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

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

2011-06-21

arxiv.org/abs/1106.4171v1

Physics

Mathematical Physics

15 pages, 2 figures

Scientific paper

We prove that Haag duality holds for cones in the toric code model. That is, for a cone Lambda, the algebra R_Lambda of observables localized in Lambda and the algebra R_{Lambda^c} of observables localized in the complement Lambda^c 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 N such that R_{Lambda_1} \subset N \subset R_{Lambda_2}. We demonstrate this by explicitly constructing N.

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