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

### Submission summary

 As Contributors: Abhinav Prem Arxiv Link: https://arxiv.org/abs/1905.06309v3 (pdf) Date accepted: 2019-11-11 Date submitted: 2019-10-22 Submitted by: Prem, Abhinav Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approach: Theoretical

### 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.

### Ontology / Topics

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Published as SciPost Phys. 7, 068 (2019)

Dear Editor and Referee,

Thank for your careful consideration and review of our work. We thank the referee for their kind remarks regarding our manuscript. In accordance with the referee's report, we have clarified the caption for Fig. 2, where the two colours (blue/green) are used to distinguish between the distinct layers.

Sincerely,
Abhinav Prem and Dominic Williamson

### List of changes

1) We have clarified the caption for Figure 2.

### Submission & Refereeing History

Resubmission 1905.06309v3 on 22 October 2019
Submission 1905.06309v2 on 5 June 2019