Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

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 function of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.