In this talk we will discuss (2+1)-dimensional topological phases of matter. In particular we will recall how they arise as degenerate ground states of lattice systems having a gapped Hamiltonian.
Examples of this are the Kitaev toric code, based on a lattice of spin-1/2 particles, as well as its generalisations - the Kitaev lattice model based on Hopf algebras, and the Levin-Wen model based on fusion categories.
The focus of this talk is going to be a construction allowing one to engineer a new topological order out of anyonic excitations of a given one.
This construction is an analogue of the aforementioned lattice models and is best described using a universal language of topologcial quantum field theories with defects, which we will also recall.
