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We consider a fermionic many body system in Zd with a short range interactionand quasi-periodic disorder. In the strong disorder regime and assuming aDiophantine condition on the frequencies and on the chemical potential, weprove at $T=0$ the exponential decay of the correlations and the vanishing ofthe Drude weight, signaling Anderson localization in the ground state. Theproof combines Ward Identities, Renormalization Group and KAM Lindstedt seriesmethods.

Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder