Walker-Wang models and axion electrodynamics

We connect a family of gauge theories (Maxwell theories with a magnetoelectric coupling $θ= 2 πk, k \in \mathbb{Z}$) to the family of 3D topological lattice models introduced by Walker and Wang. In particular, we show that the lattice Hamiltonians capture a certain strong-coupling limit of these gauge theories, in which the system enters a gapped (confined) phase. We discuss the relationship between the topological order exhibited by certain of these lattice Hamiltonians and the characteristic electromagnetic response of the symmetry-protected bosonic topological insulator.

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