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The Peierls instability in one-dimensional electron-phonon systems is knownto be qualitatively well described by the Mean-Field theory, however therelated self-consistent problem so far has only been able to predict a partialsuppression of the transition even with proper account of classical latticefluctuations. Here the Hartree-Fock approximation scheme is extended to thefull quantum regime, by mapping the momentum-frequency spectrum oforder-parameter fluctuations onto a continuous two-parameter space. For theone-dimensional half-filled Su-Schrieffer-Heeger model the ratio $d=\Omega/2\piT_c^0$, 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 latticefluctuations. By integrating out finite-frequency phonons, it is found that avariation 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 finitecrossover $d=d_c$. This finite crossover decreases within the range $0\leq d\approx 1$ as the electron-phonon coupling strength increases but remainingsmall enough for weak-coupling considerations to still hold. Implications of$T_c$ supression on the Ginzburg criterion is discussed, and evidence is givenof a possible coherent description of the charge-density-wave problem withinthe framework of a renormalized Mean-Field theory encompassing several aspectsof the transition including its thermodynamics close to the quantum criticalpoint.

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