We present microscopic definitions of both the F symbol and R symbol - two pieces of algebraic data that characterize anyon excitations in (2+1)-dimensional systems. An important feature of our definitions is that they are operational; that is, they provide concrete procedures for computing these quantities from microscopic models. In fact, our definitions, together with known results, provide a way to extract a complete set of anyon data from a microscopic model, at least in principle. We illustrate our definitions by computing the F symbol and R symbol in several exactly solvable lattice models and edge theories. We also show that our definitions of the F symbol and R symbol satisfy the pentagon and hexagon equations, thereby providing a microscopic derivation of these fundamental constraints.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics