Tube algebras, excitations statistics and compactification in gauge models of topological phases

Understand

We consider lattice Hamiltonian realizations of ($d$+1)-dimensional Dijkgraaf-Witten theory.

• In (2+1)d, it is well-known that the Hamiltonian yields point-like excitations classified by irreducible representations of the twisted quantum double.
• This can be confirmed using a tube algebra approach.
• In this paper, we propose a generalization of this strategy that is valid in any dimensions.