Fractonic order in infinite-component Chern-Simons gauge theories

Xiuqi Ma, Wilbur Shirley, Meng Cheng, Michael Levin, John McGreevy, Xie Chen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Fracton order features point excitations that either cannot move at all or are only allowed to move in a lower-dimensional submanifold of the whole system. In this paper, we generalize the (2+1)-dimensional [(2+1)D] U(1) Chern-Simons (CS) theory, a powerful tool in the study of (2+1)D topological orders, to include infinite gauge field components and find that they can describe interesting types of (3+1)-dimensional fracton order beyond what is known from exactly solvable models and tensor gauge theories. On the one hand, they can describe foliated fractonic systems for which increasing the system size requires insertion of nontrivial (2+1)D topological states. The CS formulation provides an easier approach to study the phase relation among foliated models. More interestingly, we find simple examples that lie beyond the foliation framework, characterized by 2D excitations of infinite order and irrational braiding statistics. This finding extends our realm of understanding of possible fracton phenomena.

Original languageEnglish
Article number195124
JournalPhysical Review B
Issue number19
StatePublished - 15 May 2022
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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