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Kitaev's model of spins interacting on a honeycomb lattice describes aquantum spin-liquid, where an emergent static $\mathbb{Z}_2$ gauge field iscoupled to Majorana fermions. In the presence of an external magnetic field andfor a range of interaction strengths, the system behaves as a gapped,non-Abelian quantum spin-liquid. In this phase, the vortex excitations of theemergent $\mathbb{Z}_2$ gauge field have Majorana zero modes bound to them.Motivated by recent experimental progress in measuring and characterizing realmaterials that could exhibit spin-liquid behavior, we analytically calculatethe dynamical spin structure factor in the non-Abelian phase of the Kitaev'shoneycomb model. In particular, we treat the case of quenched disorder in thevortex configurations. Our calculations reveal a peak in the low-energydynamical structure factor that is a signature of the spin-liquid behavior. Wemap the effective Hamiltonian to that of a chiral p-wave superconductor byusing the Jordan-Wigner transformation. Subsequently, we analytically calculatethe wave functions of the Majorana zero modes, the energy splitting for finiteseparation of the vortices and finally, the dynamical structure factor inpresence of quenched disorder.

Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder