Localization from shattering: higher dimensions and physical realizations

In recent work [{\it arXiv: 1904.04815}] two of us explained how the twin constraints of charge and dipole moment conservation `shatter' the Hilbert space of a one dimensional quantum system into emergent disconnected dynamical sectors, giving rise to an exactly localized subspace of dimension exponentially large in volume in which the localization does not rely on disorder, and is robust to noise. The dimensions of the emergent dynamical subsectors have a wide distribution, leading to a strong initial state dependence in the dynamics and the coexistence of low and high entanglement eigenstates reminiscent of quantum scarring. Here we explain how this phenomenology may be extended to higher dimensional systems on hypercubic lattices. We also explain how the key phenomena may be readily observed in near term ultracold atom experiments. In experimental realizations, the conservation laws are approximate rather than exact, so the localization only survives up to a prethermal timescale that we estimate. We comment on the implications of these results for recent predictions of Bloch/Stark many-body localization.