Vanishing of Drude Weight in Interacting Fermions on $${\mathbb Z}^d$$ with Quasi-Periodic Disorder

We consider a fermionic many body system in Zd with short range interaction and quasi-periodic disorder. In the strong disorder regime assuming Diophantine condition on frequencies chemical potential, we prove at $T=0$ exponential decay of correlations vanishing Drude weight, signaling Anderson localization ground state. The proof combines Ward Identities, Renormalization Group KAM Lindstedt series methods.