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Title: Fractal Symmetric Phases of Matter

Abstract

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.

Authors:
ORCiD logo [1];  [1];  [2];  [1]
  1. Princeton University
  2. University of Minnesota
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1491047
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 6 Journal Issue: 1
Publisher:
Stichting SciPost
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

Devakul, Trithep, You, Yizhi, Burnell, F. J., and Sondhi, Shivaji. Fractal Symmetric Phases of Matter. Country unknown/Code not available: N. p., 2019. Web. doi:10.21468/SciPostPhys.6.1.007.
Devakul, Trithep, You, Yizhi, Burnell, F. J., & Sondhi, Shivaji. Fractal Symmetric Phases of Matter. Country unknown/Code not available. doi:10.21468/SciPostPhys.6.1.007.
Devakul, Trithep, You, Yizhi, Burnell, F. J., and Sondhi, Shivaji. Wed . "Fractal Symmetric Phases of Matter". Country unknown/Code not available. doi:10.21468/SciPostPhys.6.1.007.
@article{osti_1491047,
title = {Fractal Symmetric Phases of Matter},
author = {Devakul, Trithep and You, Yizhi and Burnell, F. J. and Sondhi, Shivaji},
abstractNote = {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.},
doi = {10.21468/SciPostPhys.6.1.007},
journal = {SciPost Physics},
number = 1,
volume = 6,
place = {Country unknown/Code not available},
year = {2019},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.6.1.007

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Works referenced in this record:

Topological Insulators in Three Dimensions
journal, March 2007


Topological invariants of time-reversal-invariant band structures
journal, March 2007