Phase diagram and dynamic response functions of the Holstein-Hubbard model

We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half-filling and at zero temperature. The calculations are based on the dynamical mean field theory (DMFT). The effective impurity model is solved using exact diagonalization (ED) and the numerical renormalization group (NRG). Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal-insulator transitions