We study the one-dimensional extended Hubbard model coupled with an optical cavity, which describes an interplay of the effect of vacuum fluctuation of light and the quantum phase transition between the charge- and spin-density-wave phases. The ground state and excitation spectrum of the model are calculated by numerically exact tensor-network methods. We find that the photon number of the ground state is enhanced (suppressed) along the quantum phase transition line when the light-matter coupling is comparable to (much smaller than) the cavity frequency. We also show that the exciton peak in the optical conductivity and single photon excitation peak in the photon spectrum exhibit the vacuum Rabi splitting at resonance due to the light-matter interaction. This behavior is in contrast to the case without excitons, where the photon spectrum is merely broadened without splitting due to the lack of a sharp resonance.

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• Cavity quantum electrodynamics
• Strongly correlated systems
• Tensor network methods