论文标题
Chern数字在Kitaev Honeycomb模型和16倍的方式中的均等
Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
论文作者
论文摘要
在两个维度中，众所周知，根据\ mathbb {z} $的Chern Number $ν\，已知可以根据Chern号$ν\对$ \ mathbb {z} _2 $ gauge字段进行拓扑阶段。它的值mod 16指定了任何人激发的类型。在本文中，我们在Kitaev Honeycomb模型中研究了三角形涡旋配置（及其双重），并表明可以通过添加时间转换对称性术语来获得这16个阶段中的14个。缺少阶段为$ν= \ pm 7 $。更一般而言，我们证明，每个几何单元单元只能容纳Chern数字的任何周期性涡流配置，而奇数单元的数量也只能在其他情况下找到奇数。
In two dimensions, topological phases of free Majorana fermions coupled to a $\mathbb{Z}_2$ gauge field are known to be classified according to the Chern number $ν\in \mathbb{Z}$. Its value mod 16 specifies the type of anyonic excitations. In this paper, we investigate triangular vortex configurations (and their dual) in the Kitaev honeycomb model and show that fourteen of these sixteen phases can be obtained by adding a time-reversal symmetry-breaking term. Missing phases are $ν=\pm 7$. More generally, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases.
