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The Yao-Lee model is an example of exactly solvable spin-orbital models thatare generalizations of the original Kitaev honeycomb model with extra localorbital degrees of freedom. Similar to the Kitaev model, both spin and orbitaldegrees of freedom are effectively represented using sets of three-flavoredMajorana fermions. The Yao-Lee model exhibits a quantum spin liquid groundstate with gapped and immobile $Z_2$ fluxes and three-fold degenerate itinerantMajorana fermions. Our work demonstrated that by introducing differenttime-reversal symmetry (TRS) breaking fields one can split the degeneracy ofMajorana fermions and close the gap for some of the bands, thus changing itstopology. We calculated a comprehensive topological phase diagram for theYao-Lee model by considering various combinations of TRS-breaking fields. Thisinvestigation revealed the emergence of distinct topological regions, eachseparated by nodal lines, signifying an evolution in the model's topologicalproperties. We also investigated the impact of vacancies in the system. Ourfindings revealed that while vacancies modify the low-energy spectrum of themodel, their presence has a limited impact on the topological properties of themodel, at least for small enough concentrations.

Topological transitions in the Yao-Lee spin-orbital model and effects of site disorder