Localization of Interacting Fermions in the Aubry-André Model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Many-Body Physics

Background:

• The study focuses on electrons in a one-dimensional lattice subjected to an incommensurate Aubry-André potential.
• The research operates in a regime where single-particle eigenstates are known to be localized.

Purpose of the Study:

• To rigorously establish the persistence of ground state localization.
• To investigate the impact of weak many-body interactions on this localization.
• To determine the conditions (chemical potentials) under which localization remains stable.

Main Methods:

• A quantum many-body extension of established methods for analyzing nearly integrable Hamiltonian systems was employed.
• The proof critically relies on the number-theoretic properties of the incommensurate frequency of the potential.
• The approach rigorously analyzes the stability of the system's ground state.

Main Results:

• Ground state localization is rigorously proven to persist.
• This persistence is demonstrated in the presence of weak many-body interactions.
• The stability of localization holds for almost all chemical potentials considered.

Conclusions:

• Weak interactions do not destroy ground state localization in this specific 1D system.
• The findings underscore the robustness of localization phenomena in disordered quantum systems.
• The number-theoretic properties of the potential are crucial for maintaining localization.