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Interplay of electron-phonon interaction and strong correlations: DMFT+Sigma approach

We discuss interaction of strongly correlated electrons (described within the Hubbard model solved by dynamical mean-field theory (DMFT)) with Debye and Einstein phonons using recently developed DMFT+Sigma computational scheme. Electron-phonon interaction (EPI) is analyzed in adiabatic approximation (assuming the validity of Migdal theorem), allowing the neglect of EPI vertex corrections. This approach is valid for EPI coupling constant L < e_F/w_ph~10, where e_F is Fermi energy and w_ph is Debye or Einstein frequency. For moderate values of L only small changes in the electronic density of states are observed in DMFT+Sigma approximation for both weakly and strongly correlated metallic regimes. Metal-insulator (Mott) transition due to the increase of Hubbard interaction U is slightly inhibited by EPI. Our main aim is to discuss the interplay of "kinks" in electronic dispersion due to EPI and recently discovered kinks of electronic origin. For the certain region of model parameters coexistence of phonon "kinks" in electronic dispersion with purely electronic "kinks" is readily observed and we formulate some simple criteria of such coexistence. However, for most general combinations of model parameters phonon "kinks" make electronic "kinks" hardly observable. In the general case an increase of Hubbard interaction U rapidly suppresses the slope of electronic dispersion within the phonon "kink". These results are important for deeper understanding of the shape and evolution of electronic dispersions in strongly correlated systems such as copper oxides, where different kinds of "kinks" were recently observed in ARPES experiments.