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We study cavity-mediated interactions that are generated in a two-dimensionaltwo-band Hubbard model coupled to an optical cavity, when it is driven in-gapby a strong laser. Starting from a Floquet description of the driven system, wederive effective low-energy Hamiltonians by projecting out the high-energydegrees of freedom and treating intrinsic interactions on a mean field level.We then investigate how the emergence of high-energy Frenkel excitons from theelectronic interband coupling, which form near the upper electronic band,affects the interactions as well as the laser-induced Floquet renormalizationof the electronic band structure. Cavity-mediated interactions are enhancedstrongly when the light couples to an excitonic transition. Additionally, theinteraction as well as the Floquet renormalization are strongly broadened inreciprocal space, which could further boost the impact of cavity-mediatedinteractions on the driven-dissipative steady state.

Excitonic enhancement of cavity-mediated interactions in a two-band Hubbard model