Hilbert space shattering and disorder-free localization in polar lattice gases.

Emerging dynamical constraints resulting from inter-site interactions severely limit the mobility of polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the $1/r^3$ tail of the dipolar interaction results in Hilbert space shattering even for moderate interaction strengths, that leads to interaction-induced many-body localization. At half-filling, shattering just requires strong-enough next-to-nearest-neighbor interactions. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body localization may be within reach of future experiments with magnetic atoms and polar molecules.