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

### Submission summary

 As Contributors: Weslei Fontana Arxiv Link: https://arxiv.org/abs/2006.10071v4 (pdf) Date accepted: 2021-04-26 Date submitted: 2021-04-15 13:53 Submitted by: Fontana, Weslei Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy 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.

Published as SciPost Phys. Core 4, 012 (2021)

Dear Editor,

We are grateful to the referee for the pertinent criticisms. Following her/his comments, we revised the manuscript. We have addressed all the requested changes.

Sincerely,

The Authors

### List of changes

*We added to the manuscript an additional appendix (Appendix E) with the discussion on how to determine the elements of the K-matrix;
*We have also included in the additional Appendix E the discussion of how theories with different K-matrices are equivalent,
*We have added to the manuscript equations (22) and (23) and a discussion about the compactification of the fields;
*We have included in the manuscript a discussion about the level quantization in Sec. IV A, and
also a new appendix (Appendix D) with further details of the calculation;
*In addition to the major changes required by the referee, we have also addressed all the listed
minor changes.

We thank the referee for the constructive and valuable criticism.