Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron-Phonon Systems: a Dynamic Self-Consistent

Abstract

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-parameter space. For the one-dimensional half-filled Su-Schrieffer-Heeger model the ratio $d=\Omega /2\pi T_c^0$, where $\Omega$ is the characteristic phonon frequency and $2\pi T_c^0$ the lowest finite phonon Matsubara frequency at the mean-field critical point $T_c^0$, provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of $d$ from the classical regime $d=0$ continuously connects $T_c^0$ to a zero-temperature charge-density-wave transition setting up at a finite crossover $d=d_c$. This finite crossover decreases within the range $0\le d\approx 1$ as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of $T_c$ supression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized Mean-Field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point.

arXiv comment20 pages, 8 figures

References in corpus (8)

• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Mechanism of CDW-SDW Transition in One Dimension
• Peierls transition in the presence of finite-frequency phonons in the one-dimensional extended Peierls-Hubbard model at half-filling
• Retardation effects in the Holstein-Hubbard chain at half-filling
• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Quantum phonons and the charge density wave transition temperature: a dynamical mean field study
• Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systems
• Charge-density-wave instability in the Holstein model with quartic anharmonic phonons

Cited by in corpus (2)

• Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa2Cu_3 O_7 - δ, Bi_2 Sr_2CaCu_2 O_8+δand KOs_2 O_6 compounds
• Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé-Kofané double-well potentials