A Microscopic Definition of the F-symbol

The theory of anyons is a powerful tool for studying interacting topological phases of matter in two spatial dimensions. In this approach, topological phases are characterized by the properties of their anyonic excitations --- in particular, the statistical phases associated with braiding or fusing anyons. Some of these statistical phases, however, are missing a precise definition that would allow for their computation from a microscopic Hamiltonian. In this talk, we will address this issue by giving a microscopic definition of the “F-symbol” --- one of the most poorly understood pieces of data that characterize anyons. We will show that our definition is consistent with known values of the F-symbol and can easily be applied to new systems as well.