Localization in interacting fermionic chains with quasi-random disorder

TL;DR

This paper proves that interacting fermionic chains with quasi-random disorder exhibit localization of the ground state, demonstrated through exponential decay of correlations using Renormalization Group techniques.

Contribution

It extends previous localization results to systems with chemical potentials outside spectral gaps, employing advanced Renormalization Group methods.

Findings

Exponential decay of correlations in the ground state.

Localization persists for weak hopping and interactions.

Results hold for almost all frequencies and phases.

Abstract

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 \cite{M} to chemical potentials outside spectral gaps. The proof is based on Renormalization Group and is inspired by techniques developed to deal with KAM Lindstedt series.