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, ${\mathrm{\Delta }}_{\mathrm{\parallel }}$ and ${\mathrm{\Delta }}_{\mathrm{\perp }}$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear σ model and a free-boson model. We also study the S=1/2 excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of S=1/2 spins coupled to the free bosons.