We study the delocalization effect of a short-range repulsive interaction onthe ground state of a finite density of spinless fermions in stronglydisordered one dimensional lattices. The density matrix renormalization groupmethod is used to explore the charge density and the sensitivity of the groundstate 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 andlimiting conditions. For weak interaction strength, one has a Fermi glass ofAnderson localized states, while in the opposite limit of strong interaction,one has a correlated array of charges (Mott insulator). In the two cases, thesystem is strongly insulating and the ground state energy is essentiallyinvariant under a twist of the boundary conditions. Reducing the interactionstrength from large to intermediate values, the quantum melting of the solidarray gives rise to a more homogeneous distribution of charges, and the groundstate energy changes when the boundary conditions are twisted. In individualchains, this melting occurs by abrupt steps located at sample-dependent valuesof the interaction where an (avoided) level crossing between the ground stateand the first excitation can be observed. Important charge reorganizations takeplace at the avoided crossings and the persistent currents are stronglyenhanced around the corresponding interaction value. These large delocalizationeffects become smeared and reduced after ensemble averaging. They mainlycharacterize half filling and strong disorder, but they persist away of thisoptimal condition.
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