Dynamical structure factor at small q for the XXZ spin-1/2 chain

We combine Bethe ansatz and. field theory methods to study the longitudinal dynamical structure factor Szz( q,w,.) for the anisotropic spin- 1/ 2 chain in the gapless regime. Using bosonization, we derive a low- energy e. ective model, including the leading irrelevant operators ( band curvature terms) which account for boson decay processes. The coupling constants of the e. ective model for. nite anisotropy and. nite magnetic. eld are determined exactly by comparison with corrections to thermodynamic quantities calculated by Bethe ansatz. We show that a good approximation for the shape of the on- shell peak of Szz( q,.) in the interacting case is obtained by rescaling the result for free fermions by certain coe. cients extracted from the e. ective Hamiltonian. In particular, the width of the on- shell peak is argued to scale like delta w(q) similar to q(2) and this prediction is shown to agree with the width of the two- particle continuum at. nite. elds calculated from the Bethe ansatz equations. An exception to the q2 scaling is found at. nite. eld and large anisotropy parameter ( near the isotropic point). We also present the calculation of the high- frequency tail of Szz( q,.) in