Metal-Insulator Transition of the One-Dimensional U-V Model at Quarter Filling

The metal-insulator transition of the one-dimensional extended Hubbard model with both on-site U and nearest neighbor V interactions is studied by a combination of the numerical diagonalization and the renormalization group (RG) method. We diagonalize finite size systems numerically and calculate the Luttinger-liquid parameter Kρ. Substituting the numerical result to the RG equations as the initial condition, we explicitly calculate the renormalized Kρ and the renormalized umk-lapp scattering parameter G. This approach gives the critical properties of the Kρ and the charge gap near the metal-insulator transition beyond the usual nite-size scaling for the numerical diagonalization result. We also obtain a contour map of the charge gap by the numerical diagonalization method on the U-V plain