A Q-operator for the quantum transfer matrix

Details A Q-operator for the quantum transfer matrix A Q-operator for the quantum transfer matrix

2006-10-12

arxiv.org/abs/math-ph/0610028v2

J. Phys. A: Math. Gen. 40 (2007) 3749-3774

Physics

Mathematical Physics

20 pages, v2: some minor style improvements

Scientific paper

10.1088/1751-8113/40/14/002

Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed 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 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.

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