Parafermionic Bound States in 1D Lattices of Spinful Fermions

Parafermions are emergent excitations, potentially relevant to topological quantum information, which generalize Majorana fermions. Many features of the latter are well captured by the seminal Kitaev model, a 1D lattice of spinless fermions with p-wave superconductivity. Here we present a non-trivial generalization of this model to the Ζ₄ parafermionic case. In particular, we identify and characterize a whole family of spinful fermionic Hamiltonians on a 1D lattice which support zero-energy parafermions, localized at the two ends of the system. Their properties are discussed as well as their robustness with respect to variations of parameters in the fermionic Hamiltonian. Our study provides a starting point to make a connection between fermionic lattice models and the low energy field theory description of 1D interacting systems featuring parafermionic bound states.