title: String order in half-integer-spin antiferromagnetic Heisenberg chains.
abstract: We derive the extended string order parameter O(S) for antiferromagnetic Heisenberg chains with half-integer spin S in the valence-bond-solid picture. We obtain the analytic power-law scaling of O(S) versus the chain length L and show that O(S) scales at an extremely slow pace that decreases rapidly with growing spin magnitude. Furthermore, accurate numerical calculations show that the power-law scaling sets in only when L exceeds a characteristic length scale l(S) which increases very fast with growing S. Consequently, a pseudo-long-range string order exists in half-integer-spin Heisenberg chains. The implications of this result and its relationship to other topological features such as the end-chain states are discussed.
authors.affiliation: Department of Physics, University of Nevada, Las Vegas, NV 89154, USA.
authors.forename: Jizhong
authors.initials: J
authors.lastname: Lou
authors.forename: Shaojin
authors.initials: S
authors.lastname: Qin
authors.forename: Changfeng
authors.initials: C
authors.lastname: Chen