# Many-body localization in presence of cavity mediated long-range interactions

## TL;DR

This paper demonstrates that a 1D Hubbard model with cavity-mediated long-range interactions can exhibit many-body localization, observable through dynamics of emitted light, expanding understanding of localization phenomena in long-range interacting systems.

## Contribution

It introduces a model showing many-body localization with cavity-mediated long-range interactions and provides numerical evidence and observable signatures.

## Key findings

- Localization occurs in a 1D Hubbard model with all-to-all coupling.
- Time evolution shows features consistent with many-body localization.
- Localization can be observed via light emitted from optical cavities.

## Abstract

We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and finite-size scaling. The time evolution from a random initial state exhibits features consistent with the localization picture. The dynamics can be observed with quantum gases in optical cavities, localization can be revealed through the time-dependent dynamics of the light emitted by the resonator.