We aim at presenting a simple context where known results on Anderson localization for systems of non-interacting particles in a random environment may be extended to systems with weak interactions.
Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit single particle localization, suitably defined as exponential decay of eigenfunction correlators for the effective Hamiltonian. Our result holds in any dimension in the regime of large disorder and at any disorder in the one dimensional case. A constructive criterion for Green's function decay will also be discussed. (Based on joint work with Jeffrey Schenker).