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

摘要

We calculate the charge and spin Drude weight of the one-dimensional extendedHubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ atquarter filling using the density-matrix renormalization group method combinedwith a variational principle. Our numerical results for the Hubbard model (V=0)agree with exact results obtained from the Bethe ansatz solution. We obtain thecontour map for both Drude weights in the $UV$-parameter space for repulsiveinteractions. We find that the charge Drude weight is discontinuous across theKosterlitz-Thouless transition between the Luttinger liquid and thecharge-density-wave insulator, while the spin Drude weight varies smoothly andremains finite in both phases. Our results can be generally understood usingbosonization and renormalization group results. The finite-size scaling of thecharge Drude weight is well fitted by a polynomial function of the inversesystem size in the metallic region. In the insulating region we find anexponential decay of the finite-size corrections with the system size and auniversal relation between the charge gap $\Delta_c$ and the correlation length$\xi$ which controls this exponential decay.