二维中的拓扑序编织：实现Kitaev十六重方式的严格可解模型
Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
AI总结：
本研究构建了一族二维自旋1/2严格可解模型，通过一维路径Jordan-Wigner变换将其映射为耦合静态$\u2124_2$规范场的ν种Majorana费米子模型，总陈数为ν，验证了环面基态拓扑简并规律，可通过量子模拟实现Kitaev十六重任意子理论。
摘要：
研究人员构建了一族二维（2D）自旋1/2模型，用于实现Kitaev的任意子理论十六重方式。通过定义一条遍历所有格点的一维（1D）路径，并借助该1D路径进行Jordan-Wigner变换，研究发现这类自旋1/2模型等价于一个包含ν种Majorana费米子、且耦合静态$\u2124_2$规范场的模型。其中每种Majorana费米子对应一条携带陈数$\u2118=1$的能带，总陈数为$\u2118=ν$。研究表明，当ν为奇数（偶数）时，系统在环面上的基态具有三重（四重）拓扑简并。这些严格可解模型可通过量子模拟实现。
英文摘要：
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.
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