Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

N. Kitanine (1) , Karol K. Kozlowski (2) , 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 | RAS - Steklov Mathematical Institute [Moscow]
4 LPTA - Laboratoire de Physique Théorique et Astroparticules

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.

Mots clés: Correlation functions; Integrable models; Bethe ansatz; Asymptotic analysis

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Physique des Hautes Energies - Théorie [hep-th]

N. Kitanine, Karol K. 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, 2009, 2009 (04), pp.P04003. ⟨10.1088/1742-5468/2009/04/P04003⟩. ⟨ensl-00308844v2⟩