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The presence of flat bands is a source of localization in lattice systems.While flat bands are often unstable with respect to interactions between theparticles, they can persist in certain cases. We consider a diamond ladder withtransverse hopping that possesses such stable flat bands and show thatmany-body localization appears in the presence of interactions without quencheddisorder. We numerically demonstrate that the eigenstate thermalizationhypothesis is violated. We show that the influence of degenerate flat bandstates spreads across the full energy spectrum and grows extensively in thethermodynamic limit. Furthermore, we verify localization in terms of timeevolution of some local observable, revival probability, participation ratioand entanglement entropy.

Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands