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arXiv:solv-int/9902001 · Journal of Physics A Mathematical and General

Spontaneous polarization of the Kondo problem associated with the higher-spin six-vertex model

Nobuhisa Fukushima, Takeo Kojima

Published Aug 13, 1999• 0 citations
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Abstract

We study the multi-channel Kondo model associated with an integrable higher-spin analogue of the anti-ferroelectric six-vertex model, which is constructed by inserting spin ½ to spin 1 lines: We formulate the problem in terms of representation theory of quantum affine algebra [1]. We derive an exact formula for the spontaneous staggered polarization for our model, which corresponds to Baxter's formula [2] for the six-vertex model.

DOI
10.1088/0305-4470/32/34/304

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We study the multi-channel Kondo model associated with an integrable higher-spin analogue of the anti-ferroelectric six-vertex model, which is constructed by inserting spin ½ to spin 1 lines: We formulate the problem in terms of representation theory of quantum affine algebra [1]. We derive an exact formula for the spontaneous staggered polarization for our model, which corresponds to Baxter's formula [2] for the six-vertex model.
In this paper we continue the study of Q-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin R-matrix associated with the affine quantum algebra Uq(sl(2)ˆ). Taking a special limit in this R-matrix we obtained new formulas for the Q-operators acting in the tensor product of representation spaces with arbitrary complex spin. Here we use a different strategy and construct Q-operators as integral operators with factorized kernels based on the original Baxter's method used in the solution of the eight-vertex model. We compare this approach with the method developed in [1] and find the explicit connection between two constructions. We also discuss a reduction to the case of finite-dimensional representations with (half-)integer spins.
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