The Double Semion State in Infinite Volume

We describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. We extract from this category its fusion ring as well as its F and R-symbols. We then construct the double semion state in infinite volume and extract the braided tensor category describing its semion, anti-semion, and bound state excitations. We verify that this category is equivalent to the representation category of the twisted quantum double \(\mathcal {D}^{\phi }(\mathbb {Z}_2)\) ${\mathcal{D}}^{\varphi }({\mathbb{Z}}_2)$ .