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Journal of the Physical Society of Japan

Dynamical Correlation of Electrons and Phonons Coupled via Site-Off-Diagonal Interaction: Exact Calculation in Two-Site-Two-Electron Model

Yasuzi Inada, Chikara Ishii

Published Feb 15, 1990• 9 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.59.612

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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.
For a general class of correlated electron-phonon systems (1d generalised Peierls-Hubbard models) it is shown that the explicit electron-electron interaction can be eliminated exactly by a unitary transformation, resulting in an effective electron-lattice coupling. The transformed Hamiltonians may serve as a better starting point for analytical and numerical calculations. The properties of the transformations are illustrated in two limiting cases: in a two-site model and in the atomic limit. Furthermore, a variational ansatz for the ground state is proposed.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
The two-site two-electron Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found out considering up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections of different orders to the ground state energy as well as to different correlation functions are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon (eee-ph) coupling for different values of adiabaticity parameter and Coulomb repulsion. The simultaneous effect of the eee-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.
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.
We investigate the general applicability of the standard Peierls-Hubbard model, involving both on-site (UUU) and nearest-neighbor (VVV) Coulomb repulsions, by adding nearest-neighbor off-diagonal terms representing the bond (WWW) and mixed bond-site (XXX) electron-electron repulsive interactions. For a broad range of the site-diagonal Hubbard parameters (U,VU,VU,V), we find that the off-diagonal terms (W,XW,XW,X) initially enhance dimerization, thereby stabilizing the dimerized ground state.
The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with dynamical mean-field theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low energy, while this reduction is not present at high energy. The renormalization of the electron-phonon coupling induced by the Hubbard repulsion depends in a surprisingly strong and nontrivial way on the phonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully taken into account when the effects of the electron-phonon interaction in a strongly correlated system, like the superconducting cuprates, are discussed.