Localization from Hilbert space shattering: From theory to physical realizations

Known routes to ergodicity breaking -- integrability and many-body localization -- require extensively many explicit or emergent conservation laws. Here we show that two conservation laws are sufficient to provably and robustly break ergodicity by ``shattering'' Hilbert space into exponentially many dynamically disconnected sectors. This represents a new paradigm for localization, which does not rely on disorder or energy conservation, which works in any number of spatial dimensions, and which should be realizable in near-term ultracold atom experiments.