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Heisenberg XXZ Model and Quantum Galilei Group
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The 1D Heisenberg spin model with 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 we 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 us to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.
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