The Dynamical Correlation Function of the XXZ Model

TL;DR

This paper analytically computes the dynamical correlation function of the spin 1/2 XXZ model using form factors, revealing key contributions below the four-particle threshold and providing detailed plots across parameters.

Contribution

It introduces a spectral decomposition approach for the XXZ model's dynamical correlation function, utilizing recent form factor integral expressions and expanding to twelfth order in q.

Findings

Two-particle contributions dominate below the four-particle threshold.

Explicit plots of $S(w,k)$ at various anisotropies and momenta.

Validation of form factor expansion methods for dynamical correlations.

Abstract

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 $\pi$.