Classifying local fractal subsystem symmetry protected topological phases

Abstract

We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a small number of phases are actually realizable by local Hamiltonians. Which phases are possible depends crucially on the spatial structure of the symmetries, and we show that in many cases no non-trivial SPT phases are possible at all. In cases where non-trivial SPT phases do exist, we give an exhaustive enumeration of them in terms of their locality.

arXiv comment22 pages, 5 figures

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• Towards classification of Fracton phases: the multipole algebra
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Topological Gaps by Twisting
• Searching for Fracton Orders via Symmetry Defect Condensation
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