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Fifth-neighbour spin-spin correlator for the anti-ferromagnetic Heisenberg chain. (English) Zbl 1064.82008

Summary: 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 Knizhnik–Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to \(n = 6\). Accordingly we can obtain the spin–spin correlator \(\langle S^z_jS^z_{j+k}\rangle\) up to \(k = 5\).

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D40 Statistical mechanics of magnetic materials
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