?3 parafermionic chain emerging from Yang-Baxter equation.

ABSTRACT: We construct the 1D ?3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ?3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ?3 parafermionic model is a direct generalization of 1D ?2 Kitaev model. Both the ?2 and ?3 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 H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ?-parity P [formula in text] and emergent parafermionic operator ?, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ?3 parafermionic model and H123 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.

SUBMITTER: Yu LW 

PROVIDER: S-EPMC4794089 | biostudies-other | 2016

REPOSITORIES: biostudies-other