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Twist defects and projective non-Abelian braiding statistics

机译：扭曲缺陷和非阿贝尔射影编织统计

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045130-1%It has recently been realized that a general class of non-Abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductor-ferromagnet domain walls in conventional quantum Hall states or topological insulators. In this paper, we begin by placing these defects within the broader conceptual scheme of extrinsic twist defects associated with symmetries of the topological state. We explicitly study several classes of examples, including Z_2 and Z_3 twist defects, where the topological state with N twist defects can be mapped to a topological state without twist defects on a genus g ∝ N surface. To emphasize this connection we refer to the twist defects as genons. We develop methods to compute the projective non-Abelian braiding statistics of the genons, and we find the braiding is given by adiabatic modular transformations, or Dehn twists, of the topological state on the effective genus g surface. We study the relation between this projective braiding statistics and the ordinary non-Abelian braiding statistics obtained when the genons become deconfined, finite-energy excitations. We find that the braiding is generally different, in contrast to the Majorana case, which opens the possibility for fundamentally novel behavior. We find situations where the genons have quantum dimension 2 and can be used for universal topological quantum computing (TQC), while the host topological state is by itself nonuniversal for TQC.
机译：045130-1％最近意识到，可以通过在常规量子霍尔态或拓扑绝缘体中引入非本征缺陷（例如晶格位错或超导体-铁磁畴壁）来在常规拓扑状态中创建一般类别的非阿贝尔缺陷。在本文中，我们首先将这些缺陷放入与拓扑状态对称性相关的外部扭曲缺陷的更广泛概念方案中。我们显式地研究了几类示例，包括Z_2和Z_3扭曲缺陷，其中具有N扭曲缺陷的拓扑状态可以映射到在g ∝ N属曲面上没有扭曲缺陷的拓扑状态。为了强调这种联系，我们将扭曲缺陷称为genons。我们开发了计算该基因子的射影非阿贝尔编织统计的方法，并且发现该编织是通过有效属g曲面上的拓扑状态的绝热模转换或Dehn扭曲给出的。我们研究了这种射影编织统计数据与普通的非阿贝尔编织统计数据之间的关系，这些普通的非阿贝尔编织统计数据是在有限元激发被限制的情况下获得的。我们发现，与马约拉纳案相反，编织大体上是不同的，这为根本上新颖的行为打开了可能性。我们发现了这样的情况，其中的子具有量子尺寸2，可以用于通用拓扑量子计算（TQC），而宿主拓扑状态本身对于TQC来说是非通用的。

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