Bethe's equation is incomplete for the XXZ model at roots of unity

Details Bethe's equation is incomplete for the XXZ model at roots of unity Bethe's equation is incomplete for the XXZ model at roots of unity

2000-09-19

arxiv.org/abs/cond-mat/0009279v2

J.Stat.Phys.103:647-678,2001

Physics

Condensed Matter

Statistical Mechanics

34 pages, 2 figures, references added

Scientific paper

10.1023/A:1010380116927

We demonstrate for the six vertex and XXZ model parameterized by $\Delta=-(q+q^{-1})/2\neq \pm 1$ that when q^{2N}=1 for integer $N\geq 2$ the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl_2 loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl_2 loop algebra can be used to complete this specification.

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