Multipolar topological field theories: Bridging higher order topological insulators and fractons
Multipolar topological field theories: Bridging higher order topological insulators and fractons
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DOI：
10.1103/physrevb.103.245128
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发表时间：
2019-09
影响因子：
3.7
通讯作者：
Yizhi You;F. Burnell;T. Hughes
中科院分区：
文献类型：
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作者：
Yizhi You;F. Burnell;T. Hughes
最近提出的两类新的拓扑相，即分形子和高阶拓扑绝缘体（HOTI），至少有表面上的相似之处。这些阶段的各种各样的建议要求一个通用的场论描述，捕捉其关键特征的物理现象。在这项工作中，我们构建拓扑多极响应理论，捕捉一些类的分形和高阶拓扑绝缘体的基本特征。值得注意的是，我们发现，尽管他们独特的对称结构，一些类的分形和HOTI可以连接通过其本质上相同的拓扑响应理论。更确切地说，我们提出了一个拓扑四极响应理论，描述了一个二维对称性丰富的分形相和相关的玻色子四极HOTI强的相互作用。这样的拓扑四极项封装了受保护的角电荷模式，并且对于HOTI，预测了具有分数偶极矩的异常边缘。在3D中，我们提出了一个偶极陈-西蒙斯理论与量化系数作为描述的响应的二阶HOTI窝藏手征铰链电流，和相关的分形相位。该理论正确地预测了铰链上的手征电流和表面上的反常偶极电流。我们将这些结果推广到更高的维度，揭示了一个家庭的多极陈-西蒙斯条款和相关的$\theta$-长期行动，可以通过降维或扩展从陈-西蒙斯理论。
Two new recently proposed classes of topological phases, namely fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field theory description that captures their key characteristic physical phenomena. In this work, we construct topological multipolar response theories that capture the essential features of some classes of fractons and higher order topological insulators. Remarkably, we find that despite their distinct symmetry structure, some classes of fractons and HOTIs can be connected through their essentially identical topological response theories. More precisely, we propose a topological quadrupole response theory that describes both a 2D symmetry enriched fracton phase and a related bosonic quadrupolar HOTI with strong interactions. Such a topological quadrupole term encapsulates the protected corner charge modes and, for the HOTI, predicts an anomalous edge with fractional dipole moment. In 3D we propose a dipolar Chern-Simons theory with a quantized coefficient as a description of the response of both second order HOTIs harboring chiral hinge currents, and of a related fracton phase. This theory correctly predicts chiral currents on the hinges and anomalous dipole currents on the surfaces. We generalize these results to higher dimensions to reveal a family of multipolar Chern-Simons terms and related $\theta$-term actions that can be reached via dimensional reduction or extension from the Chern-Simons theories.