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 (CDW) transition temperature of the half-filled Holstein model as a function of typical phonon frequency in the physically relevant adiabatic limit of phonon frequency Omega much less than electron bandwidth t. Our work is a systematic expansion of the charge-density-wave problem in Omega /t. Quantum phonon effects are found to suppress T-co 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 similar tot). We suggest that this is why there are very few CDW systems with mean-field transition temperatures much less than a typical phonon frequency.