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Fractal Symmetric Phases of Matter

by Trithep Devakul, Yizhi You, F. J. Burnell, S. L. Sondhi

This Submission thread is now published as SciPost Phys. 6, 007 (2019)

Submission summary

As Contributors: Trithep Devakul
Arxiv Link: (pdf)
Date accepted: 2018-12-19
Date submitted: 2018-10-09 02:00
Submitted by: Devakul, Trithep
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach. Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge. Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry. In 3D, our construction leads additionally to FSPT phases protected by higher form fractal symmetries and fracton topologically ordered phases enriched by the additional fractal symmetries.

Published as SciPost Phys. 6, 007 (2019)

Author comments upon resubmission

We have implemented a number of changes based on the useful comments by the referee.

List of changes

The changes are in response to the referee comments, which include:

* The edge modes in Sec 5.3 are worked out in more detail.
* Added an explanation for the correlation function of the Newman-Moore model.
* Some wording changes through to distinguish between various concepts such as the total symmetry group as opposed to a particular element of the group, and so on.
* Other small changes in wording as suggested by the referee.

Submission & Refereeing History

Published as SciPost Phys. 6, 007 (2019)

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Resubmission 1805.04097v3 on 9 October 2018

Reports on this Submission

Anonymous Report 1 on 2018-12-7 (Invited Report)


My previous concern was that the argument for the protected edges was insufficient. The present revision contains satisfactory explanation on how to find symmetry operators that "localizes" on edges, so as to induce a projective representation on one of the edges. I believe this manuscript is suitable for publication.

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