Lan Tian, Wang Juven C, Wen Xiao-Gang
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5.
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Phys Rev Lett. 2015 Feb 20;114(7):076402. doi: 10.1103/PhysRevLett.114.076402. Epub 2015 Feb 18.
Gapped domain walls, as topological line defects between (2+1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which (2+1)D topological orders must have gapless edge modes, namely, which (1+1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix W, whose entries are the fusion-space dimensions W(ia), to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.
我们研究了作为（2 + 1）维拓扑有序态之间拓扑线缺陷的带隙畴壁。我们提供了确定带隙畴壁存在的简单标准，这些标准适用于阿贝尔和非阿贝尔拓扑序。我们的标准还确定了哪些（2 + 1）维拓扑序必须具有无隙边缘模式，即哪些（1 + 1）维全局引力反常确保无隙性。此外，我们引入了一个新的数学对象，隧穿矩阵W，其元素是融合空间维度W(ia)，用于标记不同类型的带隙畴壁。通过研究许多例子，我们发现有证据表明隧穿矩阵是对不同类型带隙畴壁进行分类的有力工具。由于带隙边界是体拓扑序与被视为平凡拓扑序的真空之间的带隙畴壁，我们的带隙畴壁理论包含了带隙边界理论。此外，我们推导了一个拓扑基态简并公式，该公式适用于具有带隙畴壁的任意可定向空间二维流形，包括具有带隙边界的封闭二维流形和开放二维流形。
