The double semion state in infinite volume

TL;DR

This paper constructs the double semion state in infinite volume and extracts its associated unitary braided fusion category, linking it to the twisted quantum double of Z_2, thus advancing understanding of anyonic excitations in quantum spin systems.

Contribution

It provides a simple method to derive the unitary braided fusion category from superselection sectors in a 2D quantum spin system, specifically for the double semion state.

Findings

The double semion state in infinite volume is explicitly constructed.

The associated unitary braided fusion category is identified with the twisted quantum double of Z_2.

The structure of anyonic excitations is characterized by F and R-symbols.

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.