Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

\(\mathbb{Z}_3\) Parafermionic Chain Emerging From Yang-Baxter Equation

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      We construct the 1D \(\mathbb{Z}_3\) parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the \(\mathbb{Z}_3\) parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the \(\mathbb{Z}_3\) parafermionic model is a direct generalization of 1D \(\mathbb{Z}_2\) Kitaev model. Both the \(\mathbb{Z}_2\) and \(\mathbb{Z}_3\) 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 \(\hat{H}_{123}\) based on Yang-Baxter equation. Different from the Majorana doubling, the \(\hat{H}_{123}\) holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, \(\omega\)-parity \(P\)(\(\omega=e^{{\textrm{i}\frac{2\pi}{3}}}\)) and emergent parafermionic operator \(\Gamma\), which are the generalizations of parity \(P_{M}\) and emergent Majorana operator in Lee-Wilczek model, respectively. Both the \(\mathbb{Z}_3\) parafermionic model and \(\hat{H}_{123}\) 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.

      Related collections

      Author and article information

      Journal
      2015-07-19
      2016-02-04
      1507.05269

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      Main text: 12 pages; Supplementary: 4 pages
      quant-ph math-ph math.MP

      Comments

      Comment on this article