Ergodicity breaking with long-range cavity-induced quasiperiodic interactions

Many-body localization (MBL) behavior is analyzed in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is assumed. The analysis of the level statistics and of the eigenstates' entanglement entropy shows that a significant fraction of eigenstates becomes localized as the strength of the global interactions is increased. This behavior scales differently depending on the choice of the thermodynamic limit. The system is asymptotically ergodic by scaling the interaction strength so as to keep the energy extensive. On the other hand, the MBL regime seems to be stable if one allows for a superextensive scaling of the energy. We argue that our findings can be experimentally verified in many-body cavity quantum electrodynamics setups by means of the so-called quench spectroscopy. The latter can allow one, amongst others, to reveal the presence of a mobility edge.