Dynamical transition in the Kitaev spin liquid under an external magnetic field

We investigate magnetic-field-induced transitions in the dynamical spin correlation functions of the Kitaev spin liquid (KSL). Using time-dependent Majorana mean-field theory, we show that in the ferromagnetic KSL, the real-space propagation of spin correlations evolves from isotropic to highly anisotropic with increasing field strength. Notably, the anisotropy emerges as a unidirectional propagation of spin correlations, whose direction is dictated by the orientation of the magnetic field relative to the underlying Kitaev bond geometry. We analyze this phase transition through both Majorana mean-field framework and perturbative approach, and propose some experimental signatures and possible detection schemes. We further demonstrate that a similar transition occurs in the antiferromagnetic KSL, and discuss why previous studies focus on the [111] field direction have overlooked this phenomenon, which further suggests possibility to identify such anisotropic dynamics in candidate Kitaev materials.