Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain

I introduce two continuous transformations between the $S=1$ Heisenberg chain and the antiferromagnetic $S=1/2$ Heisenberg ladder. Both transformations couple diagonally situated {\it next nearest neighbor} $S=1/2$'s to form each $S=1$. Using the density matrix renormalization group, I demonstrate that the two systems are in the same phase. Furthermore, I find that the hidden topological long-range order characterizing the $S=1$ system is even stronger in the isotropic two-chain system.