二维拓扑超导体的精确可解模型
Exactly Solvable Model for Two Dimensional Topological Superconductor
摘要：
本文提出了一个具有时间反演对称性保护的螺旋Majorana边模的二维拓扑超导体的精确可解模型。我们的构造是基于装饰畴壁的思想，并利用二维晶格上的Kasteleyn取向，这是用于构造具有$Z_2$对称性的对称保护费米子相的参考文献\onlinecite{Tarantino2016,Ware2016}。通过用自旋Majorana链修饰时间反转畴壁，我们能够构造一个具有零相关长度基态波函数的可交换投影哈密顿量，实现了强相互作用的二维拓扑超导体.从我们的构造中可以看出，费米子的$T^2=-1$变换规则对于这种非平凡相的存在是至关重要的;使用$T^2=1$，我们的构造不起作用。
英文摘要：
In this paper, we present an exactly solvable model for two dimensional topological superconductor with helical Majorana edge modes protected by time reversal symmetry. Our construction is based on the idea of decorated domain walls and makes use of the Kasteleyn orientation on a two dimensional lattice, which was used for the construction of the symmetry protected fermion phase with $Z_2$ symmetry in Ref. \onlinecite{Tarantino2016,Ware2016}. By decorating the time reversal domain walls with spinful Majorana chains, we are able to construct a commuting projector Hamiltonian with zero correlation length ground state wave function that realizes a strongly interacting version of the two dimensional topological superconductor. From our construction, it can be seen that the $T^2=-1$ transformation rule for the fermions is crucial for the existence of such a nontrivial phase; with $T^2=1$, our construction does not work.
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