Entanglement Entropy of One-dimensional Gapped Spin Chains

We investigate the entanglement entropy (EE) of gapped S=1 and $S=1/2$ spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to the EE. For the $S=1/2$ dimerized Heisenberg chain, the EE of the sufficiently long chain is essentially explained by the localized $S=1/2$ effective spins on the boundaries. As for S=1, the effective spins are also $S=1/2$ causing a Kennedy triplet that yields a lower bound for the EE. In this case, the residual entanglement reduces substantially by a continuous deformation of the Heisenberg model to that of the AKLT Hamiltonian.