  We prove the occurrence of Anderson localisation for a system of infinitely
many particles interacting with a short range potential, within the ground
state Hartree-Fock approximation. We assume that the particles hop on a
discrete lattice and that they are submitted to an external periodic potential
which creates a gap in the non-interacting one particle Hamiltonian. We also
assume that the interaction is weak enough to preserve a gap. We prove that the
mean-field operator has exponentially localised eigenvectors, either on its
whole spectrum or at the edges of its bands, depending on the strength of the
disorder.
