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.