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理论物理通讯：英文版

An Anyon Model in a Toric Honeycomb Lattice

Long Liang, 虞跃

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

我们在一个环形圆纹曲面的蜂房格子学习一个 anyon 模型。扎根的状态和低刺激 Kitaev 环形圆纹曲面的代码模型与那些与一致然后刺激服从相互的 semionic 统计。这个模型是有用的以一个更对称的方法理解 anyons 的环形圆纹曲面的代码。在另一方面，在这个环形圆纹曲面的蜂房模型之间有一种直接关系，一条边界经由 JordanWigner 转变在一个方形的格子联合 Ising 链数组。我们在低部门讨论在这二个模型之间的等价并且在一个常规费米子系统认识到这些 anyon 刺激。为在最后节的扎根的州的退化的分析能也被认为是我们的以前的工作的补充[Phys。A：数学。Theor。43 (2010 ) 105306 ] 。

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我们在一个环形圆纹曲面的蜂房格子学习一个 anyon 模型。扎根的状态和低刺激 Kitaev 环形圆纹曲面的代码模型与那些与一致然后刺激服从相互的 semionic 统计。这个模型是有用的以一个更对称的方法理解 anyons 的环形圆纹曲面的代码。在另一方面，在这个环形圆纹曲面的蜂房模型之间有一种直接关系，一条边界经由 JordanWigner 转变在一个方形的格子联合 Ising 链数组。我们在低部门讨论在这二个模型之间的等价并且在一个常规费米子系统认识到这些 anyon 刺激。为在最后节的扎根的州的退化的分析能也被认为是我们的以前的工作的补充[Phys。A：数学。Theor。43 (2010 ) 105306 ] 。
We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan—Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system. The analysis for the ground state degeneracy in the last section can also be thought of as a complementarity of our previous work [ Phys. A: Math. Theor. 43 (2010) 105306 ].
We propose a coupled-layer construction of a class of fracton topological orders in three spatial dimensions, which has no immobile excitations but is characterized by single quasiparticle excitations constrained in one-dimensional subspaces and dipole excitations mobile in two-dimensional subspaces. The simplest model is obtained by stacking and coupling layers of the two-dimensional toric codes on the square lattice and can be exactly solved in the strong-coupling limit. The resulting subdimensional excitations are understood as a consequence of anyon pair condensation induced by the coupling between layers. We also present generalizations of the construction for layers of the Kitaev-honeycomb models, the ZN{Z}_{N}ZN​ toric codes, and the toric codes and the doubled semion models on the honeycomb lattice.
The honeycomb lattice Kitaev model H K with two kinds of Wen–Toric-code four-body interactions H W T is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan–Wigner transformation is obtained as a special case of this formula. The model H K + H W T is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.