FINITE-LATTICE EXTRAPOLATIONS FOR A HALDANE-GAP ANTIFERROMAGNET

We present results of exact diagonalizations of the isotropic antiferromagnetic S = 1 Heisenberg chain by the Lanczos method, for finite rings of up to N = 22 sites. The Haldane gap G(N) and the ground-state energy per site e(N) converge, with increasing N, faster than a power law. By Vanden Broeck-Schwartz and Shanks transformations, the extrapolated values are G(infinity) = 0.41049(2) and e(infinity) = -1.401485(2). The spin-spin correlation function is well fit by exp(-r/xi)/square-root r with xi = 6.2.