Title: Link invariants and anyon models
Speaker: Colleen Delaney (UC Santa Barbara)
Abstract: When the spacetime trajectories of anyons in (2+1)D topological phases of matter trace out knots or links, the probability amplitudes of these physical processes is given by a knot or link invariant. These invariants can be computed from the algebraic theory of anyons, which is given by a unitary modular tensor category (UMTC). An interesting question is when a family of UMTCs can be distinguished by the invariants they produce for a finite set of knots and links. I will report on some recent progress in this direction based on joint work with Alan Tran, Parsa Bonderson, Cesar Galindo, Eric Rowell, and Zhenghan Wang.
I will introduce UMTCs, explain how they give rise to link invariants, and interpret our results in the context of topological phases of matter and their application to quantum computation.
