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The exact 2-spinon part of the dynamic spin structure factor$S_{xx}(Q,\omega)$ for the one-dimensional $s$=1/2 $XXZ$ model at $T$=0 in theantiferromagnetically ordered phase is calculated using recent advances byJimbo and Miwa in the algebraic analysis based on (infinite-dimensional)quantum group symmetries of this model and the related vertex models. The2-spinon excitations form a 2-parameter continuum consisting of two partlyoverlapping sheets in $(Q,\omega)$-space. The spectral threshold has a smoothmaximum at the Brillouin zone boundary $(Q=\pi/2)$ and a smooth minimum with agap at the zone center $(Q=0)$. The 2-spinon density of states has square-rootdivergences at the lower and upper continuum boundaries. For the 2-spinontransition rates, the two regimes $0 \leq Q < Q_\kappa$ (near the zone center)and $Q_\kappa < Q \leq \pi/2$ (near the zone boundary) must be distinguished,where $Q_\kappa \to 0$ in the Heisenberg limit and $Q_\kappa \to \pi/2$ in theIsing limit. The resulting 2-spinon part of $S_{xx}(Q,\omega)$ is thensquare-root divergent at the spectral threshold and vanishes in a square-rootcusp at the upper boundary. In the regime $0 < Q_\kappa \leq \pi/2$, bycontrast, the 2-spinon transition rates have a smooth maximum inside thecontinuum and vanish linearly at either boundary. Existing perturbation studieshave been unable to capture the physics of the regime $Q_\kappa < Q \leq\pi/2$. However, their line shape predictions for the regime $0 \leq Q <Q_\kappa$ are in good agreement with the new exact results if the anisotropy isvery strong.Comment: 11 pages, 5 Postscript figure

physical review. b, condensed matter

Exact two-spinon dynamic structure factor of the one-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>Heisenberg-Ising antiferromagnet

Exact two-spinon dynamic structure factor of the one-dimensionals=12Heisenberg-Ising antiferromagnet