## SciPost Submission Page

# Gauging permutation symmetries as a route to non-Abelian fractons

### by Abhinav Prem, Dominic J. Williamson

### Submission summary

As Contributors: | Abhinav Prem |

Arxiv Link: | https://arxiv.org/abs/1905.06309v2 |

Date submitted: | 2019-06-05 |

Submitted by: | Prem, Abhinav |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

We discuss the procedure for gauging on-site $\mathbb{Z}_2$ global symmetries of three-dimensional lattice Hamiltonians that permute quasi-particles and provide general arguments demonstrating the non-Abelian character of the resultant gauged theories. We then apply this general procedure to lattice models of several well known fracton phases: two copies of the X-Cube model, two copies of Haah's cubic code, and the checkerboard model. Where the former two models possess an on-site $\mathbb{Z}_2$ layer exchange symmetry, that of the latter is generated by the Hadamard gate. For each of these models, upon gauging, we find non-Abelian subdimensional excitations, including non-Abelian fractons, as well as non-Abelian looplike excitations and Abelian fully mobile pointlike excitations. By showing that the looplike excitations braid non-trivially with the subdimensional excitations, we thus discover a novel gapped quantum order in 3D, which we term a "panoptic" fracton order. This points to the existence of parent states in 3D from which both topological quantum field theories and fracton states may descend via quasi-particle condensation. The gauged cubic code model represents the first example of a gapped 3D phase supporting (inextricably) non-Abelian fractons that are created at the corners of fractal operators.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-8-5 Invited Report

### Report

This paper presents the explicit construction of exactly solvable fracton models with novel features. In particular, the models are obtained by gauging a Z2 permutation symmetry in known fracton models and they exhibit new features like the co-existence of the topological type excitations and fracton type excitations, inextricably non-abelian fractons, etc. These features were not present in the models that were previously known, therefore the new models expand our knowledge about fracton models and the paper presents an important contribution to the field.

The paper is written in an amazingly clear way. Pedagogical examples were explained in detail. Moreover, a systematic discussion was given to explain the appearance of the new features under a generic setup. The paper should be easy to follow for people working in the field. Therefore, I recommend publication of this paper pretty much as it is. I only have one minor comment: The caption of figure 2 is a bit confusing. The figure contains (a) and (b) parts which are not referred to in the caption. How is the blue region different from the green region in figure (b)?