Condensation of non-Abelian $SU(3)_{N_f}$ anyons in a one-dimensional fermion model

Abstract

The color excitations of interacting fermions carrying an $SU(3)$ color and $U(N_f)$ flavor index in one spatial dimension are studied in the framework of a perturbed $SU(3)_{N_f}$ Wess-Zumino-Novikov-Witten model. Using Bethe ansatz methods the low energy quasi-particles are found to be massive solitons forming $SU(3)$ quark and antiquark multiplets. In addition to the color index the solitons carry an internal degree of freedom with non-integer quantum dimension. These zero modes are identified as non-Abelian anyons satisfying $SU(3)_{N_f}$ fusion rules. Controlling the soliton density by external fields allows to drive the condensation of these anyons into various collective states. The latter are described by parafermionic cosets related to the symmetry of the system. Based on the numerical solution of the thermodynamic Bethe ansatz equations we propose a low temperature phase diagram for this model.