$2+1$ d拓扑超导体中涡旋的堆垛编织统计
Braiding Statistics of Vortices in $2+1$d Topological Superconductors from Stacking
摘要：
已知$2+1$维度中的D类拓扑超导体在存在相互作用的情况下具有$\mathbb{Z}_{16}$分类，其中$16$不同的拓扑顺序是$16$不同相的基础。通过应用费米子堆积定律，其中包括任何子凝聚，在有效的哈密顿描述的拓扑相互作用的涡旋在$p+ip$超导体，产生的$16$其他阶段，我们恢复的编织系数的涡旋为所有剩余的阶段，以及$\mathbb{Z}_{16}$群定律。我们也将这种堆叠法应用于时间反演不变的DIII类超导体（它们本身可以通过堆叠两个D类超导体获得），并恢复它们的$\mathbb{Z}_2$分类。
英文摘要：
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.
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