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We study the generating function of the spin-spin correlation functions inthe ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain withoutmagnetic field. We have found its fundamental functional relations from thosefor general correlation functions, which originate in the quantumKnizhink-Zamolodchikov equation. Using these relations, we have calculated theexplicit form of the generating functions up to n=6. Accordingly we couldobtain the spin-spin correlator <S_j^z S_{j+k}^z> up to k=5.Comment: 10 page

Fifth-neighbour spin–spin correlator for the anti-ferromagnetic Heisenberg chain