Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence

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

Cited by in corpus (6)

• Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations
• Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
• Edge-following topological states
• Spectral and Combinatorial Aspects of Cayley-Crystals
• Lieb-Schultz-Mattis Theorem and the Filling Constraint
• Fractional Quantum Numbers, Complex Orbifolds and Noncommutative Geometry