The Haldane Gap of the S=1 Heisenberg Antiferromagnetic Chain

The one-dimensional Heisenberg antiferromagnet of S = 1 spins is studied by the numerical diagonalization method based on the Lanczos algorithm. The Haldane gap of this system is numerically estimated from finite-size clusters under the twisted boundary condition up to the 30-site system. The finite-size results are analyzed by a convergence acceleration technique; the multistep procedure of the convergence acceleration is successfully carried out. The present estimate for the gap magnitude is more precise than the previously reported value obtained in a Lanczos-diagonalization study. It also agrees well with the result of a study based on the density matrix renormalization group calculation. In this study, we clarify that Lanczos-diagonalization calculations can sufficiently contribute to the precise estimation of an energy gap, although this method can treat only small clusters.