Charge and spin Drude weight of the one-dimensional extended Hubbard model at quarter filling

We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion U and nearest-neighbor repulsion V at quarter filling using the density-matrix renormalization-group method combined with a variational principle. Our numerical results for the Hubbard model $(V=0)$ agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization-group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region, we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap Δc and the correlation length ξ which controls this exponential decay.