Wire constructions of Abelian topological phases in three or more dimensions
Wire constructions of Abelian topological phases in three or more dimensions
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三个或多个维度的阿贝尔拓扑相的线结构
DOI：
10.1103/physrevb.93.195136
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发表时间：
2016
影响因子：
3.7
通讯作者：
C. Mudry
中科院分区：
文献类型：
--
作者：
Thomas Iadecola;T. Neupert;C. Chamon;C. Mudry
耦合线结构已被证明是有用的工具来表征阿贝尔和非阿贝尔拓扑状态的物质在两个空间维度。在许多情况下，他们的成功得到了大量其他理论工具的补充，可用于研究此类系统。然而，在三维空间中，人们对拓扑相位的了解要少得多。由于这种情况下的理论武器库较小，因此基于一维物理的线结构可以在发展对三维拓扑相的更深入的微观理解方面发挥有用的作用。在本文中，我们提供了一个全面的战略，基于几何安排的通勤投影仪的环面代码，产生和表征耦合线实现强相互作用的三维拓扑相位。我们展示了如何使用这种方法来构建点状和线状激发，并确定拓扑退化。我们还指出，如何进行微小的修改，机械已经开发的二维可以自然地应用于研究这些系统的表面状态，一个事实，具有影响的表面拓扑秩序的研究。最后，我们表明，战略开发的三维拓扑相位的建设推广容易到任意尺寸，大大扩展了现有的景观耦合线理论。在整个文件中，我们讨论了$\mathbb {Z}^{\，}_m $在三维和四维的拓扑秩序作为这种方法的一个具体例子，但方法本身并不限于这种类型的拓扑秩序。
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly-interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss $\mathbb{Z}^{\,}_m$ topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.