Haag duality and the distal split property for cones in the toric code
arXiv:1106.4171 · doi:10.1007/s11005-012-0572-7
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.
15 pages, 2 figures, v2: extended introduction
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Cited by in corpus (15)
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