(color online) Entanglement entropy for the ground state of the Heisenberg spin chain. (a) Converged entanglement entropy, S(∞) = S(n → ∞), as a function of L with D = 8 (squares) and 12 (circles), compared with the corresponding results obtained using a single MPS, S(n = 0) (up and down triangles), and those obtained with DMRG by keeping 1024 states (solid line). The horizontal axis is logarithmic. (b) Difference between S(n) and S(∞) as a function of n, which shows the convergence speed of S(n), for D = 8. The inset shows the size-dependence of the restarted Lanczos number n₀ at which the entanglement entropy arrives within 1% of its converged value, i.e., 1 − S(n₀)/S(∞) ≤ 1%.