Identifying Cn -symmetric higher-order topology and fractional corner charge using entanglement spectra
Identifying Cn -symmetric higher-order topology and fractional corner charge using entanglement spectra
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DOI：
10.1103/physrevb.101.115140
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发表时间：
2019-10
影响因子：
3.7
通讯作者：
Penghao Zhu;Kieran Loehr;T. Hughes
中科院分区：
文献类型：
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作者：
Penghao Zhu;Kieran Loehr;T. Hughes
研究了二维$Cn $对称二阶拓扑绝缘体的纠缠谱。我们表明，一些特征高阶拓扑可观量，例如，填充异常及其相关的分数角电荷，可以从原子和脆性TI的ES中确定。通过构造真实的空间中不同对称切割下Wannier轨道的构型与ES中被保护的能隙态数目之间的关系，我们用ES中被保护的能隙态数目来表示分数角电荷.结果表明，只要电子-电子相互作用保持$Cn $旋转对称性和电荷守恒对称性，我们的公式在电子-电子相互作用存在的情况下是稳健的.此外，我们还讨论了多体ES中可能存在的高阶拓扑签名。我们的方法允许识别某些类别的高阶拓扑结构，而不需要使用嵌套的威尔逊环或嵌套纠缠谱。
We study the entanglement spectrum (ES) of two-dimensional $C_{n}$-symmetric second-order topological insulators (TIs). We show that some characteristic higher order topological observables, e.g., the filling anomaly and its associated fractional corner charge, can be determined from the ES of atomic and fragile TIs. By constructing the relationship between the configuration of Wannier orbitals and the number of protected in-gap states in the ES for different symmetric cuts in real space, we express the fractional corner charge in terms of the number of protected in-gap states of the ES. We show that our formula is robust in the presence of electron-electron interactions as long as the interactions preserve $C_{n}$ rotation symmetry and charge-conservation symmetry. Moreover, we discuss the possible signatures higher order topology in the many-body ES. Our methods allow the identification of some classes of higher order topology without requiring the usage of nested Wilson loops or nested entanglement spectra.