论文标题
组成拓扑结构域墙和任何人的移动性
Composing topological domain walls and anyon mobility
论文作者
论文摘要
分隔2+1维拓扑阶的拓扑结构层壁可以从描述批量拓扑秩序中任何人的UMTC之间的智慧等价来理解。但是，此图片并不能为将多个域壁的堆栈分解为超选择扇区，即将任何本地操作员都无法混合的框架。在拓扑顺序无异常的情况下，可以使用替代框架来理解这种分解，从而可以通过通勤投影仪晶格模型来实现它。通过将这些威特等效置于3类潜在异常（2+1）d拓扑顺序的背景下，我们开发了一个框架，用于计算平行拓扑结构域壁的分解为不可塑性的超级选择扇区，将以前的理解扩展到以非平凡性异常的拓扑结构。我们以域壁颗粒的迁移率来表征超选择扇区，我们在隧道操作员方面对其进行了形式化。三类拓扑顺序的数学模型是富含固定统一模块化张量类别的融合类别的三类类别。
Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors - i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.
