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

## TL;DR

This paper demonstrates how local constraints in quantum systems can fragment Hilbert space into many disconnected subsectors, enabling localized quantum states and scars, which could be useful for robust quantum information storage.

## Contribution

It introduces the concept of Hilbert space shattering via local constraints, exemplified by a fractonic circuit model, revealing new pathways for quantum information protection.

## Key findings

- Hilbert space fractures into exponentially many localized subsectors.
- Localized subsectors exhibit strictly localized dynamics without disorder.
- The mechanism produces quantum many body scars with varying entanglement.

## Abstract

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.