Classification and construction of higher-order symmetry-protected topological phases of interacting bosons
Classification and construction of higher-order symmetry-protected topological phases of interacting bosons
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DOI：
10.1103/physrevb.101.085137
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发表时间：
2018-09
影响因子：
3.7
通讯作者：
Alex Rasmussen;Yuan-Ming Lu
中科院分区：
文献类型：
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作者：
Alex Rasmussen;Yuan-Ming Lu
受最近发现的高阶拓扑绝缘体的启发，我们研究了它们在强相互作用玻色子中的对应物：“高阶对称保护拓扑(HOSPT)相”。D维空间中通常的(一阶)SPT相支持反常(d-1)维表面态，而d维HOSPT相的特征是(d-2)或更小的拓扑边界态，受某些整体对称性的保护，并且对无序具有很强的抵抗力。基于降维分析，我们证明了HOSPT相可以从低维的SPT相以一种保持相关的晶体对称性的方式构建。当总对称性是整体对称性群和晶体对称性群的直积时，我们可以用群上同调的kunneth公式对HOSPT相进行分类。基于一幅昆尼思公式的装饰磁区壁图，我们展示了如何系统地构造HOSPT相，并用二维和三维的许多例子演示了我们的构造。
Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: `higher-order symmetry protected topological (HOSPT) phases'. While the usual (1st-order) SPT phases in d spatial dimensions support anomalous (d-1)-dimensional surface states, HOSPT phases in d dimensions are characterized by topological boundary states of dimension (d-2) or smaller, protected by certain global symmetries and robust against disorders. Based on a dimensional reduction analysis, we show that HOSPT phases can be built from lower-dimensional SPT phases in a way that preserves the associated crystalline symmetries. When the total symmetry is a direct product of global and crystalline symmetry groups, we are able to classify the HOSPT phases using the Kunneth formula of group cohomology. Based on a decorated domain wall picture of the Kunneth formula, we show how to systematically construct the HOSPT phases, and demonstrate our construction with many examples in two and three dimensions.