Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

TL;DR

This paper presents a novel approach to generating Hilbert space fragmentation and fractonic behavior in higher dimensions by leveraging subsystem and higher-form symmetries, unifying various phenomena and proposing new models.

Contribution

It introduces a new method to achieve strong Hilbert space fragmentation and fractons in higher dimensions through subsystem and higher-form symmetries, expanding the theoretical framework.

Findings

Higher-dimensional strong fragmentation achieved via subsystem symmetries.

Lifting 1D models with higher-form symmetries results in topologically robust weak fragmentation.

Mixing subsystem and higher-form symmetries leads to models like X-cube fractons.

Abstract

We introduce a new route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and "lifting" to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a new route to higher-dimensional strong fragmentation, and also a new route to fractonic behavior. Meanwhile, lifting one-dimensional strongly fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust weak fragmentation. In three or more spatial dimensions, one can also "mix and match" subsystem and higher-form symmetries, leading to canonical fracton models such as X-cube. We speculate that this approach could also yield a new route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with novel properties.