  The antiferromagnetic Heisenberg spin chain with integer spin has short-range
magnetic order and an excitation energy gap above the ground state. This
so-called Haldane gap is proportional to the exchange coupling $J$ of the
Heisenberg chain. We discuss recent results about the spin dependence of the
Haldane gap and conjecture an analytical formula valid asymptotically for large
spin values. We next study the robustness of the edge states of the spin one
chain by studying by the DMRG algorithm a spin one ladder. We show that the
peculiar hidden topological order of the spin one chain disappears smoothly by
increasing the ladder rung coupling without any intervening phase transition.
This is evidence for the fragile character of the topological order of the spin
one chain.
