Interplay disorder-interaction in one-dimensional quantum models

We show that the crossover from the weak interaction limit towards the stro ng interaction limit may be accompanied by a delocalization effect in one d imensional disordered quantum models. The spin degrees of freedom are froze n and the spatial wave functions remain symmetric or antisymmetric when the strength U of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state For a fin ite density of carriers. First, for two particles in a chain of length L, we establish a duality tra nsformation mapping the behavior at weak U onto the behavior at strong U. F or intermediate U, the mixing of the one body states and the interaction in duced delocalization effect are maximum. Furthermore, if L approximate to L -1 (the one particle localization length), the system becomes weakly chaoti c with critical spectral statistics. This weak chaos is related to the mult ifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time t(1) nece ssary to propagate over L-1, U de-favors the propagation. On the contrary, U favors a very slow delocalization after t(1), characterized by a log(t) s preading of the center of mass. Similarly, the curvatures of the energy lev els with respect to an enclosed magnetic flux decrease as a function of U f or L < L-1 and increase for L > L-1. The changes of the curvatures can be d escribed by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its ch ange under twisted boundary conditions. For a large disorder, a charge reor ganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (And erson insulator) and the homogeneous one driven by repulsive interactions ( Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when ther e are many particles on a scale L-1.