Localization Dichotomy for Hall Insulators on the Lattice

Abstract

We prove the localization dichotomy conjecture for non-periodic Hall insulators on the lattice. That is, we show that the Fermi projector $P$ of a gapped exponentially local Hamiltonian on $l^2({\mathbb{Z}}^2)\otimes {\mathbb{C}}^n$ admits an exponentially localized Wannier basis if and only if $P$ has vanishing Chern number.

arXiv comment40 pages, 2 figures