Full Dyon Excitation Spectrum in Generalized Levin-Wen Models

Understand

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two dimensional topological phases, it is relatively easy to describe only single fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations.

• To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper.
• We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex, to describe the internal charge degrees of freedom at the vertex.
• Then we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations.