The Dynamical Correlation Function of the XXZ Model

We perform a spectral decomposition of the dynamical correlation function of the spin \(1/2\) XXZ model into an infinite sum of products of form factors. Beneath the four-particle threshold in momentum space the only non-zero contributions to this sum are the two-particle term and the trivial vacuum term. We calculate the two-particle term by making use of the integral expressions for form factors provided recently by the Kyoto school. We evaluate the necessary integrals by expanding to twelfth order in \(q\). We show plots of \(S(w,k)\), for \(k=0\) and \(\pi\) at various values of the anisotropy parameter, and for fixed anisotropy at various \(k\) around \(0\) and \(\pi\).