Non-Abelian statistics of vortices with multiple Majorana fermions
Non-Abelian statistics of vortices with multiple Majorana fermions
复制标题
具有多个马约拉纳费米子的涡旋的非阿贝尔统计
DOI：
10.1103/physrevb.86.014508
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发表时间：
2012
影响因子：
3.7
通讯作者：
Muneto Nitta
中科院分区：
文献类型：
--
作者：
Yuji Hirono;Shigehiro Yasui;Kazunori Itakura;Muneto Nitta
我们考虑涡旋的交换统计，每个涡旋捕获奇数 () 个马约拉纳费米子。我们假设涡旋中的费米子变换为 SO 群的向量表示。两个涡旋的交换被证明是非阿贝尔的，并且相应的算子被进一步分解为两部分：本质上相当于每个涡旋中具有单个马约拉纳费米子的涡旋交换算子的部分，以及代表考克塞特群的部分。在 的情况下已经发现了类似的分解，这里显示的结果是对任意奇数情况的推广。我们可以获得希尔伯特空间中交换算子的矩阵表示，该矩阵是通过使用由分离涡中捕获的马约拉纳费米子非局部定义的狄拉克费米子构造的。我们还表明，交换算子的分解在其矩阵表示中隐含着张量积结构。
We consider the exchange statistics of vortices, each of which traps an odd number () of Majorana fermions. We assume that the fermions in a vortex transform in the vector representation of the SOgroup. Exchange of two vortices turns out to be non-Abelian, and the corresponding operator is further decomposed into two parts: a part that is essentially equivalent to the exchange operator of vortices having a single Majorana fermion in each vortex, and a part representing the Coxeter group. Similar decomposition was already found in the case with, and the result shown here is a generalization to the case with an arbitrary odd. We can obtain the matrix representation of the exchange operators in the Hilbert space that is constructed by using Dirac fermions nonlocally defined by Majorana fermions trapped in separated vortices. We also show that the decomposition of the exchange operator implies tensor-product structure in its matrix representation.