Edge Z3 parafermions in fermionic lattices

Parafermion modes are non-Abelian anyons which were introduced as ZN generalizations of Z(2) Majorana states. In particular, Z(3) parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of the theoretical work on Z(3) parafermions has relied on bosonization methods or parafermionic quasiparticles. In this paper, we introduce a representation of Z(3) parafermions in terms of purely fermionic models. We establish the equivalency of a family of lattice fermionic models written in the basis of the t - J model with a Kitaev-like chain supporting free Z3 parafermionic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients towards realizing Z(3) parafermions in strongly interacting electronic systems.