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 (21)

• Anyons in an exactly solved model and beyond
• Topological Field Theory of Time-Reversal Invariant Insulators
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Seeing the magnetic monopole through the mirror of topological surface states
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Superconductors are topologically ordered
• Boson topological insulators: A window into highly entangled quantum phases
• Symmetry protected topological phases from decorated domain walls
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Three-dimensional topological lattice models with surface anyons
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Generalizations and limitations of string-net models
• String and Membrane condensation on 3D lattices
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Topological order in a correlated three-dimensional topological insulator
• Quantization and $2\pi$ Periodicity of the Axion Action in Topological Insulators
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

Cited by in corpus (15)

• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Free-fermion descriptions of parafermion chains and string-net models
• Theory of oblique topological insulators
• Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime
• Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions
• Higher SPT's and a generalization of anomaly in-flow
• Finite-temperature quantum topological order in three dimensions
• Boundary topological entanglement entropy in two and three dimensions
• Instanton effects in lattice models of bosonic symmetry-protected topological states
• Generalized symmetry enriched criticality in (3+1)d
• Holographic duality between bulk topological order and boundary mixed-state order