The double semion state in infinite volume

Abstract: We describe in a simple setting how to extract a unitary braided fusion category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. The structure of the unitary braided fusion category is given by F and R-symbols, which describe fusion and braiding of the anyons. We then construct the double semion state in infinite volume and extract the unitary braided fusion category describing its semion, anti-semion, and bound state excitations. We verify that this category corresponds to the representation category of the twisted quantum double of Z_2.