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The \(XXZ\) model with Beraha values. (English) Zbl 0745.17020

The \(XXZ\) model of spin-1/2 chains with the quantum \(sl(2)\) symmetry is studied. First, it is shown how to construct quantum Young operators from Temperley-Lieb algebras. Then, in terms of the multiplication rules of the Temperley-Lieb algebras, the general rules for reducing the Hamiltonian equation to a set of coupled linear algebraic equations are obtained. The relations with the Bethe ansatz method are illustrated on two simple examples. The case of \(q\) equal to a root of unity is also considered.

MSC:

17B81 Applications of Lie (super)algebras to physics, etc.
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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