Symmetric fracton matter: Twisted and enriched

Yizhi You, Trithep Devakul, F. J. Burnell, S. L. Sondhi

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that these can realize subsystem symmetry protected topological phases with gapless boundary modes. Gauging the planar subsystem symmetry leads to a fracton order in which particles restricted to move along lines exhibit a new type of statistical interaction that is specific to the lattice geometry. We show that both the gapless boundary modes of the ungauged theory, and the statistical interactions after gauging, are naturally captured by a higher-rank version of Chern–Simons theory. We also show that gauging only part of the subsystem symmetry can lead to symmetry-enriched fracton orders, with quasiparticles carrying fractional symmetry charge.

Original languageEnglish (US)
Article number168140
JournalAnnals of Physics
StatePublished - May 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Fracton
  • Higher rank gauge theory
  • Topological phase


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