Phase Diagram of the $t$--$U$--$V_1$--$V_2$ Model at Quarter Filling

TL;DR

This paper maps the ground-state phase diagram of a one-dimensional Hubbard model at quarter filling, revealing charge-density-wave and metallic phases with detailed critical exponents using advanced numerical methods.

Contribution

It provides the first comprehensive phase diagram of the $t$--$U$--$V_1$--$V_2$ model at quarter filling, highlighting the effects of Coulomb interactions and frustration.

Findings

Identified three phases: $2k_{ m F}$-charge-density-wave, $4k_{ m F}$-charge-density-wave, and a metallic Tomonaga-Luttinger-liquid.

Determined the critical exponent $K_{ ho}$ varies with interaction parameters, reaching 0.25 at phase boundaries.

Showed maximum $K_{ ho}$ occurs around $V_1=2V_2$, indicating frustration effects.

Abstract

We examine the ground-state properties of the one-dimensional Hubbard model at quarter filling with Coulomb interactions between nearest-neighbors $V_1$ and next-nearest neighbors $V_2$. Using the density-matrix renormalization group and exact diagonalization methods, we obtain an accurate ground-state phase diagram in the $V_1$-$V_2$ plane with three different phases: $2k_{\rm F}$- and $4k_{\rm F}$-charge-density-wave and a broad metallic phase in-between. The metal is a Tomonaga-Luttinger-liquid whose critical exponent $K_{\rho}$ is largest around $V_1=2V_2$, where $V_1$ and $V_2$ are frustrated, and smallest, $K_{\rho}=0.25$, at the boundaries between the metallic phase and each of the two ordered phases.