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)

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Publisher's URL: http://dx.doi.org/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, Dr 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

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