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Recently it has been suggested that many-body localization (MBL) can occur intranslation-invariant systems, and candidate 1D models have been proposed. Wefind that such models, in contrast to MBL systems with quenched disorder,typically exhibit much more severe finite-size effects due to the presence oftwo or more vastly different energy scales. In a finite system, this can easilycreate an artificial splitting of the density of states (DOS) into bandsseparated by large energy gaps. We argue that in order for such models tofaithfully represent the physics of the thermodynamic limit, the ratio of therelevant coupling parameters must be larger than a certain cutoff that dependson system size, and should be chosen in such a way that various bands in theDOS of a given model overlap with one another. By setting the parameters inthis way to minimize the finite-size effects, we then perform exactdiagonalization studies of several translation-invariant MBL candidate models.Based on the variety of diagnostics, including entanglement properties and thebehaviour of local observables, we find the systems exhibit thermal (ergodic),rather than MBL-like behaviour. Our results suggest that MBL intranslation-invariant systems with two or more very different energy scales isless robust than perturbative arguments suggest, possibly pointing to theimportance of non-perturbative effects which induce delocalization in thethermodynamic limit.

Many-body localization in disorder-free systems: the importance of finite-size constraints