ON THE CONNECTION BETWEEN THE ONE-DIMENSIONAL S = 1/2 HEISENBERG CHAIN AND HALDANE-SHASTRY MODEL

Extra integrals of motion and the Lax representation are found for interacting spin systems with the Hamiltonian H = (J/2) ∑j, k=1, j ≠ kNP(j - k) σjσk, where one of the periods of the Weierstrass P function is equal to N. 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 of H corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version. © 1990 Plenum Publishing Corporation.