Kitaev honeycomb models in magnetic fields: Dynamical response and dual models

Motivated by recent reports of a field-induced intermediate phase (IP) in the antiferromagnetic honeycomb Kitaev model that may be a spin liquid whose nature is distinct from the Kitaev Z₂ phase, we present a detailed numerical study on the nature and dynamical response (such as dynamical spin-structure factors and resonant inelastic x-ray scattering intensities) of this field-induced IP and neighboring phases in a family of Kitaev-based models related by hidden symmetries and duality transformations. We further show that the same field-induced IP can appear in models relevant for α-RuCl₃, which exhibit a ferromagnetic Kitaev coupling and additional interactions. In α-RuCl₃, the IP represents a new phase, that is likely independent from the putative field-induced (spin-liquid) phase recently reported from thermal Hall conductivity measurements.