Many-Body Self-Localization in a Translation-Invariant Hamiltonian*

We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasi-periodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground-state of this system, being also present at infinite
temperatures. Unlike in standard studies of many-body localization, what triggers the breakdown of ergodicity in our model is the magnitude of the interactions and not a disorder amplitude.