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

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arxiv 1712.02952 v4 pith:MVZSVPAB submitted 2017-12-08 cond-mat.str-el hep-thmath-phmath.MPmath.OA

Varghese Mathai , Guo Chuan Thiang This is my paper · ORCID
classification cond-mat.str-elhep-thmath-phmath.MPmath.OA
keywords fractionalhyperbolicbulk-boundarycorrespondencegeometryindicesphasesplane
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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.

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  1. Edge-following topological states

    math-ph 2019-08 conditional novelty 7.0 of 10

    Chern insulator boundary states are proven to follow corners and rough edges because the topological exponential map maps the bulk Chern class to a nonvanishing edge-translation invariant.

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