Highly precise numerical calculations using a variation of the Lanczos method devised by Paige were performed for s = 2 antiferromagnetic Heisenberg finite chains up to sizes N=28. Several interesting physical quantities, including the ground-state energy, the mass gap, and the spin-wave velocity, were computed and fitted for logarithmic finite-size corrections, as suggested by conformal invariance and Bethe ansatz calculations. A crossover size for a maximum of the spin-wave velocity is predicted for N-50, well above the current available sizes in a typical Lanczos simulation. A list

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A leading exponential dependence of the mass gap with size has been numerically tested in the whole axial-anisotropy region for the spin-XXZ antiferromagnetic chain. Exact results for finite chains are obtained via a modified Lanczos method due to Paige, allowing calculations up to X =28 spins. Our results show that the ground state is doubly degenerate and displays long-range order throughout the whole anisotropic regime.

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