The exact ground state properties of the Peierls-Hubbard model with site-off-diagonal electron-phonon (e-ph) coupling are numerically calculated. It is shown that the lattice is always distorted however the e-ph coupling constant is small. Dynamical bond strength (DBS) including the effects of the correlated motion of electrons and ions is introduced to describe the itinerancy of the electron in this system. From the analysis of DBS, the Coulomb repulsion is shown to enhance itinerancy of the electrons in the strongly coupled e-ph system with higher phonon frequency. This can be interpreted in terms of the concept of coherent hopping which is the consequence of the cooperative motion of the strongly correlated electrons and rapidly oscillating lattice system.
We present detailed studies of the self-interaction-corrected local-spin-density method. As an application, we consider ground-state properties of a highly correlated many-electron system interacting with phonons, namely, the one- and two-dimensional Hubbard-Peierls model. An efficient minimization method is presented which allows one to find fully self-consistent solutions to the self-interaction-corrected local-spin-density total-energy functional without assuming any symmetry of the one-electron states. Charge- and spin-correlation functions, the energy gap, and phonon-induced electronic energy gains for the two-dimensional Hubbard-Peierls model are in significantly better agreement with numerically exact results than the standard local-density method. Noticeably, we find that phonons tend to de- stabilize the antiferromagnetic ground state in two dimensions and show a negative-U behavior in the energy gap, in contrast to the situation in one dimension. This is relevant for the theory of high-temperature superconductivity.
Using the Lanczos method for exact diagonalization on systems up to 14 sites, combined with a novel phase randomization'' technique for extracting more information from these small systems, we investigate several aspects of the one-dimensional Peierls-Hubbard Hamiltonian, in the context of trans-polyacetylene: the dependence of the ground state dimerization on the strength of the electron-electron interactions, including the effects of off-diagonal'' Coulomb terms generally ignored in the Hubbard model; the phonon vibrational frequencies and dispersion relations, and the optical absorption properties, including the spectrum of absorptions as a function of photon energy. These three different observables provide considerable insight into the effects of electron-electron interactions on the properties of real materials and thus into the nature of strongly correlated electron systems. 29 refs., 11 figs.
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 Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling
g to the phonons drives the system towards a Peierls charge density wave state, whereas increasing the electron-electron interaction
U drives the fermions into a Mott antiferromagnet. At low
g and
U, or when doped, the system is metallic. In one dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long-range coupling to phonons, with characteristic range $\ensuremath{\xi}$, interpolating between the Holstein and Fr\"ohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $\ensuremath{\xi}$ and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction
U will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U\ensuremath{\ne}0$ case, even for small values of the coupling range.
The density matrix renormalization group method is used to investigate the Peierls transition for the extended Hubbard model coupled to quantized phonons. Following our earlier work on spin-Peierls systems, we use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit and a gapless, dispersive (Debye) limit to investigate the entire frequency range. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, and bipartite quantum entanglement. All these probes indicate that a transition of Berezinskii-Kosterlitz-Thouless type is observed at a nonzero electron-phonon coupling
gc for a nonvanishing electron-electron interaction. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in
gc for a fixed optical ($q=\ensuremath{\pi}$) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective electron-lattice coupling for the Peierls-active mode. By varying the Coulomb interaction
U, we observe a generalized Peierls transition, intermediate between the uncorrelated (
U=0) and spin-Peierls ($U\ensuremath{\rightarrow}\ensuremath{\infty}$) limits, where
U is the Hubbard Coulomb parameter. Using the extended Hubbard model with Debye phonons, we investigate the Peierls transition in trans-polyacetylene and show that the transition is close to the critical regime.