  We consider a quasi-one-dimensional system of spin-1 Heisenberg
antiferromagnetic chains in 2D and 3D hypercubic lattices with interchain
coupling $J$ and uniaxial single-ion anisotropy $D$. Using large scale
numerical simulations, we map out the $J-D$ phase diagram and investigate the
low lying excitations of the Haldane phase in the $J\ll1$ limit. We also
provide direct evidence that the Haldane phase remains a non-trivial symmetry
protected topological state for small but finite $J$.
