Cheshire charge in (3+1)-dimensional topological phases
Cheshire charge in (3+1)-dimensional topological phases
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(3 1) 维拓扑相中的柴郡电荷
DOI：
10.1103/physrevb.96.045136
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发表时间：
2017
影响因子：
3.7
通讯作者：
C. Nayak
中科院分区：
文献类型：
--
作者：
D. Else;C. Nayak
我们发现，（3+1）维拓扑相位的物质一般支持圈激发拓扑简并。环带有“柴郡电荷”：拓扑电荷不是局部定义的拓扑电荷密度的积分。柴郡荷以前曾在非阿贝尔规范理论中讨论过，但我们表明，它是所有（3+1）-D拓扑相位（即使是那些从阿贝尔规范群构造）的一个通用功能。事实上，柴郡电荷与非平凡的三环编织密切相关。我们使用降维参数来计算与Dijkgraaf-Witten规范理论相关的（3+1）维拓扑相中圈激发的拓扑简并性。我们明确地构建膜运营商与这种激发在可溶性微观晶格模型在${\martbb {Z}_2}\times{\martbb {Z}_2}$ Dijkgraaf-Witten阶段，并推广到任意的膜网络模型。我们解释了为什么这些回路激发是编织融合2-范畴$Z（\mathbf{2 Vect}_G^{\omega}）$中的对象，从而支持2-范畴是（3+1）维拓扑相位的正确数学框架的假设。
We show that (3+1)-dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally-defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to non-trivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3+1)-dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in ${\mathbb{Z}_2}\times{\mathbb{Z}_2}$ Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category $Z(\mathbf{2Vect}_G^{\omega})$, thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3+1)-dimensional topological phases.