Topological scaling behavior in antiferromagnetic Heisenberg chains with half-integer spin S>1/2

We study the topological string order parameter OS in antiferromagnetic Heisenberg chains with half-integer spin S>1/2. The OS is factorized into a product of an integer-spin component OS-1/2 and a phase factor of an effective spin-1/2 chain. This result is obtained in the valence-bond-solid (VBS) picture and is supported by density-matrix renormalization group calculations. We use a modified integer-spin component for its intuitive physical picture and simplified formalism. We show that the original and modified versions lead to identical scaling parameters for S=3/2 and 5/2 at all chain lengths and asymptotically (in the large-L limit) equivalent description for S>=7/2. These results provide justification for the use of the simplified OS in the study of topological scaling behavior in general half-integer-spin chains