Exact solution of anS=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

The S=1/2 Heisenberg Hamiltonian H=1/2Jₙ₌₁^N-1{J}ₘ₌₁NJₙ{{{σ}}}ₘ·{{{σ}}}ₘ₊ₙ$, with ${J}ₙ$=${J}₀$/${sin}²$(n{π}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.