Topological order and fractons from gauging exponential symmetries

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…

• NS
  National Science Foundation

  Awards: DMR-2439118, 2439118
• UD
  U.S. Department of Energy

  Awards: DE-FG02-06ER46316, FG02-06ER46316, DE-FG02-, DE-FG02
• DO
  Division of Materials Research