I'm trained in physical chemistry, rather than physics, so I don't have the firmest grasp of quantum field theory, but I think the analogous "phonon field" woul

I'm trained in physical chemistry, rather than physics, so I don't have the firmest grasp of quantum field theory, but I think the analogous "phonon field" would be the Born-Oppenheimer potential energy surface (PES). Vibrations, and hence phonons, are collective excitations on the PES.