Quantum phonons and the charge density wave transition temperature: a   dynamical mean field study
  We use the dynamical mean-field method to calculate the charge density wave transition temperature of the half-filled Holstein model as function of typical phonon frequency in the physically relevant adiabatic limit of phonon frequency Omega much less than electron bandwidth t. Our work is the first systematic expansion of the charge density wave problem in Omega/t. Quantum phonon effects are found to suppress Tco severely, in agreement with previous work on one dimensional models and numerical studies of the dynamical mean field model in the extreme antiadiabatic limit (Omega ~ t). We suggest that this is why there are very few CDW systems with mean-field transition temperatures much less than a typical phonon frequency. 
S. Blawid and A. J. Millis