Entanglement in a second order topological insulator on a square lattice

Abstract

In a $d$-dimensional topological insulator of order $d$, there are zero energy states on its corners which have close relationship with its entanglement behaviors. We studied the bipartite entanglement spectra for different subsystem shapes and found that only when the entanglement boundary has corners matching the lattice, exact zero modes exist in the entanglement spectrum corresponding to the zero energy states caused by the same physical corners. We then considered finite size systems in which case these corner states are coupled together by long range hybridizations to form a multipartite entangled state. We proposed a scheme to calculate the quadripartite entanglement entropy on the square lattice, which is well described by a four-sites toy model and thus provides another way to identify the higher order topological insulators from the multipartite entanglement point of view.

5 pages, 3 figures

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• Topological Multipartite Entanglement in a Fermi Liquid
• Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Quantized charge-pumping in higher-order topological insulators
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• Fermionic tensor networks for higher order topological insulators from charge pumping
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models