Capturing non-perturbative electron-phonon effects in real materials using DMFT

Dynamical Mean Field Theory (DMFT) can capture dynamical correlation effects on real materials by combining with Density Functional Theory (DFT) and solving the DMFT equation self-consistently within the multi-orbital Hubbard model extracted from DFT. Using a similar philosophy, we show that a multi-orbital Hubbard-Holstein model can be constructed from DFT electron-phonon calculations. We then derive an effective Hubbard model with a frequency-dependent electron-electron interaction U(ω) by integrating out the phonon degrees of freedom. This model can be solved using DMFT to capture the non-perturbative electron-phonon and electron-electron interaction effects. As a proof of the concept, we calculate phase diagrams of the two-orbital Hubbard-Holstein model as functions of the Coulomb interaction, the electron-phonon coupling, and temperature. We use Niobium to illustrate the process on a real material by obtaining model parameters from DFT, obtaining new insights on the effect of electron-phonon interactions in Niobium.