Abstract
It is shown that the description of the states of infiniteS=1/2 interacting spin systems with the Hamiltonian
can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in eachN-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spacesX −N =SL(N,H)/Sp(N) of negative curvature. The usual Bethe Ansatz for the XXX Heisenberg model corresponds to asymptotic forms of these wave functions at small values ofa −1 or large distances between spins turned over the ferromagnetic ground state.
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Communicated by N. Y. Reshetikhin
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Inozemtsev, V.I. The extended Bethe Ansatz for infiniteS=1/2 quantum spin chains with non-nearest-neighbor interaction. Commun.Math. Phys. 148, 359–376 (1992). https://doi.org/10.1007/BF02100866
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DOI: https://doi.org/10.1007/BF02100866