Topological phases from higher gauge symmetry in 3+1D

TL;DR

This paper introduces an exactly solvable 3+1D topological phase model based on higher gauge symmetry using finite 2-groups, connecting lattice gauge theory with topological quantum field theory and revealing dualities with Walker-Wang models.

Contribution

It presents a new Hamiltonian model for 3+1D topological phases employing higher lattice gauge theory and explicitly relates it to homotopy 2-type TQFTs, extending the understanding of topological matter.

Findings

Model is a Hamiltonian realization of Yetter's homotopy 2-type TQFT.

Ground state degeneracy computed for various manifolds and 2-groups.

Subset of models shown to be dual to Abelian Walker-Wang models for topological insulators.

Abstract

We propose an exactly solvable Hamiltonian for topological phases in $3+1$ dimensions utilising ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a Hamiltonian realisation of Yetter's homotopy 2-type topological quantum field theory whereby the groundstate projector of the model defined on the manifold $M^3$ is given by the partition function of the underlying topological quantum field theory for $M^3\times [0,1]$. We show that this result holds in any dimension and illustrate it by computing the ground state degeneracy for a selection of spatial manifolds and 2-groups. As an application we show that a subset of our model is dual to a class of Abelian Walker-Wang models describing $3+1$ dimensional topological insulators.