论文标题
$ 2+1 $ D的涡流统计数据
Braiding Statistics of Vortices in $2+1$d Topological Superconductors from Stacking
论文作者
论文摘要
$ 2+1 $尺寸的D类拓扑超导体具有$ \ mathbb {z} _ {16} $在存在互动的情况下的分类，其中$ 16 $不同的拓扑订单是$ 16 $不同的阶段。通过应用涉及任何凝结的费米子堆叠法，在有效的哈密顿量上描述了$ p+ip $ $超导体中涡流的拓扑相互作用，从而产生了$ 16 $的其他阶段，我们恢复了所有剩余阶段的编织系数以及$ \ mathbbbbbb c {z}} ^ $ fluand and $ \ mathbb c} {我们还将此堆叠法应用于时间反转类DIII超导体（本身可以从堆叠两个D类超导体）中获得，并恢复其$ \ Mathbb {z} _2 _2 $分类。
Class D topological superconductors in $2+1$ dimensions are known to have a $\mathbb{Z}_{16}$ classification in the presence of interactions, with $16$ different topological orders underlying the $16$ distinct phases. By applying the fermionic stacking law, which involves anyon condensation, on the effective Hamiltonian describing the topological interaction of vortices in the $p+ip$ superconductor, which generates the $16$ other phases, we recover the braiding coefficients of vortices for all remaining phases as well as the $\mathbb{Z}_{16}$ group law. We also apply this stacking law to the time-reversal invariant Class DIII superconductors (which can themselves be obtained from stacking two Class D superconductors) and recover their $\mathbb{Z}_2$ classification.
