Heisenberg XXZ model and quantum Galilei group

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Abstract
The 1D Heisenberg spin model with an anisotropy of the XXZ type is analysed in terms of the symmetry given by the quantum Galilei group Gamma q(1). For a chain with an infinite number of sites the authors show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. In this case the Gamma q(1) symmetry provides a description naturally compatible with the Bethe ansatz. The recurrence relations determined by Gamma q(1) permit one to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.
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