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 increases. At U=10 and =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/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=+, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability remains small. Conversely, increasing V can effectively open the single-particle gap and make the spinon and holon bands more prominent.
Xu et al. (Wed,) studied this question.