The light-matter interaction in optical cavities offers a promising ground to create hybrid states and manipulate material properties. In this work, we examine the effect of light-matter coupling in the excitonic insulator phase using a quasi-one-dimensional lattice model with two opposite parity orbitals at each site. We show that the model allows for a coupling between the collective phase mode and cavity photons. Our findings reveal that the collective mode of the excitonic state significantly impacts the dispersion of the cavity mode, giving rise to an avoided band crossing in the photon dispersion. This phenomenon is absent in trivial and topological insulator phases and also in phonon-mediated excitonic insulators, underscoring the unique characteristics of collective excitations in excitonic insulators. Our results demonstrate the significant impact of light-matter interaction on photon propagation in the presence of excitonic collective excitations.

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• Excitons
• Feynman diagrams
• Quasiparticles & collective excitations
• 1-dimensional systems
• Many-body techniques