论文标题
多极拓扑阶段中的高格式对称性
Higher-form Gauge Symmetries in Multipole Topological Phases
论文作者
论文摘要
在本文中，我们研究了多极拓扑绝缘子的现场理论方面。先前的研究表明，由于测量偶极子或子系统$ u（1）$ symmetries，这种系统自然而然地将其逐渐搭配到更高的张量规场。在这里，我们提出了使用电高型对称性的互补框架。我们利用这样一个事实，即测量1形式的电气对称性会导致一个2型仪表场，该电场自然而然地与延长的线状对象结合在一起：威尔逊线。在我们的背景下，威尔逊线是与系统的电偏振相关的电通线。这使我们能够为偶极子定义概括的2型PEIERLS的替代，这表明rank-2张量规范围$ a_ {ij} $的偏外成分可以作为晶格PEIERLS因子而产生，由背景防压2型2型领域产生。该框架具有直接的应用：（i）允许我们构建一个明显的拓扑四极响应动作，由dixmier-douady不变式给出 - 对2型量规场的Chern号的概括 - 在某些晶体符号的存在下，在四型尺度的情况下量化了四翼矩的量化； （ii）它允许对四极力矩的等级-2浆果相计算进行更清晰的解释； （iii）它允许证明用于偶极式连接系统的通用Lieb-Schultz-Mattis定理。
In this article we study field-theoretical aspects of multipolar topological insulators. Previous research has shown that such systems naturally couple to higher-rank tensor gauge fields that arise as a result of gauging dipole or subsystem $U(1)$ symmetries. Here we propose a complementary framework using electric higher-form symmetries. We utilize the fact that gauging 1-form electric symmetries results in a 2-form gauge field which couples naturally to extended line-like objects: Wilson lines. In our context the Wilson lines are electric flux lines associated to the electric polarization of the system. This allows us to define a generalized 2-form Peierls' substitution for dipoles that shows that the off-diagonal components of a rank-2 tensor gauge field $A_{ij}$ can arise as a lattice Peierls factor generated by the background antisymmetric 2-form gauge field. This framework has immediate applications: (i) it allows us to construct a manifestly topological quadrupolar response action given by a Dixmier-Douady invariant -- a generalization of a Chern number for 2-form gauge fields -- which makes plain the quantization of the quadrupole moment in the presence of certain crystal symmetries; (ii) it allows for a clearer interpretation of the rank-2 Berry phase calculation of the quadrupole moment; (iii) it allows for a proof of a generic Lieb-Schultz-Mattis theorem for dipole-conserving systems.
