The effect of quantum lattice fluctuations is investigated in a half-filled one-dimensional Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated by introducing the polaronic transformation and the squeezed-phonon state. The electronic correlations are treated by means of a modified Gutzwiller approach and a unified description for the long-range charge-density-wave (CDW) ordering state and the short-range antiferromagnetic correlated state has been developed. The main result is a rather good description of the continuous variation of the dimerization as functions of the Hubbard U and \ensuremath{\omega} is given, which is in good agreement with that of the numerical simulations. The results of the squeezed-polaron theory are shown to be better than those of the ordinary polaron theory. A continuous phase transition is found between the long-range CDW ordering state and the short-range antiferromagnetic correlated state with a transition point different from the prediction of the Hartree-Fock decoupling. The effect of quantum lattice fluctuations on the transition point is also discussed.
The effect of quantum lattice fluctuations is investigated in a half-filled one-dimensional Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated by introducing the polaronic transformation and the squeezed-phonon state. The electronic correlations are treated by means of a modified Gutzwiller approach and a unified description for the long-range charge-density-wave (CDW) ordering state and the short-range antiferromagnetic correlated state has been developed. The main result is a rather good description of the continuous variation of the dimerization as functions of the Hubbard U and \ensuremath{\omega} is given, which is in good agreement with that of the numerical simulations. The results of the squeezed-polaron theory are shown to be better than those of the ordinary polaron theory. A continuous phase transition is found between the long-range CDW ordering state and the short-range antiferromagnetic correlated state with a transition point different from the prediction of the Hartree-Fock decoupling. The effect of quantum lattice fluctuations on the transition point is also discussed.
The effect of quantum lattice fluctuations on the dimerized ground state is studied in the half-filled-band Takayama-Lin-Liu-Maki model. The nonadiabatic effect due to finite phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$\ensuremath{\gtrsim}0 is treated through an energy-dependent electron-phonon scattering function \ensuremath{\delta}(${\mathit{k}}^{\ensuremath{'}}$,k) introduced by means of a unitary transformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state and results in four-fermion interaction. By decoupling of the electronic correlations we show that our approach gives a good description of the continuous variation of the dimerization as functions of the dimensionless coupling constant g2 and the phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ when the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t (t is the electron hopping integral) is not large. Our results show that, at least in the weak-coupling limit, quantum lattice fluctuations change the functional dependence of the dimerization parameter mp on the coupling constant even if the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is small (but finite). In the spin-1/2 case our result is the same as that predicted by Fradkin and Hirsch. But in the spinless case we still predict a long-range dimerization order even if the coupling is weak and ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is finite. In the large ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ (antiadiabatic) limit we show that our effective Hamiltonian becomes an n-component Gross-Neveu model and the ratio mp(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=\ensuremath{\infty})/mp(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=0) is equal to 1/cosh(\ensuremath{\pi}/2ng2) (n=1: spinless; n=2: spin-1/2). By using the same input parameters as those of some previous authors we get a 7.2% reduction of the dimerization parameter mp compared with the adiabatic value. \textcopyright{} 1996 The American Physical Society.
We study the one-dimensional Holstein model with spin-21 electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
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.
Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.
"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."
The quantum phase transition between a repulsive Luttinger liquid and an insulating Peierls state is studied in the framework of the one-dimensional spinless Holstein model. We focus on the adiabatic regime but include the full quantum dynamics of the phonons. Using continuous-time quantum Monte Carlo simulations, we track, in particular, the dynamic charge structure factor and the single-particle spectrum across the transition. With increasing electron-phonon coupling, the dynamic charge structure factor reveals the emergence of a charge gap and a clear signature of phonon softening at the zone boundary. The single-particle spectral function evolves continuously across the transition. Hybridization of the charge and phonon modes of the Luttinger liquid description leads to two modes, one of which corresponds to the coherent polaron band. This band acquires a gap upon entering the Peierls phase, whereas the other mode constitutes the incoherent, high-energy spectrum with backfolded shadow bands. Coherent polaronic motion is a direct consequence of quantum lattice fluctuations. In the strong-coupling regime, the spectrum is described by the static, mean-field limit. Importantly, whereas finite electron density in general leads to screening of polaron effects, the latter reappear at half-filling due to charge ordering and lattice dimerization.