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Gaplessness of Landau Hamiltonians on Hyperbolic Half-planes via Coarse Geometry

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Ludewig, Matthias ; Thiang, Guo Chuan
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Date of publication of this fulltext: 22 Apr 2021 08:40


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.

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