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

Naaijkens, Pieter 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: 14 Feb 2020 16:45
URI: http://orca.cf.ac.uk/id/eprint/129630

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