  Using the density-matrix renormalization-group, we investigate the critical
behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show
that through the relations arising from the conformal invariance and the DMRG
technique it is possible to obtain accurate finite-size estimates of the
conformal anomaly $c$, the sound velocity $v_{s}$, the anomalous dimension
$x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$
Heisenberg chains with relatively good accuracy without fitting parameters. Our
results indicate that the entanglement entrop $S(L,l_{A},S)$ of the spin-$S$
Heisenberg chains satisfies the relation $S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1)$
for $S>3/2$ in the thermodynamic limit.
