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

C. Bourne, A. Rennie

研究成果: Article査読

19 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号16
ジャーナルMathematical Physics Analysis and Geometry
21
3
DOI
出版ステータスPublished - 2018 9月 1

ASJC Scopus subject areas

  • 数理物理学
  • 幾何学とトポロジー

フィンガープリント

「Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル