One-dimensional extended Hubbard model coupled with an optical cavity

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 photon spectrum that exists without the cavity exhibits 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.

💡 Research Summary

This paper investigates the interplay between vacuum fluctuations of a quantized electromagnetic field and the quantum phase transition (QPT) between charge‑density‑wave (CDW) and spin‑density‑wave (SDW) phases in a one‑dimensional extended Hubbard model coupled to a single‑mode optical cavity. The electronic part of the Hamiltonian contains an on‑site repulsion U and a nearest‑neighbor repulsion V, which together produce an SDW phase for V ≲ U/2, a CDW phase for V ≳ U/2, and a narrow bond‑order‑wave (BOW) region in between. The cavity mode of frequency Ω interacts with the electrons via a Peierls‑phase coupling G/√L, where G is a collective light‑matter coupling constant and L is the system length. The total Hamiltonian reads
 H = Ω a†a − W∑_{j,σ}