论文标题
在二维中划分拓扑订单：Kitaev的十六倍方式的可解决模型
Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
论文作者
论文摘要
已经构建了一个二维（2D）Spin-1/2模型的家族，以实现Kitaev的16倍对任何理论的方式。在所有晶格站点上定义一维（1D）路径，并在1D路径的帮助下执行Jordan-Wigner转换，我们发现这种Spin-1/2模型等于具有$ν$ Majorana fermions的模型，并与静态的$ \ MathBb {z} _2 $ GAUGE couge couply相连。在这里，Majorana fermions的每个规格都产生了一个能量频段，该能量频段带有Chern Number $ \ Mathcal {C} = 1 $，产生了总计Chern Number $ \ Mathcal {C} =ν$。已经表明，当$ν$是一个奇数（偶数）时，地面状态在拓扑上是三（四个）的拓扑归化。这些确切的可解决模型可以通过量子模拟来实现。
A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner transformation with the help of the 1D path, we find that such a spin-1/2 model is equivalent to a model with $ν$ species of Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Here each specie of Majorana fermions gives rise to an energy band that carries a Chern number $\mathcal{C}=1$, yielding a total Chern number $\mathcal{C}=ν$. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when $ν$ is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.
