Sep 1, 2018
Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases
Mathematical Physics Analysis and Geometry
- ,
- Volume
- 21
- Number
- 3
- Language
- English
- Publishing type
- Research paper (scientific journal)
- DOI
- 10.1007/s11040-018-9274-4
- Publisher
- Springer Netherlands
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.
- Link information
- ID information
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- DOI : 10.1007/s11040-018-9274-4
- ISSN : 1572-9656
- ISSN : 1385-0172
- ORCID - Put Code : 46667731
- SCOPUS ID : 85049107636