Abstract
We study symmetry-protected topological (SPT) phases of matter in 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 nontrivial SPT phases are possible at all. In cases where nontrivial SPT phases do exist, we give an exhaustive enumeration of them in terms of their locality.
- Received 7 February 2019
- Revised 29 May 2019
DOI:https://doi.org/10.1103/PhysRevB.99.235131
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