论文标题
Kitaev Honeycomb模型属属$ g \ geq 2 $
The Kitaev honeycomb model on surfaces of genus $g \geq 2$
论文作者
论文摘要
我们在任意较高的属表面上提出了基塔夫蜂窝晶格模型的结构。我们首先将基于Jordan-Wigner fermionization的模型的精确解决方案概括到具有$ g = 2 $的表面，然后将其用作基本模块，以将解扩展到任意属的晶格。我们通过在Abelian中计算模型的基态来演示我们的方法，这两者都将$ \ Mathbb {Z} _2 $ apeas和非亚伯利亚的ISING拓扑阶段和固定属的非 - 亚伯利亚式拓扑阶段，最高$ g = 6 $。我们在拓扑阶段验证了系统的预期基态退化，并进一步阐明了费米斯平价在阿贝尔阶段的作用。
We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan-Wigner fermionization to a surface with genus $g = 2$, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled $\mathbb{Z}_2$ phase and the non-Abelian Ising topological phase on lattices with the genus up to $g = 6$. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.
