Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence
arXiv:1712.02952 · doi:10.4310/ATMP.2019.v23.n3.a5
Abstract
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models used in the Euclidean setting, a model for the bulk-boundary correspondence of fractional indices is proposed, guided by the geometry of hyperbolic boundaries.
27 pages, 3 figures, minor update, to appear in ATMP