The Tomonaga--Luttinger parameter Kρ determines the critical behavior
in quasi one-dimensional correlated electron systems, e.g., the exponent
α for the density of states near the Fermi energy. We use the numerical
density-matrix renormalization group method to calculate Kρ 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 Kρ in the phase
diagram of the extended Hubbard model at quarter filling, nc=1/2, and
confirm the bosonization results Kρ=nc2=1/4 on the critical
line and KρCDW=nc2/2=1/8 at infinitesimal doping of the
charge-density-wave (CDW) insulator for all interaction strengths. The doped
CDW insulator exhibits exponents α>1 only for small doping and strong
correlations.Comment: 7 pages, 4 figure