Computation of dynamical correlation functions of Heisenberg chains: the gaplessanisotropic regime

Abstract

We compute all dynamical spin–spin correlation functions for thespin-1/2 XXZ anisotropic Heisenberg model in the gapless antiferromagnetic regime at zerotemperature, using numerical sums of exact determinant representations for formfactors of spin operators on the lattice. Contributions from intermediate statescontaining many particles and string (bound) states are included. We present modifieddeterminant representations for the form factors valid in the general case with stringsolutions to the Bethe equations. Our results are such that the available sumrules are saturated to high precision. We Fourier transform our results back toreal space, allowing us in particular to make a comparison with known exactformulae for equal-time correlation functions for small separations in zero field,and with predictions for the zero-field asymptotics from conformal field theory.