Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra

Abstract

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.

arXiv comment11+4 pages, 8 figures in the main text, 3 figures in appendices

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• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological obstructed atomic limit by annihilating Dirac fermions
• Protected Gapless Edge States In Trivial Topology
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• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Higher-order topological insulator in cubic semiconductor quantum wells