Metal-insulator transition in an one-dimensional extended Hubbard model at quarter filling

•We study a 1D extended Hubbard Hamiltonian model at quarter filling.•We present the ground-state phase diagram at weak coupling.•We construct a theoretical argument for the metal-insulator transition.•The study provides insight into 1D quantum electron systems.

Using the g-ology technique, we analytically study an one-dimensional quarter-filled extended Hubbard model incorporating the most general charge (V) and spin (J) interactions in the weak-coupling regime. With the charge-spin separation hypothesis, the calculation of charge stiffness parameter and renormalization-group analysis predict the occurrence of metal-insulator transition and spin-gap transition, respectively. The correlation functions at large distances are used to determine the dominant phases. The ground state phase diagram consists of two insulating density waves (CDW, SDW) and two superconducting correlations (SS, TS), while the CDW and TS phases are based on V/J > (V/J)c or V/J < (V/J)c with (V/J)c = −1/4. The study provides an insignificant insight into 1D quantum electron systems.