Tomonaga-Luttinger parameters for doped Mott insulators

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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, n c=1/2, and confirm the bosonization results Kρ=n c²=1/4 on the critical line and Kρ CDW=n c²/2=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.