Large-scale geometry obstructs localization
Mathematical Physics
2022-09-23 v2 Mesoscale and Nanoscale Physics
K-Theory and Homology
math.MP
Operator Algebras
Abstract
We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an orthonormal basis of localized wavefunctions, with respect to any uniformly discrete set of localization centers. This is a robust result requiring neither spatial homogeneity nor symmetries, and applies to Landau levels of disordered quantum Hall systems on general Riemannian manifolds.
Cite
@article{arxiv.2204.12895,
title = {Large-scale geometry obstructs localization},
author = {Matthias Ludewig and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2204.12895},
year = {2022}
}
Comments
12 pages, Minor improvements made