Exact solution of an S=½ Heisenberg antiferromagnetic chain with long-ranged interactions

Abstract

The S=½ Heisenberg Hamiltonian H = ½ ^{N - 1}Σ_{n = 1}^NΣ_{m = 1} J_n σ_M · σ_m+n with J_n=J₀/sin² (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.