  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.
