Interacting electrons coupled to vibrations of lattices and molecules are at the heart of modern condensed matter physics under the name of electron-phonon (or polaron) problems. These problems often challenge the Born-Oppenheimer approximation made in most quantum chemistry calculations. Going beyond the Born-Oppenheimer approximation while handling the electron-electron correlation leads to different kinds of theoretical challenges.
At the same time, there have been interesting physical phenomena such as light-induced exciton condensation that are driven by electrons interacting with electromagnetic waves (i.e., photons). Both phonons and photons are bosons and methodologies to describe systems of electrons coupled to phonons and/or to photons should not be so different.
We are generally interested in developing scalable approaches along these lines and understanding new experimental phenomena related to them.