Edge $\mathbb{Z}_3$ parafermions in fermionic lattices

Abstract

Parafermions modes are non-Abelian anyons which were introduced as ZN generalizations of Z2 Majorana states. In particular, Z3 parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of theoretical work on Z3 parafermions has relied on bosonization methods or parafermionic quasiparticles. In this work, we introduce a representation of Z3 parafermions in terms of purely fermionic models operators in the t-J regime. We establish the equivalency of a family of lattice fermionic models written in the t − J model basis with a Kitaev-like chain supporting free Z3 parafermonic 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 Z3 parafermions in strongly interacting electronic systems.