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Lattice Clifford fractons and their Chern-Simons-like theory

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

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Submission summary

As Contributors: Weslei Fontana · Pedro Gomes
Arxiv Link: (pdf)
Date accepted: 2021-04-26
Date submitted: 2021-04-15 13:53
Submitted by: Fontana, Weslei
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


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)

Author comments upon resubmission

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.


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.

Submission & Refereeing History

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Resubmission 2006.10071v4 on 15 April 2021

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