Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
Mathematical Physics
2021-10-12 v3 Mesoscale and Nanoscale Physics
K-Theory and Homology
math.MP
Operator Algebras
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 counterpart.
Keywords
Cite
@article{arxiv.2009.07688,
title = {Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry},
author = {Matthias Ludewig and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2009.07688},
year = {2021}
}
Comments
23 pages, 4 figures; Added proofs in Section 1.4; further minor revisions; to appear in Comm. Math. Phys