Foliated fracton order from gauging subsystem symmetries

TL;DR

This paper presents a general procedure for gauging models with subsystem symmetries, revealing how such gauging can produce foliated fracton order and establishing a link between symmetry charges and fracton phases.

Contribution

It explicitly summarizes the gauging process for subsystem symmetries and demonstrates its application to 3D paramagnetic states, connecting symmetry charges to fracton order.

Findings

Gauging subsystem symmetries can produce foliated fracton order.

The species of symmetry charges determine the resulting fracton phase.

Gauging linear subsystem symmetries exhibits a self-duality similar to 1D global symmetry gauging.

Abstract

Based on several previous examples, we summarize explicitly the general procedure to gauge models with subsystem symmetries, which are symmetries with generators that have support within a sub-manifold of the system. The gauging process can be applied to any local quantum model on a lattice that is invariant under the subsystem symmetry. We focus primarily on simple 3D paramagnetic states with planar symmetries. For these systems, the gauged theory may exhibit foliated fracton order and we find that the species of symmetry charges in the paramagnet directly determine the resulting foliated fracton order. Moreover, we find that gauging linear subsystem symmetries in 2D or 3D models results in a self-duality similar to gauging global symmetries in 1D.