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

Chris Heinrich, Fiona Burnell, Lukasz Fidkowski, Michael Levin

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47 Scopus citations


We construct exactly solvable models for a wide class of symmetry-enriched topological (SET) phases. Our construction applies to two-dimensional (2D) bosonic SET phases with finite unitary on-site 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 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 Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples.

Original languageEnglish (US)
Article number235136
JournalPhysical Review B
Issue number23
StatePublished - Dec 15 2016

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© 2016 American Physical Society. ©2016 American Physical Society.


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