{
"id": "1905.06309",
"version": "v1",
"published": "2019-05-15T17:33:29.000Z",
"updated": "2019-05-15T17:33:29.000Z",
"title": "Gauging permutation symmetries as a route to non-Abelian fractons",
"authors": [
"Abhinav Prem",
"Dominic J. Williamson"
],
"comment": "19 pages, 9 figures. Author order is swappable",
"categories": [
"cond-mat.str-el",
"quant-ph"
],
"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.",
"revisions": [
{
"version": "v1",
"updated": "2019-05-15T17:33:29.000Z"
}
],
"analyses": {
"keywords": [
"non-abelian fractons",
"gauging permutation symmetries",
"fully mobile pointlike excitations",
"gauged cubic code model represents",
"subdimensional excitations"
],
"note": {
"typesetting": "TeX",
"pages": 19,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}