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We use a generalized spin wave approach and large scale quantum Monte Carlo(QMC) simulations to study the quantum phase diagram and quasiparticleexcitations of the S=1 Heisenberg model with an easy-plane single-ionanisotropy in dimensions d=2 and 3. We consider two alternative approximationsfor describing the quantum paramagnetic state: the standard Holstein-Primakoffapproximation and a modified treatment in which the local constraint (finitedimension of the local Hilbert space) is enforced by introducing a Lagrangemultiplier. While both approximations produce qualitatively similar results,the latter approach is the only one that is in good quantitative agreement withthe quantum phase diagram and the quasiparticle dispersions obtained with QMC.This result is very important for low-temperature studies of quantumparamagnets in magnetic fields because it shows that a simple modification ofthe standard analytical approach should produce much better quantitativeagreement between theory and experiment.

Phase Diagram and Magnetic Excitations of Anisotropic Spin-One Magnets