Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases

C. Bourne, A. Rennie

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable C-algebra by a twisted ℝd-action. The spectral triple allows us to employ the non-unital local index formula to obtain the higher Chern numbers in the continuous setting with complex observable algebra. In the case of the crossed product of a compact disorder space, the pairing can be extended to a larger algebra closely related to dynamical localisation, as in the tight-binding approximation. The Kasparov module allows us to exploit the Wiener–Hopf extension and the Kasparov product to obtain a bulk-boundary correspondence for continuous models of disordered topological phases.

Original languageEnglish
Article number16
JournalMathematical Physics Analysis and Geometry
Volume21
Issue number3
DOIs
Publication statusPublished - 2018 Sep 1

Keywords

  • Crossed product
  • Kasparov theory
  • Topological states of matter

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

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