Random phase approximation for the 1D anti-ferromagnetic Heisenberg   model
  The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the symmetry unbroken phase. In a preliminary application of Self-Consistent RPA to finite size chains strongly improved results are obtained. 
A. Rabhi, P. Schuck and J. Da Providencia