Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

N. Kitanine 1 Karol Kozlowski 2 Jean Michel Maillet 2 N. A. Slavnov 3 Véronique Terras 2, 4
1 LPTM - 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 describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin correlation function of the XXZ Heisenberg spin-1/2 chain (with magnetic field) in the disordered regime as well as to the density-density correlation func- tion of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.
Keywords : Correlation functions Integrable models Bethe ansatz Asymptotic analysis
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N. Kitanine, Karol Kozlowski, Jean Michel Maillet, N. A. Slavnov, Véronique Terras. Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2009, 2009 (04), pp.P04003. ⟨10.1088/1742-5468/2009/04/P04003⟩. ⟨ensl-00308844v2⟩

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