Effect of coulomb interaction on Anderson localization

We study the quantum mechanics of interacting particles in a disordered system, and in particular, what happens to Anderson localisation when interaction is taken into account. In the first part, one looks at the excited states of two particles in one dimension. For this model, it has been shown (Shepelyansky 1994) that a local repulsive interaction can partially destroy Anderson localisation. Here, we show that this model has similarities with the three-dimensional Anderson model at the metal-insulator transition. In particular, the maximum of rigidity obtained in the spectral statistics correspond to some intermediary statistics that cannot be described by random matrix theory neither by a Poisson statistics. The wave functions show a multifractal behaviour and the spreading of the center of mass of a wave packet is logarithmic in time. The second part deals with the ground state of a finite density of spinless fermions in two dimensions. After the scaling theory of localisation, it was commonly accepted that there was no metal in two dimensions. This idea has been challenged by the observation of a metal-insulator transition in low density electron gas (Kravchenko et al. 1994). We propose a scenario in which a metallic phase occurs between the Anderson insulator and the pinned Wigner crystal. This intermediate phase is characterized by an alignment of the local currents flowing in the system. (author)