Realizing Z₃ parafermionic edge modes in 1D fermionic lattices.

Parafermionic bound states, Z_n-symmetric generalizations of Majorana zero modes, can emerge as edge states in strongly correlated systems displaying fractionalized excitations. The non-trivial fractional nature of Z₃ parafermions, in particular, can be used to produce Fibonacci anyons, a key ingredient in a universal topological quantum computer. Due to their fractional nature, much of the theoretical work on Z₃ parafermions has relied on bosonization methods or parafermionic quasiparticles. In this contribution, we introduce a representation of Z₃ parafermions in terms of purely fermionic operators. 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 for realizing Z₃ parafermions in strongly interacting electronic systems.