Localization in Interacting Fermionic Chains with Quasi-Random Disorder

We consider a system of fermions with a quasi-random almost-Mathieu disorder interacting through a many-body short range potential. We establish exponential decay of the zero temperature correlations, indicating localization of the interacting ground state, for weak hopping and interaction and almost everywhere in the frequency and phase; this extends the analysis in Mastropietro (Commun Math Phys 342(1):217–250, 2016) to chemical potentials outside spectral gaps. The proof is based on Renormalization Group and it is inspired by techniques developed to deal with KAM Lindstedt series.