  Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic
field are Luttinger liquids, whose parameters depend on the actual
magnetization of the chain. Here we present precise numerical estimates of the
Luttinger liquid dressed charge $Z$, which determines the critical exponents,
by calculating the magnetization and quadrupole operator profiles for $S=1/2$
and S=1 chains using the density matrix renormalization group method. Critical
amplitudes and the scattering length at the chain ends are also determined.
Although both systems are Luttinger liquids the characteristic parameters
differ considerably.
