AI 中文总结
研究在广义Kitaev模型环面码相中把涡旋映射为任意子的理论，用马约拉纳费米子表示法，利用任意子融合规则等，适用于一般模型参数，能重现已知方案、推导不变性条件，通过计算说明理论，揭示不同映射与对称性破缺及拓扑序的关系。
AI 中文摘要
我们提出了一种全面的理论，用于在二维空间中，将Kitaev蜂窝模型推广的环面码相中的磁通激发（即涡旋）映射为电和磁粒子。我们的方法用马约拉纳费米子表示法构建，利用阿贝尔任意子的融合规则和费米子奇偶性的物理约束，适用于包括任何微扰极限在内的一般模型参数。我们不仅能重现二聚体极限下已知的映射方案，还推导出单个涡旋任意子种类不变性的条件。我们证明，在无涡旋和双涡旋扇区中不关闭费米子能隙的模型参数的任何连续演化，都不会改变任意子的映射，这使得在具有平凡陈数的单个相中，与不同映射相关的多个区域之间能够进行精确划分。我们通过对一些选定模型的大量计算来说明我们的理论，特别是在具有凯库勒结构的方八角晶格和蜂窝晶格上定义的模型。我们还证明，任意子的不同映射仍可表现出相同的弱对称性破缺，并进一步认为它们属于相同的对称性丰富拓扑序。
英文摘要
We present a comprehensive theory of mapping flux excitations, or vortices, to electric and magnetic particles in the toric code phases of generalizations of the Kitaev honeycomb model in two spatial dimensions. Our method, which is formulated with the Majorana fermion representation, utilizes the fusion rule of the Abelian anyons and the physical constraint on the fermion parity, and applies to generic model parameters including any perturbative limit. Not only are we able to reproduce the known mapping scheme in the dimer limit, we also derive the conditions for the invariance of anyon species of individual vortices. We prove that the mapping of anyons is left unchanged by any continuous evolution of model parameters that does not close the fermion gap in both the vortex-free and two-vortex sectors, which enables precise demarcations between multiple regimes associated with different maps within a single phase characterized by a trivial Chern number. We illustrate our theory via extensive computations for a number of selected models, in particular those defined on the square-octagon lattice and the honeycomb lattice with a Kekulé structure. We also demonstrate that distinct mappings of anyons can nevertheless exhibit the same weak symmetry breaking, and further argue that they belong to the same symmetry-enriched topological order.
Comments20+16 pages, 10+9 figures, 2+0 tables
