  We present exact diagonalization and density matrix renormalization group
results for the entanglement entropy of critical spin-1/2 XXZ chains. We find
that open boundary conditions induce an alternating term in both the energy
density and the entanglement entropy which are approximately proportional,
decaying away from the boundary with a power-law. The power varies with
anisotropy along the XXZ critical line and is corrected by a logarithmic
factor, which we calculate analytically, at the isotropic point. A heuristic
resonating valence bond explanation is suggested.
