The exactly solvable spin-1/2 Kitaev model on a honeycomb lattice has drawn significant interest, as it offers a pathway to realizing a quantum spin liquid. Notably, such bond-dependent interaction not only gives rise to the Kitaev spin liquid, but is also ubiquitious in spin-orbit coupled magnetic materials, leading to unconventional effects in various ways. As an example, I will first present a microscopic theory for CoNb2O6, which has served as an exemplar of the 1D Ising model. Our theory elucidates the roles of Kitaev and another bond-dependent interaction, known as Gamma interaction, in shaping Ising anisotropy and domain excitations.[1] I will then discuss the Yao-Lee spin liquid, another exactly solvable model on an unusual star lattice featuring non-abelian spinons, built upon the Kitaev model. The additional pseudospin degrees of freedom in this model could provide greater stability against perturbations, making this model appealing. However, a mechanism to realize such an interaction in a standard honeycomb lattice remains unknown. I will present a microscopic theory to obtain the Yao-Lee model on a honeycomb lattice.[2] This mechanism leads to the desired bond-dependent interaction among spins rather than orbitals, unique to our model, implying that the orbitals fractionalize into gapless Majorana fermions and fermionic octupolar excitations emerge. Since the conventional Kugel-Khomskii interaction also appears, the phase diagram including these interactions using classical Monte Carlo simulations and exact diagonalization techniques will be presented. Several open questions will be also discussed.
[1] Transforming from Kitaev to Disguised Ising Chain: Application to CoNb2O6, Phys. Rev. Lett. 133, 056703 (2024).
[2] Microscopic roadmap to a Kitaev-Yao-Lee spin-orbital liquid, npj Quantum Materials 10, 26 (2025).