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arXiv · 2610.08278

Localization Dichotomy for Hall Insulators on the Lattice

Alex Bols
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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.

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Alex Bols. 2026-10-06. Localization Dichotomy for Hall Insulators on the Lattice. https://arxiv.org/abs/2610.08278

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