PreprintCC0arXiv
Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap
Abstract
We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.
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BibTeX
@misc{becker2026dont,
title = {{Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap}},
author = {Simon Becker and Mengxuan Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25000},
eprint = {2609.25000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25000},
note = {CC0},
}
RIS
TY - UNPB
TI - Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap
AU - Simon Becker
AU - Mengxuan Yang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25000
UR - https://arxiv.org/abs/2609.25000
AB - We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.
ER -