# Flat-band many-body localization and ergodicity breaking in the Creutz ladder

## TL;DR

This paper investigates disorder-free many-body localization in the flat-band Creutz ladder, revealing robust localization phenomena and ergodicity breaking in both non-interacting and weakly disordered regimes, with a crossover to disorder-induced localization at strong disorder.

## Contribution

It demonstrates disorder-free many-body localization in the flat-band Creutz ladder and analyzes the robustness and crossover behavior of localization with disorder strength.

## Key findings

- Poisson-like level spacing distribution indicates disorder-free localization.
- Inverse participation ratio supports localization observations.
- Non-ergodic dynamics with preserved initial density wave pattern.

## Abstract

We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.