# Many-body self-localization in a translation-invariant Hamiltonian

## TL;DR

This paper investigates many-body localization in a translation-invariant Hamiltonian using quasi-periodic long-range interactions, revealing evidence of non-thermalizing, glassy behavior at both ground state and infinite temperature regimes.

## Contribution

It demonstrates many-body localization phenomena without disorder, utilizing experimentally feasible long-range interactions in a translation-invariant system.

## Key findings

- Evidence of divergent time-scales for charge inhomogeneities
- Observation of non-thermalization and information preservation
- Glassy behavior at ground state and infinite temperature

## Abstract

We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasi-periodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground-state of this system, being also present at infinite temperatures.