Numerical renormalization group study of the Anderson-Holstein impurity model

We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin susceptibilities. Being non-perturbative, the NRG is applicable for all parameter regimes. Our calculations cover both weak and strong electron-phonon coupling for zero and finite electron-electron interaction. We interpret the high- and low-energy features and compare our results to atomic limit calculations and perturbation theory. In certain restricted parameter regimes for strong electron-phonon coupling, a soft phonon mode develops inducing a very narrow resonance at the Fermi level.