Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields

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.