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 $t.\mathrm{}$ Our work is a systematic expansion of the charge-density-wave problem in $\Omega /t.\mathrm{}$ Quantum phonon effects are found to suppress $T_{\mathrm{co}}$ severely, in agreement with previous work on one-dimensional models and numerical studies of the dynamical mean-field model in the extreme antiadiabatic limit $\left(\Omega \sim t\right).\mathrm{}$ We suggest that this is why there are very few CDW systems with mean-field transition temperatures much less than a typical phonon frequency.