ℤ3 parafermionic chain emerging from Yang-Baxter equation.
ℤ3 parafermionic chain emerging from Yang-Baxter equation.
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DOI：
10.1038/srep21497
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发表时间：
2016-02-23
影响因子：
4.6
通讯作者：
Ge ML
中科院分区：
文献类型：
--
作者：
Yu LW;Ge ML
我们基于Yang-Baxter方程的解构建了一维顺费米子模型，并用三种类型的费米子来表达该模型。结果表明，顺费米子链同时具有三重简并基态和非平凡的拓扑缠绕数。因此，顺费米子模型是一维 Kitaev 模型的直接推广。和 模型都可以从 Yang-Baxter 方程得到。另一方面，为了直观地展示顺费米三重代数，我们基于Yang-Baxter方程定义了一个新的三体哈密顿量。与马约拉纳倍增不同，它在每个能级上都具有三重简并性。三重简并性受到系统的两个对称算子 ω-宇称 P 和涌现的顺费子算子 Г 的保护，它们分别是宇称 PM 和涌现的 Majorana 算子在 Lee-Wilczek 模型中的推广。顺子模型 和 都可以被视为颜色空间中的 SU(3) 模型。与SU(2)的Majorana模型相比，SU(3)模型确实是Yang-Baxter方程产生的Majorana模型的推广。
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 PM 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.