Fractal symmetric phases of matter

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

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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.

Original languageEnglish (US)
Article number007
JournalSciPost Physics
Issue number1
StatePublished - Jan 2019

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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