Kaleidoscope of topological phases with multiple Majorana species

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some of them exhibiting the localized Majorana fermions that feature in proposals for topological quantum computing. The Chern invariant ν is an important characterization of such phases. Here we look at the square–octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and enjoys a rich phase diagram featuring distinct Abelian and non-Abelian phases with ν = 0,±1,±2,±3 and ±4. The ν = ±1 and ν = ±3 phases all support localized Majorana modes and are examples of Ising and SU(2) 2 anyon theories, respectively.