Composing topological domain walls and anyon mobility
Composing topological domain walls and anyon mobility
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DOI：
10.21468/scipostphys.15.3.076
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发表时间：
2022-08
期刊：
影响因子：
5.5
通讯作者：
Peter Huston;F. Burnell;Corey Jones;David Penneys
中科院分区：
文献类型：
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作者：
Peter Huston;F. Burnell;Corey Jones;David Penneys
分离2+1维拓扑有序相的拓扑畴壁可以用描述任意子的umtc之间的Witt等价来理解。然而，这幅图并没有提供一个框架，将多个域墙的堆栈分解为超选择扇区，即分解为不能被任何本地操作符混合的基本域墙类型。在拓扑顺序无异常的情况下，这样的分解可以用另一种框架来理解，从某种意义上说，它可以通过交换投影格模型来实现。通过将这些Witt等价置于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，用于计算并行拓扑域壁分解为不可分解的超选择扇区，将之前的理解扩展到具有非平凡异常的拓扑顺序。我们用畴壁粒子迁移率来描述超选择扇区，我们用隧道算子来形式化。拓扑阶的三范畴数学模型是在一个固定的酉模张量范畴上丰富的融合范畴的三范畴。
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.