Phase diagrams of spin-S Kitaev ladders

We investigate the ground states of spin-Formula Presented Kitaev ladders using exact analytical solutions (for Formula Presented), perturbation theory, and the density matrix renormalization group method. We find an even-odd effect: in the case of half-integer Formula Presented, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer Formula Presented, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer Formula Presented we find a transition between two distinct SPT orders, and for integer Formula Presented we find unnecessary first-order phase transitions within a trivial phase.