Diagrammatics for Bose condensation in anyon theories

Understand

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors.

• We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs).
• These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase.
• We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates.