We consider a fermionic chain with an incommensurate external potential and a short range many body interaction.
In absence of interaction and for potentials large enough there is Anderson localization as follows from KAM-type results on the spectrum of the single particle Schroedinger equation. We show the persistence of localization even in presence of interaction in the interacting ground state, under suitable diophantine assumptions on the frequency and for suitable densities and weak interaction.
This is obtained by proving the convergence of the renormalized expansion for the correlations in the thermodynamic limit; such series have a small divisor problem somewhat similar to the one in Lindstedt series for KAM tori; however a major new difficulty is due to the presence of loops, which are absent in KAM classical problems.