Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
Mathematical Physics
2022-03-09 v1 math.MP
Quantum Physics
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 nonvanishing 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.
Keywords
Cite
@article{arxiv.2101.08603,
title = {Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice},
author = {Alex Bols and Albert H. Werner},
journal= {arXiv preprint arXiv:2101.08603},
year = {2022}
}