  We show how local constraints can globally "shatter" Hilbert space into
subsectors, leading to an unexpected dynamics with features reminiscent of both
many body localization and quantum scars. A crisp example of this phenomenon is
provided by a "fractonic circuit" - a model of quantum circuit dynamics in one
dimension constrained to conserve both charge and dipole moment. We show how
the Hilbert space of the fractonic circuit dynamically fractures into
disconnected emergent subsectors within a particular charge and dipole symmetry
sector. A large number of the emergent subsectors, exponentially many in the
size of the system, have dimension one and exhibit strictly localized quantum
dynamics---even in the absence of spatial disorder and in the presence of
temporal noise. Exponentially large localized subspaces can be proven to exist
for any one dimensional fractonic circuit with finite spatial range, and
provide a potentially new route for the robust storage of quantum information.
Other emergent subsectors display non-trivial dynamics and may be constructed
by embedding finite sized non-trivial blocks into the localized subspace. The
shattering of a particular symmetry sector into a distribution of dynamical
subsectors with varying sizes leads to the coexistence of high and low
entanglement states, i.e. this provides a general mechanism for the production
of quantum many body scars. We discuss the detailed pattern of fracturing and
its implications. We also discuss other mechanisms for similarly shattering
Hilbert space.
