Excitation basis for (3+1)d topological phases

Understand

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model.

• The corresponding lattice Hamiltonian yields excitations located at torus-boundaries.
• By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra.
• This defines an algebraic structure extending the Drinfel'd double.