Energy gap of theS=1 antiferromagnetic Heisenberg chain

Abstract

The S=1 isotropic antiferromagnetic Heisenberg chain is studied by exact diagonalizations using the Lanczös 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 Blöte. Further, it is found that a finite-size correction decays exponentially and the decay constant corresponds with the correlation length, which is about 5.