A Q-operator for the twisted XXX model

Korff, C. (2006) A Q-operator for the twisted XXX model. Journal of Physics A: Mathematical and General, 39(13), pp. 3203-3219. (doi: 10.1088/0305-4470/39/13/002)

Abstract

Taking the isotropic limit Δ → 1 in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bethe ansatz equations, one above, the other below the 'equator' of total spin S^z = 0. We discuss the limit to periodic boundary conditions at the end and explain how this construction relates to the trace functional introduced by Boos et al in the context of correlation functions on the infinite lattice. We also identify a special subclass of solutions to the quantum Wronskian and numerically verify them up to spin chains of ten sites. This special type of solutions might persist for longer chains.

• 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