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Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice

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Abstract

The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single-particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk and has a non-vanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous.

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Acknowledgements

This work was supported by VILLIUM FONDEN through the QMATH Centre of Excellence (grant no. 10059) and a Villium Young Investigator Grant (grant no. 25452).

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Authors and Affiliations

  1. QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Alex Bols & Albert H. Werner

  2. NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark

    Albert H. Werner

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  1. Alex Bols
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  2. Albert H. Werner
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Correspondence to Alex Bols.

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Communicated by Alain Joye.

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Bols, A., Werner, A.H. Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice. Ann. Henri Poincaré 23, 549–554 (2022). https://doi.org/10.1007/s00023-021-01097-2

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