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

2016/06/30 by Chris Heinrich, Fiona Burnell, Lukasz Fidkowski +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.94.235136

published as Phys. Rev. B 94, 235136 (2016) · Published version

arxiv created 2016/12/19 · arxiv updated 2016/12/21

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 ℤ₂ symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples.

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