  We present results of a study of the antiferromagnetic spin-1 chain, subject
to the simultaneous presence of single-ion anisotropy and external magnetic
fields. Using quantum Monte-Carlo based on the stochastic series expansion
method we first uncover a rich quantum phase diagram comprising N\'eel,
Haldane, Luttinger liquid, and large anisotropy phases. Second, we scan across
this phase diagram over a wide range of parameters, evaluating the transverse
dynamic structure factor, which we show to exhibit sharp massive modes, as well
as multi particle continua. For vanishing anisotropy and fields, comparison
with existing results from other analytic and numerical approaches shows
convincing consistency.
