  The interplay of light and matter gives rise to intriguing cooperative
effects in quantum many-body systems. This is even true in thermal equilibrium,
where the electromagnetic field can hybridize with collective modes of matter,
and virtual photons can induce interactions in the solid. Here, we show how
these light-mediated interactions can be treated using the dynamical mean-field
theory formalism. We consider a minimal model of a two-dimensional material
that couples to a surface plasmon polariton mode of a metal-dielectric
interface. Within the mean-field approximation, the system exhibits a
ferroelectric phase transition that is unaffected by the light-matter coupling.
Bosonic dynamical mean-field theory provides a more accurate description and
reveals that the photon-mediated interactions enhance the ferroelectric order
and stabilize the ferroelectric phase.
