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We study Haldane's honeycomb lattice model and a bilayer generalizationthereof from the perspective of edge states, entanglement spectra, and Wannierfunction behavior. For the monolayer model, we obtain the zigzag edge statesanalytically, and identify the edge state crossing point $k_c$ with where the$f = 1/2$ entanglement occupancy and the half-odd-integer Wannier centersoccur. A continuous interpolation between the entanglement states and theWannier states is introduced. We then construct a bilayer model by Bernalstacking two monolayers coupled by interlayer hopping. We analyze a particularlimit of this model where an extended symmetry, related to inversion, ispresent. The band topology then reveals a break-down of the correspondencebetween edge and entanglement spectrum, which is analyzed in detail, andcompared with the inversion-symmetric Z2 topological insulators which show asimilar phenomenon.

Edge States, Entanglement Spectra, and Wannier Functions in Haldane's Honeycomb Lattice Model and its Bilayer Generalization