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Master equation for spin-spin correlation functions of the XXZ chain

N. Kitanine 1 Jean Michel Maillet 2 N. A. Slavnov 3 Véronique Terras 2, 4
1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 SMI - Steklov Mathematical Institute
4 LPTA - Laboratoire de Physique Théorique et Astroparticules
Abstract : We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the one hand to the previously obtained multiple integral formulas for the spin-spin correlation functions and on the other hand to their expansion in terms of the form factors of the local spin operators. Hence, it provides a direct analytic link between these two representations of the correlation functions and a complete re-summation of the corresponding series. The master equation method also allows one to obtain multiple integral representations for dynamical correlation functions.
Keywords : Quantum integrable models Correlation functions Bethe ansatz spin chain
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00266563
Contributor : Jean Michel Maillet <>
Submitted on : Monday, March 24, 2008 - 10:43:23 PM
Last modification on : Tuesday, July 14, 2020 - 11:14:04 AM

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N. Kitanine, Jean Michel Maillet, N. A. Slavnov, Véronique Terras. Master equation for spin-spin correlation functions of the XXZ chain. Nuclear Physics B, Elsevier, 2005, 712 (3), pp.600-622. ⟨10.1016/j.nuclphysb.2005.01.050⟩. ⟨ensl-00266563⟩

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