Phase diagram of the frustrated spatially-anisotropic S=1 antiferromagnet on a square lattice

We study the S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings J(1x) and 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 Neel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first-order transition between the Neel state and a stripe antiferromagnet for 1/3 <= J(1x)/J(1y)<= 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.