The Density-matrix renormalization-group (DMRG) technique is used to study the one-dimensional (1D) dimerized Hubbard model at quarter filling. We carry out a precise calculation of the charge gap as a function of the interaction and dimerization strengths and evaluate the interaction strength of the effective 1D Hubbard model at half filling. We also examine the effect of nearest-neighbor repulsion on the charge gap, whereby we evaluate the realistic repulsive strengths for quasi-1D organic compounds.
Utilizing the exact diagonalization method, we investigate the one-dimensional Peierls-Hubbard model at quarter filling, where it manifests as an antiferromagnetic Mott insulator in units of dimers. By increasing the on-site Coulomb repulsion
U, we observe a significant suppression of the Drude peak, based on a nonequilibrium linear-response theory capable of capturing the zero-frequency (Drude) weight of the optical conductivity under periodic boundary conditions. However, after the ultrafast photoirradiation of this model with large
U, we detect a distinct enhancement of the Drude peak, signifying the onset of a photoinduced insulator-metal transition. Comparing these dynamics with the half-filled Hubbard model and a noninteracting spinless half-filled Su-Schrieffer-Heeger model (corresponding to the quarter-filled Peierls-Hubbard model with infinite
U), we propose a mechanism for the photoinduced metallic state: The empty-occupied and double-occupied dimers serve as the photoinduced charge carriers, akin to the holons and doublons in the Hubbard model.
We have studied the tendency of the two-dimensional half-filled Hubbard model towards dimerization as a function of the on-site repulsion U. We have found that the phonon with (\ensuremath{\pi},\ensuremath{\pi}) wave vector is the most favorable vibration mode when U is less than a critical value
Uc, where
Uc is a function of the dimerization. When U is greater than
Uc, the (\ensuremath{\pi},0) phonon becomes preferred. In leading order, the energy gain under dimerization appears to be proportional to ${\ensuremath{\delta}}^{2}$ln\ensuremath{\delta} if the (\ensuremath{\pi},\ensuremath{\pi}) phonon is favorable, so that the system displays a Peierls instability in this case. For large U the energy gain to leading order appears to be proportional to ${\ensuremath{\delta}}^{2}$ for both the (\ensuremath{\pi},\ensuremath{\pi}) and (\ensuremath{\pi},0) phonons, and the latter one is preferred; in that case the system is stable unless the electron-phonon coupling exceeds a critical value. Unlike the effect in the one-dimensional case, the on-site repulsion U seems to have essentially no effect on the tendency towards dimerization for small U, and suppresses it for large U. This difference may be related to the fact that there exists long-range antiferromagnetic order in the two-dimensional half-filled Hubbard model when U is present.