  Analytical expressions of some of the spin-spin correlation functions up to
eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at
zero temperature without magnetic field are obtained. The key object of our
method is the generating function of two-point spin-spin correlators, whose
functional relations are derived from those for general inhomogeneous
correlation functions previously obtained from the quantum
Knizhnik-Zamolodchikov equations. We show how the generating functions are
fully determined by their functional relations, which leads to the two-point
spin-spin correlators. The obtained analytical results are numerically
confirmed by the exact diagonalization for finite systems.
