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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 andthe algebra R_{Lambda^c} of observables localized in the complement Lambda^cgenerate each other's commutant as von Neumann algebras. Moreover, we show thatthe distal split property holds: if Lambda_1 \subset Lambda_2 are two coneswhose boundaries are well separated, there is a Type I factor N such thatR_{Lambda_1} \subset N \subset R_{Lambda_2}. We demonstrate this by explicitlyconstructing N.

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