Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models

The Kitaev honeycomb model hosts a fascinating fractionalized state of matter featuring emergent Majorana fermions and a vison particle that carries the flux of an emergent gauge field. In the exactly solvable model these visons are static, but certain perturbations can induce their motion. We show that the nature of the vison motion induced by a Zeeman field is sharply distinct in the ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the ferromagnetic model the vison has a trivial nonprojective translational symmetry, whereas in the antiferromagnetic Kitaev model it has a projective translational symmetry with n- flux per unit cell. The vison band of the ferromagnetic case has zero Berry curvature and no associated intrinsic contribution to the thermal Hall effect. In contrast, in the antiferromagnetic case there are two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in light of the physics of the spin liquid candidate alpha-RuCl3.

Automated summary

The Kitaev honeycomb model exhibits a fascinating fractionalized state of matter with emergent Majorana fermions and vison particles that carry emergent gauge field flux. In this solvable model, the visons are static but certain perturbations can induce their motion. We demonstrate that the motion of visons induced by a Zeeman field is distinctly different in the ferromagnetic and antiferromagnetic Kitaev models. Specifically, in the ferromagnetic model, the vison has a trivial nonprojective translational symmetry, while in the antiferromagnetic model, it has a projective translational symmetry with n-flux per unit cell. The ferromagnetic case has a vison band with zero Berry curvature and no intrinsic contribution to the thermal Hall effect. In contrast, the antiferromagnetic case has two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in relation to the spin liquid candidate alpha-RuCl3.