One-dimensional extended Hubbard model coupled with an optical cavity

TL;DR

This paper investigates how coupling an extended Hubbard model to an optical cavity influences quantum phase transitions and optical properties, revealing photon number modulation and vacuum Rabi splitting effects through tensor-network calculations.

Contribution

It introduces a detailed numerical study of light-matter interactions in a correlated electron system, highlighting novel photon spectrum features and phase transition behaviors.

Findings

Photon number is enhanced or suppressed along the phase transition line.

Vacuum Rabi splitting appears in the optical conductivity and photon spectrum.

Photon spectrum broadening occurs without excitons, lacking splitting.

Abstract

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.