Metal–insulator transition of the one-dimensional U–V model at quarter filling Original Research Article

The metal–insulator (M–I) 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 umklapp scattering parameter G. This approach gives the critical properties of the Kρ and the charge gap near the M–I transition beyond the usual finite-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.