The Algebraic Bethe Ansatz and the Correlation Functions of the Heisenberg Magnet

Jean Michel Maillet

Никита Андреевич Славнов

Rafael Hernández, Juan Miguel Nieto García

N Kitanine, Karol Kajetan Kozlowski, Jean Michel Maillet +2 more

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.

N Kitanine, Jean Michel Maillet, Slavnov, N. A. +1 more

We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz framework, and leads to a multiple integral representation of the dynamical correlation functions. We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral. Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.

S. Belliard, S Pakuliak, E. Ragoucy +1 more

We study S U (3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain a determinant representation for the particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of the XXX S U (3)-invariant Heisenberg chain.