Kaleidoscope of topological phases with multiple Majorana species

Abstract

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 v 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 v = 0,±1,±2,±3 and ±4. The v = ±1 and v = ±3 phases all support localized Majorana modes and are examples of Ising and SU(2)2 anyon theories, respectively. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.