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 nu 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 nu = 0, +/- 1, +/- 2, +/- 3 and +/- 4. The nu = +/- 1 and nu = +/- 3 phases all support localized Majorana modes and are examples of Ising and SU(2)(2) anyon theories, respectively