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

Statistical Mechanics;Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics;Quantum Gases