Figure 6: Comparison between the DMFT momentum-integrated spectral function ( being the local Green's function) for the Hubbard-Holstein model (dotted line) and the effective purely electronic Hubbard model with (solid line). The low-energy part of the spectra is perfectly reproduced by the effective model, while the high-energy features present phononic signatures that cannot be plugged in an effective static interaction (after Sangiovanni et al. [45]).