A Q-operator for the quantum transfer matrix

Korff, C. (2007) A Q-operator for the quantum transfer matrix. Journal of Physics A: Mathematical and Theoretical, 40(14), pp. 3749-3774. (doi: 10.1088/1751-8113/40/14/002)

Abstract

Baxter's concept of a Q-operator is generalized to the quantum transfer matrix of the XXZ spin-chain by employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature regime of the XXZ spin-chain are derived. For a non-vanishing magnetic field the previously known Bethe ansatz equations can be replaced by a system of quadratic equations which is an important advantage for numerical studies. For vanishing magnetic field and rational coupling values it is argued that the quantum transfer matrix exhibits a loop algebra symmetry closely related to the one of the classical six-vertex transfer matrix at roots of unity. The quantum-classical crossover is also discussed in terms of the eigenvalues of the Q-operator for a few special examples.

• 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 Theoretical
• ISSN: 1751-8113
• ISSN (Online): 1751-8121