Energy gap of theS=1 antiferromagnetic Heisenberg chain

The S=1 isotropic antiferromagnetic Heisenberg chain is studied by exact diagonalizations using the Lancz\"os algorithm. Energy gaps, structure factors at k={π}, and staggered susceptibilities at T=0 are calculated for finite rings up to N=16, and extrapolated to an infinite system using Shanks' transformation. The estimated energy gap is 0.411±{}0.001, which agrees with the result of Monte Carlo calculations by Nightingale and Bl\"ote. Further, it is found that a finite-size correction decays exponentially and the decay constant corresponds with the correlation length, which is about 5.