Physics of symmetry protected topological phases involving higher symmetries and its applications
Physics of symmetry protected topological phases involving higher symmetries and its applications
复制标题
DOI：
10.1103/physrevb.103.064426
复制
发表时间：
2020-08
影响因子：
3.7
通讯作者：
Chao-Ming Jian;Xiao-Chuan Wu;Yichen Xu;Cenke Xu
中科院分区：
文献类型：
--
作者：
Chao-Ming Jian;Xiao-Chuan Wu;Yichen Xu;Cenke Xu
我们讨论的物理结构和边界性质的各种保护的拓扑相位，涉及1-形式的对称性，从一个空间维度到四个空间维度（$4D$）。例如，包含1-形式对称性的$4d$ SPT态的原型三维（$3d$）边界态可以是无隙光子相位（量子电动力学）或由1-形式对称性丰富的有隙拓扑序;也就是说，这些拓扑序的环激发携带非平凡的1-形式对称性电荷。这项研究也服务于诊断异常的$3d$的物质状态。我们也将讨论具有1-形式对称性的SPT态与凝聚态系统之间的联系，例如在一个较低维度的量子二聚体模型。一个量子二聚体模型是否可以有一个平凡的带隙相位取决于它在一个更高的维度上对应的体态的性质。
We discuss physical constructions and the boundary properties of various symmetry-protected topological phases that involve 1-form symmetries from one spatial dimension to four spatial dimensions ($4d$). For example, the prototype three-dimensional ($3d$) boundary state of $4d$ SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries; that is, the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomalies of $3d$ states of matter. Connection between SPT states with 1-form symmetries and condensed-matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase depends on the nature of its corresponding bulk state in one higher dimension.