Vanishing of Drude Weight in Interacting Fermions on ℤᵈ with Quasi-Periodic Disorder [Vanishing of Drude Weight in Interacting Fermions on Z(d) with Quasi-Periodic Disorder]

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