Localization of interacting fermions in the Aubry-Andre' model

TL;DR

This paper proves that ground state localization persists in a one-dimensional interacting fermion system with an Aubry-Andre' potential, using advanced mathematical methods to extend single-particle localization results to many-body interactions.

Contribution

It provides a rigorous proof of the stability of many-body localization in the Aubry-Andre' model with weak interactions, leveraging number theory and Hamiltonian stability techniques.

Findings

Ground state localization persists under weak interactions

Rigorous mathematical proof of many-body localization

Applicable to almost all chemical potentials

Abstract

We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak many-body interaction, for almost all the chemical potentials. The proof uses a quantum many body extension of methods adopted for the stability of tori of nearly integrable hamiltonian systems, and relies on number-theoretic properties of the potential incommensurate frequency.