Walker-Wang models and axion electrodynamics

Abstract

We connect a family of gauge theories (Maxwell theories with a magnetoelectric coupling $\theta =2\pi k,k\in \mathbb{Z}$) 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.

Added supplementary material on surface behaviour of the models

References in corpus (3)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases