Topological order and Fractons from Gauging Exponential Symmetries

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.

24 pages, 18 figures. v5: typos fixed;

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Cited by in corpus (7)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Topological Dipole Insulator
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass