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

Study on a disorder-free many-body localization is reported for 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 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. This indicates the existence of the disorder-free localization. Calculation of the inverse participation ratio supports 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 localization phase. We also find non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.