  We review the basic properties of the Haldane phase in spin-1 Heisenberg
antiferromagnetic chains, including its persistence in quasi-one-dimensional
geometries. Using large-scale numerical simulations, we map out the phase
diagram for a realistic model applicable to experimental Haldane compounds. We
also investigate the effect of different chain coupling geometries and confirm
a general mean field universality of the critical coupling times the
coordination number of the lattice. Inspired by the recent development of
characterization of symmetry protected topological states, of which the Haldane
phase of spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we
provide direct evidence that the quasi-one-dimensional Haldane phase is indeed
a non-trivial symmetry protected topological state.
