Phase Diagram of the t--U--V₁--V₂ Model at Quarter Filling

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We examine the ground-state properties of the one-dimensional Hubbard model at quarter filling with Coulomb interactions between nearest-neighbors V₁ and next-nearest neighbors V₂. Using the density-matrix renormalization group and exact diagonalization methods, we obtain an accurate ground-state phase diagram in the V₁-V₂ plane with three different phases: 2k F- and 4k F-charge-density-wave and a broad metallic phase in-between. The metal is a Tomonaga-Luttinger-liquid whose critical exponent Kρ is largest around V₁=2V₂, where V₁ and V₂ are frustrated, and smallest, Kρ=0.25, at the boundaries between the metallic phase and each of the two ordered phases.