Haldane gap evolution in quasi-one-dimensional spin-1 Heisenberg antiferromagnets

We study a spatially anisotropic spin-1 antiferromagnetic Heisenberg model on simple cubic lattices that is equivalent to a system of coupled chains with interchain coupling $J$ and intrachain coupling set to unity. In the limit of uncoupled chains ($J=0$), the ground state is known to be gapped as per the Haldane conjecture. As the coupling is turned on, this gapped phase persists up to a critical value $J_c$ beyond which there is a quantum phase transition to the gapless N\'{e}el state with long range magnetic order. Using the stochastic series expansion quantum Monte Carlo method, we accurately determine $J_c$ and calculate the string order parameter in the gapped phase for $0