Quasiparticle statistics from the ground state wave function

A topologically ordered phase is a gapped state that can be characterized by the topological entanglement entropy (TEE) $\gamma$ and by the properties of its excitations when moved around one another. The literatures contains two approaches to extract $\gamma$ from the computable ground-state entanglement entropy $S$, the Levin-Wen construction and the Kitaev-Preskill construction, in 2D. Both approaches can be modified so that they are usable to obtain the modular $\mathcal{S}$- and $\mathcal{U}$-matrices that encode the quasiparticle properties. We compare the two approaches and comment on the issue of corner contributions using the Kalmeyer-Laughlin state as an example.