Anyon polarons as a window into competing phases of the Kitaev honeycomb model under a Zeeman field

We systematically investigate the evolution of the anyon quasiparticles of the Kitaev model perturbed by a Zeeman field away from its exactly solvable limit in order to gain insights on the competition of its chiral spin liquid and nearby phases, such as the mysterious intermediate phase observed in the antiferromagnetic model. We study the low energy quasiparticles in three superselection sectors: the non-abelian visons, the fermions and the local bosons. Both for the ferro- and antiferro-magnetic models we find that the fermion sector and single vison sector become gapless at nearly identical critical value of the Zeeman coupling. In the ferromagnetic model this is consistent with a direct transition into a polarized state. In the anti-ferromagnetic model this implies that previous theories of the intermediate phase viewed as a spin liquid with a different Chern number for the fermions are inadequate, as they presume that the vison gap does not close. Furthermore, in the antiferromagnetic Kitaev model we also find that a local bosonic quasiparticle becomes gapless at nearly the same critical Zeeman field at which the visons and fermions become gapless. This boson carries the quantum numbers of an in-plane anti-ferromagnetic order parameter, raising the possibility that intermediate mysterious phase has spontaneously broken symmetry with this order.