Fifth-neighbor spin-spin correlator for the anti-ferromagnetic   Heisenberg chain
  We study the generating function of the spin-spin correlation functions in the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without magnetic field. We have found its fundamental functional relations from those for general correlation functions, which originate in the quantum Knizhink-Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to n=6. Accordingly we could obtain the spin-spin correlator <S_j^z S_{j+k}^z> up to k=5. 
Jun Sato and Masahiro Shiroishi