Interplay of topological order and symmetry breaking

M. D. Schulz

We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of 
different string tensions. 
The resulting phase diagram includes several phases, including phases harboring Abelian and 
non-Abelian anyons as well as different topologically trivially phases.

We investigate the location and critical properties of phase transitions between these phases by 
means of high-order series expansions and exact diagonalizations.
Different phase transitions are found, including different second-order transitions out of the 
non-Abelian topological phase.