Talk Title: Edge State, Entanglement Entropy Spectra and Critical
Hopping Coupling of Anisotropic Honeycomb Lattice For a bipartite honeycomb lattice, 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 maximal entangled state with the
eigenvalue $\lambda_m=1/2$ of the reduced density matrix is shown to have
one-to-one correspondence to the zero energy states of the lattice with open
boundaries, which depends on the Berry phase. For the systems with finite bearded edges along
$x$-direction we find critical hopping couplings: the maximal entangled states
(zero-energy states) appear pair by pair if one increases the hopping coupling
$h$ over the critical couplings $h_c$s. |