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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 l2(ℤ2) ⊗ ℂn admits an exponentially localized Wannier basis if and only if P has vanishing Chern number.
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BibTeX
@misc{bols2026localization,
title = {{Localization Dichotomy for Hall Insulators on the Lattice}},
author = {Alex Bols},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08278},
eprint = {2610.08278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08278},
}
RIS
TY - UNPB
TI - Localization Dichotomy for Hall Insulators on the Lattice
AU - Alex Bols
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08278
UR - https://arxiv.org/abs/2610.08278
AB - 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(ℤ^2) ⊗ ℂ^n admits an exponentially localized Wannier basis if and only if P has vanishing Chern number.
ER -