ℤ(3) parafermionic chain emerging from Yang-Baxter equation

We construct the 1D [Image: see text] parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the [Image: see text] parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the [Image: see text] parafermionic model is a direct generalization of 1D [Image: see text] Kitaev model. Both the [Image: see text] and [Image: see text] model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian [Image: see text] based on Yang-Baxter equation. Different from the Majorana doubling, the [Image: see text] holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P[Image: see text] and emergent parafermionic operator Γ, which are the generalizations of parity P(M) and emergent Majorana operator in Lee-Wilczek model, respectively. Both the [Image: see text] parafermionic model and [Image: see text] can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.