Full dyon excitation spectrum in extended Levin-Wen models

The Levin1000-0ptWen models are discrete gauge models, leading to intrinsic two-dimensional topological order. To incorporate the charge degrees of freedom at vertices for excited states, the authors propose to extend the Levin-Wen model by adding on one of the edges of each vertex a tail, labeled by its string type. They show that the local operators associated with the dyonic excitations obey the so1000-0ptcalled tube algebra. When the input data is associated with a finite or quantum group, any dyon species is described by three quantum numbers: charge, fluxon type, and twist.