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

### 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