Affiliation:
1. Princeton University
2. University of Minnesota
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.
Funder
Alfred P. Sloan Foundation
National Science Foundation
United States Department of Energy
Cited by
75 articles.
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