Tomonaga-Luttinger parameters for doped Mott insulators

Abstract

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, $n_{\mathrm{c}}=1/2$, and confirm the bosonization results $K_{\rho }=n_{\mathrm{c}}^2=1/4$ on the critical line and $K_{\rho }^{\mathrm{CDW}}=n_{\mathrm{c}}^2/2=1/8$ 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.

7 pages, 4 figures

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