Tomonaga-Luttinger parameters for doped Mott insulators

Abstract

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