Surfaces of 3d symmetry protected phases
2015-05
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Surfaces of 3d symmetry protected phases
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2015-05
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Abstract
I will consider gapped Hamiltonians of generalized spin models, which are invariant under
a certain unbroken onsite unitary symmetry group. It is well known that such Hamiltonians
can realize topologically ordered phases, which in (2+1)d can be studied with modular tensor
categories. When a symmetry is included, the corresponding `symmetry enriched’ phases
correspond to a richer mathematical structure - e.g. braided G-crossed categories in (2+1)
d. However, in systematically constructing such braided G-crossed categories by extending
ordinary modular ones one sometimes encounters obstructions. Here we give a physical
interpretation for such obstruction, and show that the corresponding topologically ordered
theory, though it cannot be realized in 2d in a G-symmetric way, can be realized at the surface
of a 3d ‘symmetry protected’ phase. I will try to emphasize the physical interpretation of the
various mathematical concepts involved, and I will explain a specific example in detail.
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Fidkowski, Lukasz. (2015). Surfaces of 3d symmetry protected phases. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/172316.
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