Exact analysis of entanglement in gapped quantum spin chains

Abstract

We investigate the entanglement properties of the valence-bond-solid states with generic integer spin S. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, 2 log2 (S+1), is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose an application of the edge state as a qubit for quantum computation. © 2007 The American Physical Society.