Haag duality and the distal split property for cones in the toric code

Naaijkens, Pieter ORCID: https://orcid.org/0000-0001-5670-243X 2012. Haag duality and the distal split property for cones in the toric code. Letters in Mathematical Physics 101 (3) , p. 341. 10.1007/s11005-012-0572-7

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Abstract

We prove that Haag duality holds for cones in the toric code model. That is, for a cone Λ, the algebra RΛ of observables localized in Λ and the algebra RΛc 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 Λ1⊂Λ2 are two cones whose boundaries are well separated, there is a Type I factor N such that RΛ1⊂N⊂RΛ2 . We demonstrate this by explicitly constructing N

Item Type:	Article
Schools:	Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	0377-9017
Last Modified:	07 Nov 2022 09:35
URI:	https://orca.cardiff.ac.uk/id/eprint/129630

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