Emergent Anyons in Exactly Solvable Discrete Models for Topological Phases in Two Dimensions

Anyons can emerge as collective excitations in models of topological phases. Exactly solvable discrete models that describe two-dimensional topological phases were proposed by Kitaev, and Levin and Wen respectively. I will present the explicit form of the operators that create and move fluxons (anyonic quasiparticles living at the plaquettes) in the Levin-Wen models. The exchange and exclusion statistics of these fluxons are studied. In particular, I will discuss the topological properties of Fibonacci anyons emerging in a particular Levin-Wen model.