Topological aspects of quantum many-body systems: Symmetry-protected ingappable phases and anomalies

在《物理》杂志上发表的《拓扑晶体绝缘子和拓扑晶体的有效场论》一书中。(Rev.B)，我们提出了一种获得拓扑晶体绝缘子有效场论的一般方法，其特征是通过界面对空间相关质量参数的响应来表征。在这些有效场论中，确定了各种量子化的拓扑项。特别是，我们的方法实现了降维过程，使得感兴趣的状态被平滑地变形为拓扑晶体，其在一般分类中用作相的代表状态。

In the work "Effective field theories of topological crystalline insulators and topological crystals" (published in Phys. Rev. B), we presented a general approach to obtain effective field theories for topological crystalline insulators, characterized by the responses to spatially dependent mass parameters with interfaces. Various quantized topological terms are identified within these effective field theories. In particular, our approach implements the dimensional reduction procedure such that the state of interest is smoothly deformed into a topological crystal, which serves as a representative state of a phase in the general classification.