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arXiv:2610.08278

Localization Dichotomy for Hall Insulators on the Lattice

Alex Bols

Published Oct 6, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2610.08278

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