ℤ3 parafermionic chain emerging from Yang-Baxter equation

We construct the 1D parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the parafermionic model i...

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Published in:Scientific reports 2016-02, Vol.6 (1), p.21497-21497, Article 21497
Main Authors: Yu, Li-Wei, Ge, Mo-Lin
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Language:English
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639/705
639/766/483/640
Algebra
Color
Humanities and Social Sciences
multidisciplinary
Phase transitions
Science
Science (multidisciplinary)
Symmetry
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description We construct the 1D parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the parafermionic model is a direct generalization of 1D Kitaev model. Both the and 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 based on Yang-Baxter equation. Different from the Majorana doubling, the holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω -parity P and emergent parafermionic operator Γ, which are the generalizations of parity P M and emergent Majorana operator in Lee-Wilczek model, respectively. Both the parafermionic model and 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.
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subjects 639/705
639/766/483/640
Algebra
Color
Humanities and Social Sciences
multidisciplinary
Phase transitions
Science
Science (multidisciplinary)
Symmetry
title ℤ3 parafermionic chain emerging from Yang-Baxter equation
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