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, $2{\log }_2(S+1)$, 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 a novel application of the edge state as a qubit for quantum computation.

4 pages, 2 figures

References in corpus (2)

• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Valence Bond Solids for Quantum Computation

Cited by in corpus (8)

• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Entanglement in an SU(n) Valence-Bond-Solid State
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
• Single-copy entanglement in a gapped quantum spin chain
• Block Spin Density Matrix of the Inhomogeneous AKLT Model
• Entanglement of Valence-Bond-Solid on an Arbitrary Graph