Letters in Mathematical Physics

, Volume 101, Issue 3, pp 341–354

Haag Duality and the Distal Split Property for Cones in the Toric Code

Open Access
Article

Abstract

We prove that Haag duality holds for cones in the toric code model. That is, for a cone Λ, the algebra \({\mathcal{R}_{\Lambda}}\) of observables localized in Λ and the algebra \({\mathcal{R}_{\Lambda^c}}\) of observables localized in the complement Λc generate each other’s commutant as von Neumann algebras. Moreover, we show that the distal split property holds: if \({\Lambda_1 \subset \Lambda_2}\) are two cones whose boundaries are well separated, there is a Type I factor \({\mathcal{N}}\) such that \({\mathcal{R}_{\Lambda_1} \subset \mathcal{N} \subset \mathcal{R}_{\Lambda_2}}\) . We demonstrate this by explicitly constructing \({\mathcal{N}}\) .

Mathematics Subject Classification (2010)

81R15 (46L60, 81T05, 82B20) 

Keywords

Haag duality distal split property toric code 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute for Mathematics, Astrophysics and Particle PhysicsRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany

Personalised recommendations