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 $\pi$.