Symmetric Fracton Matter: Twisted and Enriched

TL;DR

This paper investigates the relationship between symmetry and fracton order in 3D systems, revealing new topological phases, boundary modes, and statistical interactions described by higher-rank Chern-Simons theory.

Contribution

It introduces a framework connecting subsystem symmetry protected topological phases with fracton order and develops a higher-rank Chern-Simons theory to describe these phenomena.

Findings

Subsystem symmetry leads to gapless boundary modes.

Gauging symmetry results in novel fracton statistical interactions.

Partial gauging yields symmetry-enriched fracton phases.

Abstract

In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that these can realize subsystem symmetry protected topological phases with gapless boundary modes. Gauging the planar subsystem symmetry leads to a fracton order in which particles restricted to move along lines exhibit a new type of statistical interaction that is specific to the lattice geometry. We show that both the gapless boundary modes of the ungauged theory, and the statistical interactions after gauging, are naturally captured by a higher-rank version of Chern-Simons theory. We also show that gauging only part of the subsystem symmetry can lead to symmetry-enriched fracton orders, with quasiparticles carrying fractional symmetry charge.