Fractal symmetries: Ungauging the cubic code. (arXiv:1603.05182v3 [quant-ph] UPDATED)

Gauging is a ubiquitous tool in many-body physics. It allows one to construct
highly entangled topological phases of matter from relatively simple phases and
to relate certain characteristics of the two. Here we develop a gauging
procedure for general submanifold symmetries of Pauli Hamiltonians, including
symmetries of fractal type. We show a relation between the pre- and
post-gauging models and use this to construct short-range entangled phases with
fractal-like symmetries, one of which is mapped to the cubic code by the

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