Electron-phonon interaction in the strongly correlated systems and its implications on the high Tc cuprates

The theory of electron-phonon interaction in the presence of strong correlation has been investigated in the present work. Due to the so called spin-charge separation, it is argued that the electron-phonon interaction in the strongly interacting systems is fundamentally different from the weakly interacting counterparts. Both spinons and holons are shown to carry electric charge and couple to the electromagnetic field and consequently to phonons. A systematic approach to calculate the dynamical charge of spinons and holons is presented, followed by a discussion of implications of this model for the high temperature superconductors. It is demonstrated that the unusual oxygen isotope effect in high Tc materials can be easily understood within this framework.