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Type: Journal article
Title: Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
Author: Ludewig, M.
Thiang, G.C.
Citation: Communications in Mathematical Physics, 2021; 386(1):87-106
Publisher: Springer
Issue Date: 2021
ISSN: 0010-3616
Statement of
Matthias Ludewig, Guo Chuan Thiang
Abstract: We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the edge states of hyperbolic quantum Hall Hamiltonians completely fill up the gaps between Landau levels, just like those of the Euclidean counterparts.
Rights: © The Author(s) 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
DOI: 10.1007/s00220-021-04068-0
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