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There have been substantial recent efforts, both experimentally andtheoretically, to find a material realization of the Kitaev spin-liquid--theground state of the exactly solvable Kitaev model on the honeycomb lattice.Candidate materials are now plentiful, but the presence of non-Kitaev termsmakes comparison between theory and experiment challenging. We rederivetime-dependent Majorana mean-field theory and extend it to include quantumphase information, allowing the direct computation of the experimentallyrelevant dynamical spin-spin correlator, which reproduces exact results for theunperturbed model. In contrast to previous work, we find that smallperturbations do not substantially alter the exact result, implying that$\alpha$-RuCl${}_3$ is perhaps farther from the Kitaev phase than originallythought. Our approach generalizes to any correlator and to any model whereMajorana mean-field theory is a valid starting point.

Dynamics of fractionalized mean-field theories: consequences for Kitaev materials