The diagrammatic valence-bond technique is adopted to investigate one-dimensional half-filled Hubbard chains with long-range e-e interactions and alternating charge-transfer integrals. Exact results for finite-size systems with different boundary conditions are carefully extrapolated to the infinite-chain limit. In addition to various ground-state properties, such as bond-charge-density wave and bond-order amplitude, we calculate the optical gap and the corresponding oscillator strength. We introduce adiabatic phonons able to modulate on-site energies and investigate the stability of the system with respect to site-charge-density wave distortion. We also evaluate the response of the electronic system to the perturbation induced by adiabatic phonons which modulate charge-transfer integrals, and calculate the corresponding screening of vibrational frequencies.
Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction
V and site-off-diagonal (bond-charge
X and bond-bond
W) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the
X term is considered as a site-off-diagonal term. Similarly to the
X term, the
W term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for
W<0 and
W>0 cases, respectively. In the strong-coupling region, however, the
W term causes ferromagnetism for
W>0, and shifts the boundary of the phase separation in the
U/t≪−1 region, which are different from the roles of the
X term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
We study extended Hubbard and Peierls-Hubbard models with up to N=10 sites and half-filled bands with modified boundary conditions. For the extended Hubbard model, the finite-size dependence of the transition from the charge-density-wave regime (CDW) to the spin-density-wave (SDW) regime and of the condensation transition is critically examined, clarifying some previous results. For the Peierls-Hubbard model and N\ensuremath{\le}10 with modified periodic boundary conditions, we always see a decrease of dimerization with U. Extrapolating these results to infinite N, we find that dimerization is enhanced by U for small electron-phonon coupling \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}0.75, whereas it decreases with U for 0.75\ensuremath{\le}1. By extending this model by a nearest-neighbor repulsion V, the amplitude of dimerization reaches a maximum at the same value U\ensuremath{\le}2V, where the CDW-to-SDW transition occurs in the extended Hubbard model.
Density-matrix renormalization-group methods are used to investigate the quantum phase transitions in a Hubbard chain with an alternating on-site energy $\ensuremath{\Delta}$ at half filling. Our results support the existence of a bond-order wave phase, which separates the band insulator from the Mott insulator even in the absence of electron-phonon coupling. The critical points are determined accurately at fixed staggered potentials. Our results indicate a slightly smaller size of the bond-order wave phase than that of previous results.
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."