  We study the S=1 square lattice Heisenberg antiferromagnet with spatially
anisotropic nearest neighbor couplings $J_{1x}$, $J_{1y}$ frustrated by a
next-nearest neighbor coupling $J_{2}$ numerically using the density-matrix
renormalization group (DMRG) method and analytically employing the
Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of
the anisotropy, within both methods we find quantum fluctuations to stabilize
the N\'{e}el ordered state above the classically stable region. Whereas SBMFT
suggests a fluctuation-induced first order transition between the N\'{e}el
state and a stripe antiferromagnet for $1/3\leq J_{1x}/J_{1y}\leq 1$ and an
intermediate paramagnetic region opening only for very strong anisotropy, the
DMRG results clearly demonstrate that the two magnetically ordered phases are
separated by a quantum disordered region for all values of the anisotropy with
the remarkable implication that the quantum paramagnetic phase of the spatially
isotropic $J_{1}$-$J_{2}$ model is continuously connected to the limit of
decoupled Haldane spin chains. Our findings indicate that for S=1 quantum
fluctuations in strongly frustrated antiferromagnets are crucial and not
correctly treated on the semiclassical level.
