Annalen Der Physik Interplay Disorder-interaction in One Dimensional Quantum Models

We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization eeect in one dimensional disordered quantum models. The spin degrees of freedom are frozen 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 nite density of carriers. First, for two particles in a chain of length L, we establish a duality transformation mapping the behavior at weak U onto the behavior at strong U. For intermediate U, the mixing of the one body states and the interaction induced delocalization eeect are maximum. Furthermore, if L L1 (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time t1 necessary to propagate over L1, U de-favors the propagation. On the contrary, U favors a very slow delocalization after t1, characterized by a log(t) spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic ux decrease as a function of U for L < L1 and increase for L > L1. The changes of the curvatures can be described by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a nite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous connguration driven by the random potential (Anderson 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 there are many particles on a scale L1. The competition between electron-electron interaction and one body kinetic energy in disordered systems is a fundamental problem of permanent interest 1]. We denote by U; t and W the parameters characterizing the interaction, the one body kinetic energy and the uctuations of the random potential for a d-dimensional system of size 1