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

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=.../2... T..., where ... is the characteristic phonon frequency and 2... T... the lowest finite phonon Matsubara frequency at the mean-field critical point T..., 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... to a zero-temperature charge-density-wave transition setting up at a finite crossover d=d... This finite crossover decreases within the range 0≤d...1 as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of T... suppression 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. (ProQuest: ... denotes formulae/symbols omitted.)