Edge states, entanglement entropy spectra and critical hopping couplings of anisotropic honeycomb lattices

摘要

For bipartite honeycomb lattices, we show that the Berry phase depends not only on the shape of the system but also on the hopping couplings. Using the entanglement entropy spectra obtained by diagonalizing the block Green's function matrices, the maximally entangled states with the eigenvalue λ_m=1/2 of the reduced density matrix are shown to have one-to-one correspondences to the zero-energy states of the lattice with open boundaries. The existence of these states depends on the Berry phase. For systems with finite bearded edges along the x-direction, we show that new maximally entangled states (zero-energy states) appear pair-by-pair when one increases the hopping coupling h over the critical values h_c's.