Dynamical mean-field theory of electron-phonon interactions in correlated systems: Application to isotope effects on electronic properties

We use a recently developed formalism (combining an adiabatic expansion and dynamical mean-field theory) to obtain expressions for isotope effects on electronic properties in correlated systems. As an example we calculate the isotope effect on electron effective mass for the Holstein model as a function of electron-phonon interaction strength and doping. Our systematic expansion generates diagrams which turn out to give the dominant contributions. The isotope effect is small unless the system is near a lattice instability. We compare this to experiment.