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

The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1\mathrm{}}^{\mathrm{N}\mathrm{-}1}$${\mathcal{J}}_{\mathit{m}=1\mathrm{}}^{\mathit{N}}$${\mathit{J}}_{\mathit{n}}$${\mathrm{\sigma }}_{\mathit{m}}$⋅ ${\mathrm{\sigma }}_{\mathit{m}+\mathit{n}}$, with $J_n$=$J_0$/${\sin }^2$(nπ/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.