Signatures of non-Abelian anyons in the thermodynamics of a perturbed SU(3)${}_{N_f}$ WZNW model

The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both SU(3) and SU(N${}_f$) degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and fields the anyons appear as zero energy modes localized at the massive kink excitations. From their quantum dimension they are identified as SU(3)${}_{N_f}$ anyons. The density of kinks (and anyons) can be controlled by external fields leading to the formation of collective states of these anyons described by various conformal embeddings of the SU(3)${}_{N_f}$ WZNW model for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.