  We describe how the entanglement renormalisation approach to topological
lattice systems leads to a general procedure for treating the whole spectrum of
these models, in which the Hamiltonian is gradually simplified along a parallel
simplification of the connectivity of the lattice. We consider the case of
Kitaev's quantum double models, both Abelian and non-Abelian, and we obtain a
rederivation of the known map of the toric code to two Ising chains; we pay
particular attention to the non-Abelian models and discuss their space of
states on the torus. Ultimately, the construction is universal for such models
and its essential feature, the lattice simplification, may point towards a
renormalisation of the metric in continuum theories.
