Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

Korff, C. (2004) Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz. Journal of Physics A: Mathematical and General, 37(29), pp. 7227-7253. (doi: 10.1088/0305-4470/37/29/005)

Abstract

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues of the Q-operator is derived. A proof is given for states which contain up to three Bethe roots. Further evidence is provided by relating the findings to the six-vertex fusion hierarchy. For the XXZ spin-chain we analyse the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Korff, Professor Christian
• Authors: Korff, C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and General
• Publisher: Institute of Physics Publishing Ltd.
• ISSN: 0305-4470