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We consider interacting electrons in a one dimensional lattice with anincommensurate Aubry-Andre' potential in the regime when the single-particleeigenstates are localized. We rigorously establish persistence of ground statelocalization in presence of weak many-body interaction, for almost all thechemical potentials. The proof uses a quantum many body extension of methodsadopted for the stability of tori of nearly integrable hamiltonian systems, andrelies on number-theoretic properties of the potential incommensuratefrequency.

Localization of interacting fermions in the Aubry-Andre' model