  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.
