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

Abstract

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 ${\Delta }_c$ and the correlation length $\xi$ which controls this exponential decay.

10 pages, 9 figures

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• Tomonaga-Luttinger parameters for doped Mott insulators
• Charge-density-wave instabilities driven by multiple umklapp scattering
• Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
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• Persistent current and Drude weight in mesoscopic rings
• Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling
• A test of the g-ology model for one-dimensional interacting Fermi systems

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