## SciPost Submission Page

# Lattice Clifford fractons and their Chern-Simons-like theory

### by Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon

### Submission summary

As Contributors: | Weslei Fontana |

Arxiv Link: | https://arxiv.org/abs/2006.10071v2 (pdf) |

Date submitted: | 2020-07-14 02:00 |

Submitted by: | Fontana, Weslei |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.

###### Current status:

Editor-in-charge assigned