论文标题
基塔夫（Kitaev）的第六倍（Anyon理论）的微观模型
Microscopic models for Kitaev's sixteenfold way of anyon theories
论文作者
论文摘要
在两个维度中，由$ \ mathbb {z} _2 $量规理论描述的拓扑顺序与非零频谱Chern Number $ν$结合使用或弱相互作用的费米子均由$ν\分类； \ Mathrm {mod} \; 16 $，如Kitaev [Ann。物理。 321，2（2006）]。在这里，我们提供了一个系统，完整的微观模型，以实现这种所谓的Anyon理论的16倍方式。这些型号由满足Clifford代数的$γ$矩阵定义，享受全局$ \ mathrm {so}（ν）$对称性，并根据$ν$的奇偶校验生活在Square或Honeycomb Lattices上。我们表明，所有这些模型都可以通过使用Majorana表示，并通过计算Anyonic Quasiparticle和基态变性的拓扑旋转来表征拓扑顺序。讨论了$ν= 2 $和$ν= 3 $模型与具有Kugel-Khomskii-Type旋转轨道相互作用的材料的可能相关性。
In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $ν$ is classified by $ν\; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by $Γ$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(ν)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $ν$. We show that all these models are exactly solvable by using a Majorana representation and characterize the topological order by calculating the topological spin of an anyonic quasiparticle and the ground-state degeneracy. The possible relevance of the $ν=2$ and $ν=3$ models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.
