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For a bipartite honeycomb lattice, we show that the Berry phase depends notonly on the shape of the system but also on the hopping couplings. Using theentanglement entropy spectra obtained by diagonalizing the block Green'sfunction matrices, the maximal entangled state with the eigenvalue$\lambda_m=1/2$ of the reduced density matrix is shown to have one-to-onecorrespondence to the zero energy states of the lattice with open boundaries,which depends on the Berry phase. For the systems with finite bearded edgesalong $x$-direction we find critical hopping couplings: the maximal entangledstates (zero-energy states) appear pair by pair if one increases the hoppingcoupling $h$ over the critical couplings $h_c$s.

Edge State, Entanglement Entropy Spectra and Critical Hopping Coupling of Anisotropic Honeycomb Lattice