Localization from Hilbert space shattering: from theory to physical realizations

TL;DR

This paper demonstrates how conservation laws can fragment Hilbert space into many disconnected parts, leading to localized and scar-like dynamics in quantum systems, with potential experimental observations.

Contribution

It introduces the phenomenon of Hilbert space shattering caused by conservation laws, especially in fractonic models, and explores its implications for localization and quantum dynamics.

Findings

Hilbert space fractures into exponentially many disconnected subsectors.

Many subsectors exhibit strictly localized dynamics without disorder.

The phenomenon can be observed in ultracold atom experiments.

Abstract

We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected 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' model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in arbitrary spatial dimensions. A large number of the emergent subsectors, exponentially many in system volume, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. While `fractonic' models provide a particularly clean realization, the shattering phenomenon is more general, as we discuss. We also discuss how the key phenomena may be readily observed in near term ultracold atom experiments. In experimental realizations, the conservation laws are approximate rather than exact, so the localization only survives up to a prethermal timescale that we estimate. We comment on the implications of these results for recent predictions of Bloch/Stark many-body localization.