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