Exact Analysis of Entanglement in Gapped Quantum Spin Chains

TL;DR

This paper provides an exact analytical study of entanglement entropy in gapped quantum spin chains, revealing its saturation value and linking it to edge states, with implications for quantum computation.

Contribution

It derives the exact entanglement entropy for valence-bond-solid states and connects it to edge states, offering new insights into quantum spin chains and potential quantum computing applications.

Findings

Entanglement entropy saturates at $2 \, \log_2 (S+1)$.

The entanglement entropy is explicitly calculated using the Schwinger boson representation.

Edge states can serve as qubits for quantum computation.

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.