Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model

Abstract

The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both $SU(2)$ spin and $SU(N_f)$ orbital 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 magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations [A. M. Tsvelik, Phys. Rev. Lett. \textbf{113} (2014) 066401]. From their quantum dimension they are identified as $SU(2)_{N_f}$ spin-$\frac{1}{2}$ anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a $Z_{N_f}$ parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.