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We prove Haag duality for conelike regions in the ground state representationcorresponding to the translational invariant ground state of Kitaev's quantumdouble model for finite abelian groups. This property says that if anobservable commutes with all observables localised outside the cone region, itactually is an element of the von Neumann algebra generated by the localobservables inside the cone. This strengthens locality, which says thatobservables localised in disjoint regions commute.  As an application we consider the superselection structure of the quantumdouble model for abelian groups on an infinite lattice in the spirit of theDoplicher-Haag-Roberts program in algebraic quantum field theory. We find that,as is the case for the toric code model on an infinite lattice, thesuperselection structure is given by the category of irreduciblerepresentations of the quantum double.

Haag duality for Kitaev's quantum double model for abelian groups