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

TL;DR

This paper proves that in a strongly disordered fermionic system on Zd with quasi-periodic disorder, correlations decay exponentially and the Drude weight vanishes at zero temperature, indicating Anderson localization.

Contribution

It demonstrates the vanishing of the Drude weight in interacting fermions with quasi-periodic disorder using advanced mathematical techniques, extending localization results to many-body systems.

Findings

Exponential decay of correlations at T=0

Vanishing Drude weight indicating localization

Application of Ward Identities, RG, and KAM methods

Abstract

We consider a fermionic many body system in Zd 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 Anderson localization in the ground state. The proof combines Ward Identities, Renormalization Group and KAM Lindstedt series methods.