  The Tomonaga--Luttinger parameter $K_{\rho}$ determines the critical behavior
in quasi one-dimensional correlated electron systems, e.g., the exponent
$\alpha$ for the density of states near the Fermi energy. We use the numerical
density-matrix renormalization group method to calculate $K_{\rho}$ from the
slope of the density-density correlation function in momentum space at zero
wave vector. We check the accuracy of our new approach against exact results
for the Hubbard and XXZ Heisenberg models. We determine $K_{\rho}$ in the phase
diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and
confirm the bosonization results $K_{\rho}=n_{\rm c}^2=1/4$ on the critical
line and $K_{\rho}^{\rm CDW}=n_{\rm c}^2/2=1/8$ at infinitesimal doping of the
charge-density-wave (CDW) insulator for all interaction strengths. The doped
CDW insulator exhibits exponents $\alpha>1$ only for small doping and strong
correlations.
