Motivated by the observation in the copper-oxide high-temperature superconductors, we investigate the appearance of kinks in the electronic dispersion due to coupling to phonons in the presence of a strong electronic repulsion. To model this strong coupling situation we present controlled calculations for the Hubbard-Holstein (HH) model
within the framework of the dynamical mean field theory combined with the numerical renormalization group.
We find that contrary to the conventional electron-phonon theory, the position
of the kink can be shifted to energies larger than the renormalized phonon
frequency $\omega_0^r$. This can be understood in terms of an effective $U$ at
low energy, which is only weakly renormalized by the phonons, such that phonon
effects are visible only at higher energy. When including antiferromagnetic
correlations for small doping we find a pronounced kink at $\omega_0^r$ due
to a cooperative effect. Our results provide a scenario of a kink position
increasing with doping, which is consistent with recent photoemission
experiments on Bi-based cuprates .
Within a similar framework we also analyze other situations which can be understood in terms of an effective low energy interaction. The ground state phase diagram of the HH model at half filling shows antiferromagnetic and charge order. The phase boundary is shown to be determined by an effective electronic interaction. Interestingly, there can be direct continuous transitions between the two ordered states [2,3].
Finally we allude to recent results from an analysis of the limitations of
Morel-Anderson retardation effects for phonon induced superconductivity when the Coulomb repulsion becomes large .
 J Bauer and G Sangiovanni, Phys. Rev. B 82 (2010), 184535.
 J Bauer, EPL 90 (2010), 27002.
 J Bauer and AC Hewson, Phys. Rev. B 81 (2010), 235113.
 J Bauer, J Han, and O Gunnarsson, in preparation (2011).