaction where an (avoided) level crossing between the ground state
and the first excitation can be observed. Important charge reorganizations take
place at the avoided crossings and the persistent currents are strongly
enhanced around the corresponding interaction value. These large delocalization
effects become smeared and reduced after ensemble averaging. They mainly
characterize half filling and strong disorder, but they persist away of this
optimal condition.
