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Understanding the metal-insulator transition in disordered many-fermionsystems, both with and without interactions, is one of the most challenging andconsequential problems in condensed matter physics. In this paper we addressthis issue from the perspective of the modern theory of the insulating state(MTIS), which has already proven to be effective for band and Mott insulatorsin clean systems. First we consider noninteracting systems with different typesof aperiodic external potentials: uncorrelated disorder (one-dimensionalAnderson model), deterministic disorder (Aubry-Andr\'e Hamiltonian and itsmodification including next-nearest neighbour hopping), and disorder withlong-range correlations (self-affine potential). We show how the many-bodylocalisation tensor defined within the MTIS may be used as a powerful probe todiscriminate the insulating and the metallic phases, and to locate thetransition point. Then we investigate the effect of weak repulsive interactionsin the Aubry-Andr\'{e} Hamiltonian, a model which describes a recent cold-atomsexperiment. By treating the weak interactions within a mean-field approximationwe obtain a linear shift of the transition point towards stronger disorder,providing evidence for delocalisation induced by interactions.

Kohn's localisation in disordered fermionic systems with and without interactions