The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory

Chris Bourne, Alan L. Carey, Adam Rennie

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We prove the bulk-edge correspondence in K-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.

Original languageEnglish
Pages (from-to)1253-1273
Number of pages21
JournalLetters in Mathematical Physics
Volume105
Issue number9
DOIs
Publication statusPublished - 2015 Sep 6
Externally publishedYes

Keywords

  • Bulk-edge correspondence
  • KK-theory
  • quantum Hall effect
  • spectral triples

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory'. Together they form a unique fingerprint.

  • Cite this