Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain

Frassek, Rouven

Abstract

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang–Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxterʼs Q-functions.

Citation

Frassek, R. (2015). Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain. Journal of Physics A: Mathematical and Theoretical, 48(29), Article 294002. https://doi.org/10.1088/1751-8113/48/29/294002

• Journal Article Type: Article
• Acceptance Date: May 19, 2015
• Publication Date: Jul 24, 2015
• Deposit Date: Jun 30, 2015
• Publicly Available Date: Mar 9, 2016
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 48
• Issue: 29
• Article Number: 294002
• DOI: https://doi.org/10.1088/1751-8113/48/29/294002
• Public URL: https://durham-repository.worktribe.com/output/1425641