Entanglement in a second-order topological insulator on a square lattice

¹ National Laboratory of Solid State Microstructures & School of Physics, Nanjing University Nanjing, 210093, China
² Collaborative Innovation Center of Advanced Microstructures, Nanjing University - Nanjing 210093, China

Received: 8 August 2018
Accepted: 28 November 2018

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 cases these corner states are coupled together by long-range hybridizations to form multipartite entangled states. 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.