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We show how local constraints can globally "shatter" Hilbert space intosubsectors, leading to an unexpected dynamics with features reminiscent of bothmany body localization and quantum scars. A crisp example of this phenomenon isprovided by a "fractonic circuit" - a model of quantum circuit dynamics in onedimension constrained to conserve both charge and dipole moment. We show howthe Hilbert space of the fractonic circuit dynamically fractures intodisconnected emergent subsectors within a particular charge and dipole symmetrysector. A large number of the emergent subsectors, exponentially many in thesize of the system, have dimension one and exhibit strictly localized quantumdynamics---even in the absence of spatial disorder and in the presence oftemporal noise. Exponentially large localized subspaces can be proven to existfor any one dimensional fractonic circuit with finite spatial range, andprovide a potentially new route for the robust storage of quantum information.Other emergent subsectors display non-trivial dynamics and may be constructedby embedding finite sized non-trivial blocks into the localized subspace. Theshattering of a particular symmetry sector into a distribution of dynamicalsubsectors with varying sizes leads to the coexistence of high and lowentanglement states, i.e. this provides a general mechanism for the productionof quantum many body scars. We discuss the detailed pattern of fracturing andits implications. We also discuss other mechanisms for similarly shatteringHilbert space.

Local constraints can globally shatter Hilbert space: a new route to quantum information protection