Many-body localization of one-dimensional degenerate Fermi gases with cavity-assisted non-local quasiperiodic interactions

TL;DR

This paper investigates many-body localization in one-dimensional degenerate Fermi gases with cavity-assisted non-local quasiperiodic interactions, revealing how spectral properties and photon number stability characterize the MBL phase.

Contribution

It demonstrates the applicability of ETH in nonlocal cavity systems and links photon number stability to the MBL phase, offering new diagnostic and device-building insights.

Findings

ETH applies depending on system parameters

Spectral range varies with parameters

Photon number remains stable in MBL phase

Abstract

The localization properties of one-dimensional degenerate Fermi gases with cavity-assisted non-local quasiperiodic interactions are numerically studied. Although the cavity-induced interaction is typically nonlocal, it is proved that the eigenstate thermalization hypothesis (ETH) is still applicable in our system depending on the system parameters. We also find the segment of the spectrum corresponding to infinite effective temperature varies for different system parameters, which indicates the spectral range employed in the spectral statistical analysis should be varied accordingly. The features of many-body localization (MBL) are numerically identified by analyzing the spectral statistics and the entanglement entropy using exact diagonalization. These features are further confirmed by our time evolution results. In addition, the number of cavity photons are found stable over long time dynamics in the MBL phase. Such a feature can not only be utilized to nondestructively diagnose the MBL phase by monitoring the number of leaking photons from the cavity, but leveraged for constructing a device to produce a stable number of photons.