Topological order and Fractons from Gauging Exponential Symmetries

TL;DR

This paper introduces a new class of discrete gauge theories derived from exponential polynomial symmetries, leading to topological order and fracton phases with UV-dependent properties and constrained quasiparticle mobility.

Contribution

It generalizes quantum field theory by gauging exponential symmetries, producing novel 2D topological orders, non-CSS codes, and 3D fracton phases with unique features.

Findings

Gauging exponential symmetries yields UV-dependent topological order.

Constructs non-CSS stabilizer codes via a Chern-Simons variant.

Extends to 3D, producing new fracton topological orders.

Abstract

We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with unconventional charge-conservation laws, which we term \textit{exponential polynomial symmetries}. Gauging these symmetries yields $\mathbb{Z}_N$ gauge theories in 2D that exhibit topological order whose quasiparticles have constrained mobility and whose ground-state degeneracy shows ultraviolet (UV) dependence. These features are reminiscent of spatial symmetry-enriched topological order, wherein quasiparticle excitations transform nontrivially under lattice translations. We further propose a Chern-Simons variant that produces non-CSS stabilizer codes and outline a framework for exponentially symmetric subsystem SPT phases. Finally, we extend this gauging procedure to 3D, obtaining new variants of fracton topological order.