Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain
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 Baxter's Q-functions.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2015
- DOI:
- 10.1088/1751-8113/48/29/294002
- arXiv:
- arXiv:1504.04501
- Bibcode:
- 2015JPhA...48C4002F
- Keywords:
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- Mathematical Physics;
- Condensed Matter - Statistical Mechanics;
- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 20 pages