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Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function

Jun Sato·Masahiro Shiroishi·Minoru Takahashi
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Abstract

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.

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Jun Sato, Masahiro Shiroishi, Minoru Takahashi. 2005-07-29. Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function. https://doi.org/10.1016/j.nuclphysb.2005.08.045

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