Spectral properties and isotope effect in strongly interacting systems: Mott-Hubbard insulator and polaronic semiconductor

We study the electronic spectral properties in two examples of strongly interacting systems: a Mott-Hubbard insulator with additional electron-boson interactions, and a polaronic semiconductor. An approximate unified framework is developed for the high energy part of the spectrum, in which the electrons move in a random field determined by the interplay between magnetic and bosonic fluctuations. When the boson under consideration is a lattice vibration, the resulting isotope effect on the spectral properties is similar in both cases, being strongly temperature and energy dependent, in qualitative agreement with recent photoemission experiments in the cuprates.