Résumé (EN)

We investigate the possibility of many-body localization in translation invariant Hamiltonian systems. A key feature of many-body localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with quenched disorder, and that they could therefore in principle delocalize the system. The motion of these resonant spots is reminiscent of motion in kinetically constrained models, the frustration effect being caused by a mismatch of energies rather than by geometric constraints. We provide examples where, in first order in the hopping, the resonant spots are effectively trapped (analogous to a jammed phase) and therefore localization is not ruled out, but we also have examples where, despite the rareness of resonant spots, the resonant spots are not trapped and hence this obvious scenario for many-body localization is not realized. We comment on the analysis of higher orders, but we did not reach a final conclusion yet.