S(k) for Haldane-gap antiferromagnets: Large-scale numerical results versus field theory and experiment

The structure function S(k) for the s=1, Haldane-gap antiferromagnetic chain is measured accurately using the recent density-matrix renormalization-group method, with a chain length of 100. Excellent agreement with the nonlinear-σ-model prediction is obtained, both at k≊π, where a single-magnon process dominates, and at k≊0, where a two-magnon process dominates. We repeat our calculation with crystal-field anisotropy chosen to model Ni(${\mathrm{C}}_2$${\mathrm{H}}_8$${\mathrm{N}}_2$${)}_2$${\mathrm{NO}}_2$(${\mathrm{ClO}}_4$), obtaining good agreement with both field-theory predictions and recent experiments. Correlation lengths, gaps, and velocities are determined for both polarizations.