Collective states of interacting D(D₃) non-Abelian anyons

We study the finite size spectrum of integrable quantum chains of interacting non-Abelian anyons constructed using the Drinfeld double of the dihedral group $D_3$. The gapless low energy modes are identified as the direct product of two conformal field theories which can be decomposed according to the residual symmetries of the chains subject to periodic boundary conditions.