# One-dimensional extended Hubbard model coupled with an optical cavity

**Authors:** Taiga Nakamoto, Kazuaki Takasan, Naoto Tsuji  
**arXiv:** [2505.09311](https://arxiv.org/abs/2505.09311)  
**Date:** 2025-05-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2505.09311v1/

## Key points

- Nakamoto, Takasan, and Tsuji studied the one-dimensional extended Hubbard model coupled with an optical cavity
- The model captures the interplay between light's vacuum fluctuation and quantum phase transition between charge- and spin-density-wave phases
- Researchers used numerically exact tensor-network methods to calculate the ground state and excitation spectrum
- Light-matter coupling comparable to cavity frequency can enhance or suppress photon number of ground state along quantum phase transition line
- Presence of excitons leads to distinctive feature known as vacuum Rabi splitting in optical conductivity and photon spectrum at resonance
- Excitonic effects significantly impact optical properties in systems coupled with optical cavities

## Summary

Nakamoto, Takasan, and Tsuji conducted a study on the one-dimensional extended Hubbard model coupled with an optical cavity. This model captures the complex interplay between light's vacuum fluctuation and the quantum phase transition between charge- and spin-density-wave phases. Using numerically exact tensor-network methods, the researchers calculated the ground state and excitation spectrum of the system. Their findings revealed intriguing behavior along the quantum phase transition line: when the light-matter coupling is comparable to the cavity frequency, it can either enhance or suppress the photon number of the ground state. This phenomenon sheds light on how different regimes of coupling strength can influence system properties. Furthermore, Nakamoto et al. demonstrated that in the presence of excitons, both the exciton peak in optical conductivity and photon spectrum exhibit a distinctive feature known as vacuum Rabi splitting at resonance. This effect arises from the interaction between light and matter within the cavity, resulting in a sharp resonance that splits the photon spectrum. In contrast, without excitons present, only broadening is observed in the photon spectrum without any splitting due to a lack of a clear resonance. These results highlight how excitonic effects can significantly impact optical properties in systems coupled with optical cavities.