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.