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arXiv · 1606.06639

Topological phases from higher gauge symmetry in 3+1D

Alex Bullivant·Marcos Calçada·Zoltán Kádár·Paul Martin·João Faria Martins
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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.

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Alex Bullivant, Marcos Calçada, Zoltán Kádár, Paul Martin, João Faria Martins. 2016-09-22. Topological phases from higher gauge symmetry in 3+1D. https://doi.org/10.1103/physrevb.95.155118

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