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

Abstract

We consider a fermionic many body system in $${\mathbb Z}^d$$ 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 $$T=0$$ 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.