Hamiltonian models for topological phases of matter in three spatial dimensions

Abstract

We present commuting projector Hamiltonian realizations of a large class of (3+1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the Crane-Yetter-Walker-Wang and 2-Group gauge theory models. We also present Hamiltonian realizations of a state sum TQFT recently constructed by Kashaev whose relation to existing models was previously unknown. We argue that this TQFT is captured as a special case of the Crane-Yetter-Walker-Wang model, with a premodular input category in some instances.

35 + 9 pages, 18 figures. v2 minor changes, references added; v3 published version

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• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
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• Exactly solvable models for U(1) symmetry-enriched topological phases
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• Dynamical generalization of Yetter's model based on a crossed module of discrete groups
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• Dynamics of a lattice 2-group gauge theory model
• 4-Manifold Invariants From Hopf Algebras
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