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The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin liquids, in which fractional quasiparticles would provide applications in decoherence-free topological quantum computing. The key ingredient is the bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which require strong entanglement between spin and orbital degrees of freedom. This study investigates the identification and design of rare-earth materials displaying robust Kitaev interactions. We scrutinize all possible $4f$ electron configurations, which require up to $6+$ million intermediate states in the perturbation processes, by developing a parallel computational program designed for massive scale calculations. Our analysis reveals a predominant interplay between the isotropic Heisenberg $J$ and anisotropic Kitaev $K$ interactions across all realizations of the Kramers doublets. Remarkably, instances featuring $4f^3$ and $4f^{11}$ configurations showcase the prevalence of $K$ over $J$, presenting unexpected prospects for exploring the Kitaev QSLs in compounds including Nd$^{3+}$ and Er$^{3+}$, respectively. Beyond the Kitaev model, our computational program also proves adaptable to a wide range of $4f$-electron magnets. |
