Abstract
Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2) ∑ N j, k=1,j ≠ k P(j − k) σ j σ k , where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version.
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Inozemtsev, V.I. On the connection between the one-dimensionalS=1/2 Heisenberg chain and Haldane-Shastry model. J Stat Phys 59, 1143–1155 (1990). https://doi.org/10.1007/BF01334745
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DOI: https://doi.org/10.1007/BF01334745