  Using (infinite) density matrix renormalization group techniques, ground
state properties of antiferromagnetic S=1 Heisenberg spin chains with exchange
and single-site anisotropies in an external field are studied. The phase
diagram is known to display a plenitude of interesting phases. We elucidate
quantum phase transitions between the supersolid and spin-liquid as well as the
spin-liquid and the ferromagnetic phases. Analyzing spin correlation functions
in the spin-liquid phase, commensurate and (two distinct) incommensurate
regions are identified.
