THE EXTENDED BETHE ANSATZ FOR INFINITE S=1/2 QUANTUM SPIN CHAINS WITH NONNEAREST-NEIGHBOR INTERACTION

It is shown that the description of the states of infinite S = 1/2 interacting spin systems with the Hamiltonian H(s) = - J/2 (j not-equal l,j,l is-an-element-of Z) SIGMA a2 sinh -2 a(j-l)(sigma(j)sigma(l)-1)/2 can be performed by studying the hyperbolic Calogero-Sutherland eigenvalue problem. The construction of multimagnon wave functions in each N-magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spaces X(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 of a-1 or large distances between spins turned over the ferromagnetic ground state.