Q-operators for the open Heisenberg spin chain

Frassek, Rouven; Szécsényi, István M.

Abstract

We construct Q-operators for the open spin-View the MathML source XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang–Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.

Citation

Frassek, R., & Szécsényi, I. M. (2015). Q-operators for the open Heisenberg spin chain. Nuclear Physics B, 901, 229-248. https://doi.org/10.1016/j.nuclphysb.2015.10.010

• Journal Article Type: Article
• Acceptance Date: Oct 22, 2015
• Publication Date: Dec 1, 2015
• Deposit Date: Nov 26, 2015
• Publicly Available Date: Mar 9, 2016
• Journal: Nuclear Physics B
• Print ISSN: 0550-3213
• Electronic ISSN: 1873-1562
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 901
• Pages: 229-248
• DOI: https://doi.org/10.1016/j.nuclphysb.2015.10.010
• Public URL: https://durham-repository.worktribe.com/output/1417748
• Related Public URLs: http://arxiv.org/abs/1509.04867