Fracton-like phases from subsystem symmetries

TL;DR

This paper explores fracton-like phases in lattice gauge theories with subsystem symmetries, revealing new topological phases, their ground state degeneracy, and entanglement properties in 2D and 3D models.

Contribution

It demonstrates the existence of fracton-like phases in standard lattice gauge theories with subsystem symmetries and analyzes their entanglement and degeneracy properties.

Findings

Ground state degeneracy grows exponentially with the square of system size.

Presence of mobile gauge charges alongside immobile fractons.

Connection between entanglement entropy and ground state degeneracy.

Abstract

We study models with fracton-like order based on $\mathbb{Z}_2$ lattice gauge theories with subsystem symmetries in $d=2$ and $d=3$ spatial dimensions. The $3d$ model reduces to the $3$-dimensional Toric Code when subsystem symmetry is broken, giving an example of a subsystem symmetry enriched topological phase (SSET). Although not topologically protected, its ground state degeneracy has as leading contribution a term which grows exponentially with the square of the linear size of the system. Also, there are completely mobile gauge charges living along with immobile fractons. Our method shows that fracton-like phases are also present in more usual lattice gauge theories. We calculate the entanglement entropy $S_A$ of these models in a sub-region $A$ of the lattice and show that it is equal to the logarithm of the ground state degeneracy of a particular restriction of the full model to $A$.