  We investigate the properties of the Heisenberg S=1 chain with bilinear and
biquadratic interactions in a magnetic field using the Density Matrix
Renormalization Group, Bethe ansatz and field theoretical considerations. In a
large region of the parameter space, we identify a magnetized ferroquadrupolar
Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This
liquid undergoes a continuous pair unbinding transition to a more conventional
Luttinger liquid region obtained by polarizing the system above the Haldane gap
region. This pair unbinding transition is shown to be in the Ising universality
class on top of a Luttinger liquid, leading to an effective central charge 3/2.
We also revisit the nature of the partially polarized Luttinger liquid around
and above the Uimin-Lai-Sutherland point. Our results confirm that this is a
two-component liquid and rule out the formation of a single-component vector
chiral phase.
