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Electron-phonon coupling, diagonal in a real space formulation, leads topolaron paradigm of smoothly varying properties. However, fundamental changes,namely the singular behavior of polarons, occur if non-diagonal pairing isinvolved into consideration. The study of polaron transformations and relatedproperties of matter is of particular interest for realistic models, sincecompetition between diagonal and non-diagonal electron-phonon contributions inthe presence of other strong interactions can result in unconventional behaviorof the system. Here we consider the multiband pd-model of cupratesuperconductors with electron-phonon interaction and analyze the features ofthe systems that are caused by the competition of diagonal and non-diagonalelectron-phonon contributions in the limit of strong electron correlations.Using the polaronic version of the generalized tight-binding method, wedescribe the evolution of the band structure, Fermi surface, density of statesat Fermi level, and phonon spectral function in the space of electron-phononparameters ranging from weak to strong coupling strength of the adiabaticlimit. On the phase diagram of polaron properties we reveal two quantum phasetransitions and show how electron-phonon interaction gives rise to Fermisurface transformation (i) from hole pockets to Fermi arcs and (ii) from holeto electron type of conductivity. We also demonstrate the emergence of newstates in the phonon spectral function of the polaron and discuss their origin.

Polaron transformations in the realistic model of the strongly correlated electron system