Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal Symmetric Phases of Matter   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.

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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: stat