Equal-time correlations in Haldane-gap antiferromagnets

The S=1 antiferromagnetic Heisenberg chain both with and without single-ion anisotropy is studied. Using the recently proposed density-matrix renormalization-group technique of White, we calculate the energy gaps as well as several different correlation functions. The two gaps, Δ∥ and Δ⊥, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions …