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arXiv · 1606.07816

Symmetry enriched string-nets: Exactly solvable models for SET phases

Chris Heinrich·Fiona Burnell·Lukasz Fidkowski·Michael Levin
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Abstract

We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group $G$ and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. Our models are designed so that they have a special property: if we couple them to a dynamical lattice gauge field with gauge group $G$, the resulting gauge theories are equivalent to modified string-net models. This property is what allows us to analyze our models in generality. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a $\mathbb{Z}_2$ symmetry which exchanges the $e$ and $m$ type anyons. We further illustrate our construction with a number of additional examples.

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Chris Heinrich, Fiona Burnell, Lukasz Fidkowski, Michael Levin. 2016-06-24. Symmetry enriched string-nets: Exactly solvable models for SET phases. https://doi.org/10.1103/physrevb.94.235136

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