Topological order and fractons from gauging exponential symmetries
Phys. Rev. B 113, 045130 – Published 16 January, 2026
DOI: https://doi.org/10.1103/vvhq-wnll
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 exponential polynomial symmetries. Gauging these symmetries yields 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 variants of fracton topological order.
