Walker-Wang models and axion electrodynamics

TL;DR

This paper establishes a connection between Walker-Wang lattice models and axion electrodynamics, showing how certain lattice Hamiltonians represent strong-coupling, gapped phases of magnetoelectric gauge theories with topological order.

Contribution

It demonstrates that Walker-Wang models can realize strong-coupling limits of axion electrodynamics, linking topological lattice models to electromagnetic responses of topological insulators.

Findings

Walker-Wang models capture a strong-coupling, gapped phase of magnetoelectric gauge theories.

The topological order in these models relates to the electromagnetic response of bosonic topological insulators.

The lattice Hamiltonians reflect the confined phase of the gauge theories.

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.