The exact two-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 the antiferr
omagnetically ordered phase is calculated using recent advances in the
algebraic analysis based on (infinite-dimensional) quantum group symm
etries of this model and the related vertex models. The two-spinon exc
itations form a two-parameter continuum consisting of two partly overl
apping sheets in (Q,omega) space. The spectral threshold has a smooth
maximum at the Brillouin zone boundary (Q=pi/2) and a smooth minimum w
ith a gap at the zone center (Q=0). The two-spinon density of states h
as square-root divergences at the lower and upper continuum boundaries
. For the two-spinon transition rates; the two regimes 0 less than or
equal to Q<Q(kappa) (near the zone center) and Q(kappa)<Q less than or
equal to pi/2 (near the zone boundary) must be distinguished, where Q
(kappa)-->0 in the Heisenberg limit and Q(kappa)-->pi/2 in the Ising l
imit. In the regime Q(kappa)<Q less than or equal to pi/2, the two-spi
non transition rates relevant for S-xx(Q,omega) are finite at the lowe
r boundary of each sheet,decrease monotonically with increasing omega,
and approach zero linearly at the upper boundary. The resulting two-s
pinon part of S-xx(Q,omega) is then square-root divergent at the spect
ral threshold and vanishes in a square-root cusp at the upper boundary
. In the regime 0<Q(kappa)less than or equal to pi/2, in contrast, the
two-spinon transition rates have a smooth maximum inside the continuu
m and vanish linearly at either boundary. In the associated two-spinon
line shapes of S-xx(Q,omega), the linear cusps at the continuum bound
aries are replaced by square-root cusps. Existing perturbation studies
have been unable to capture the physics of the regime Q(kappa)<Q less
than or equal to pi/2. However, their line-shape predictions for the
regime 0 less than or equal to Q<Q(kappa) are in good agreement with t
he exact results if the anisotropy is very strong. For weak anisotropi
es, the exact line shapes are more asymmetric.