Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model

We microscopically construct an abelian mutual Chern-Simons lattice gauge theory for magnetic field-tuned topological transitions in the Kitaev model and obtain a complete characterization of the phases, including their quasiparticles. At low fields for both ferro and antiferromagnetic (FM(AFM)) Kitaev interactions, we demonstrate nonabelian Ising topological order (ITO), and explicitly construct the Majorana anyon as an intrinsic excitation -- a twist defect in our \textit{abelian} gauge theory. For the AFM case, an abelian chiral phase appears at intermediate fields with trivial topological order and fermionic bulk excitations. Remarkably, both the ITO phase and the intermediate phase have the same chiral central charge $c=1/2,$ implying no change in the quantized thermal Hall response across the transition. For the FM case, there is a direct transition from ITO to a partially polarized nontopological phase. Our study completes the proof of Kitaev's original proposal of the low-field ITO with $c=1/2$ going beyond his mean-field arguments by including the crucial effect of the gauge fluctuations, and provides a resolution of the debate surrounding the intermediate field phase in the AFM case.