Quenching the Haldane gap in spin-1 Heisenberg antiferromagnets

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 $J\ll 1$ limit. We also provide direct evidence that the Haldane phase remains a non-trivial symmetry protected topological state for small but finite $J$.