# Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron–Phonon Systems: A Dynamic Self-Consistent Theory

@article{Dikand2013NonadiabaticFA,
title={Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron–Phonon Systems: A Dynamic Self-Consistent Theory},
author={Alain Mo{\'i}se Dikand{\'e} and Claude Bourbonnais},
journal={Journal of the Physical Society of Japan},
year={2013},
volume={82},
pages={024003}
}
• Published 15 January 2013
• Physics
• Journal of the Physical Society of Japan
The Peierls instability in one-dimensional electron–phonon systems is known to be qualitatively well described by the mean-field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree–Fock approximation scheme is extended to the full quantum regime, by mapping the momentum–frequency spectrum of order-parameter fluctuations onto a continuous two…
1 Citations

## Figures from this paper

Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa_{2}Cu_{3}O_{7-δ},Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}, and KOs_{2}O_{6} compounds.
• Physics, Medicine
Physical review. E
• 2016
It is clearly shown that the enhancement, suppression, or rounding of the specific heat jump of high-T_{c} cup-rate superconductors at the transition are indicative of the order parameter thermodynamic fluctuations according to the dimension and the nature of interactions.

## References

SHOWING 1-10 OF 34 REFERENCES
Phase diagram of one-dimensional electron-phonon systems. I. the Su-Schrieffer-Heeger model
• Physics
• 1983
We study the nature of the ground state of the Su-Schrieffer-Heeger model for electron-phonon interactions in one dimension in the half-filled-band case. We consider the cases of spinless electrons
Quantum phonons and the charge-density-wave transition temperature: A dynamical mean-field study
• Physics
• 2001
We use the dynamical mean-field method to calculate the charge-density-wave (CDW) transition temperature of the half-filled Holstein model as a function of typical phonon frequency in the physically
The influence of quantum lattice fluctuations on the one-dimensional Peierls instability
• Physics
• 1989
The interplay between quantum lattice and electronic fluctuations in one-dimensional molecular crystal electron-phonon system is analyzed by a path integral approach. By means of a high temperature
Peierls transition in the presence of finite-frequency phonons in the one-dimensional extended Peierls-Hubbard model at half-filling
• Physics
• 2003
We report quantum Monte Carlo (stochastic series expansion) results for the transition from a Mott insulator to a dimerized Peierls insulating state in a half-filled, 1D extended Hubbard model
Charge-Density-Wave Instability in the Holstein Model with Quartic Anharmonic Phonons
The molecular-crystal model, that describes a one-dimensional electron gas interacting with quartic anharmonic lattice vibrations, offers great potentials in the mapping of a relatively wide range of
Effect of quantum fluctuations on the Peierls dimerization in the one-dimensional molecular-crystal model.
• Physics, Medicine
Physical review. B, Condensed matter
• 1989
In the finite-\ensuremath{\omega} case it is shown that the lattice fluctuations are squeezed'' by the electron band motion, and the phonon subsystem is in the so-called two-phonon coherent state, in good agreement with both Monte Carlo simulations and renormalization-group analysis.
Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Physics
• 2001
We use a stochastic series-expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half-filling for small to intermediate values of the
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
• Physics
• 1996
We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
On the theory of superconductivity: the one-dimensional case
• H. Fröhlich
• Physics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1954
The one-dimensional case of free electrons interacting with lattice displacements is solved by a self-consistent method. It is found that for a certain range of the interaction parametera single
Quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Physics
• 2007
An extension of the renormalization group method that includes the effect of retardation for the interactions of a fermion gas is used to reexamine the quantum and classical properties of