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arXiv · 1106.4171

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

Pieter Naaijkens
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Abstract

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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Pieter Naaijkens. 2012-07-02. Haag duality and the distal split property for cones in the toric code. https://doi.org/10.1007/s11005-012-0572-7

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