By utilizing the twisted boundary conditions in the exact diagonalization method, we investigate the single-particle spectral function of the extended Peierls-Hubbard model at both half-filling and quarter-filling. In one-dimensional (1D) interacting systems, the spin-charge separation can typically be identified in the single-particle spectral function by observing the distinct spinon and holon bands. At half-filling, starting from the pure 1D Hubbard model with the on-site interaction $U=10$, we observe that the band structure indicative of the spin-charge separation gradually transitions to four individual bands as the Peierls instability $\delta$ increases. At $U=10$ and $\delta =0.2$ where the spin-charge separation is still observable, increasing the nearest-neighbor interaction $V$ can drive the system to a charge-density-wave state when $V\gtrsim U/2$. At quarter-filling, on the other hand, the ground state of Peierls-Hubbard model manifests an antiferromagnetic Mott insulator in units of dimers. Increasing $U$ results in only a very small gap in the single-particle spectrum because even for $U=+\infty$, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability $\delta$ remains small. Conversely, increasing $V$ can effectively open the single-particle gap and make the spinon and holon bands more prominent.

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• Peierls transition
• 1-dimensional systems
• Strongly correlated systems
• Exact diagonalization
• Extended Hubbard model