The $S=\frac{3}{2}$ Kitaev honeycomb model (KHM) is unique among the spin- $S$ Kitaev models due to a massive ground-state quasidegeneracy that hampered previous numerical and analytical studies. In a recent work [Jin et al., Nat. Commun. 13, 3813 (2022)], we showed how an SO(6) Majorana parton mean-field theory of the $S=\frac{3}{2}$ isotropic KHM explains the anomalous features of this Kitaev spin liquid (KSL) in terms of an emergent low-energy Majorana flat band. Away from the isotropic limit, the $S=\frac{3}{2}$ KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by density-matrix renormalization group simulations. In this paper, we explore the connection between the $S=\frac{3}{2}$ KHM with Kugel-Khomskii models and discover exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field Ans\"atze in the spin and orbital basis for different quantum liquid phases of the $S=\frac{3}{2}$ KHM. Finally, we investigate a proposed time-reversal symmetry-breaking spin liquid induced by [111] single-ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g., an unquantized thermal Hall response.The $S=\frac{3}{2}$ Kitaev honeycomb model (KHM) is unique among the spin-$S$ Kitaev models due to a massive ground-state quasidegeneracy that hampered previous numerical and analytical studies. In a recent work [Jin et al., Nat. Commun. 13, 3813 (2022)], we showed how an SO(6) Majorana parton mean-field theory of the $S=\frac{3}{2}$ isotropic KHM explains the anomalous features of this Kitaev spin liquid (KSL) in terms of an emergent low-energy Majorana flat band. Away from the isotropic limit, the $S=\frac{3}{2}$ KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by density-matrix renormalization group simulations. In this paper, we explore the connection between the $S=\frac{3}{2}$ KHM with Kugel-Khomskii models and discover exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field Ans\"atze in the spin and orbital basis for different quantum liquid phases of the $S=\frac{3}{2}$ KHM. Finally, we investigate a proposed time-reversal symmetry-breaking spin liquid induced by [111] single-ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g., an unquantized thermal Hall response.

arXiv:2304.13378Physical review. B./Physical review. BAug 4, 202318 citations

Γ -matrix generalization of the Kitaev model

Congjun Wu, Daniel P. Arovas, Hsiang-Hsuan Hung

We extend the Kitaev model defined for the Pauli matrices to the Clifford algebra of $\ensuremath{\Gamma}$ matrices, taking the $4\ifmmode\times\else\texttimes\fi{}4$ representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically nontrivial phase carries gapless chiral edge modes along the sample boundary. On the three-dimensional (3D) diamond lattice, the ground states can exhibit gapless 3D Dirac-cone-like excitations and gapped topological insulating states. Generalizations to even higher rank $\ensuremath{\Gamma}$ matrices are also discussed.We extend the Kitaev model defined for the Pauli matrices to the Clifford algebra of $\ensuremath{\Gamma}$ matrices, taking the $4\ifmmode\times\else\texttimes\fi{}4$ representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically nontrivial phase carries gapless chiral edge modes along the sample boundary. On the three-dimensional (3D) diamond lattice, the ground states can exhibit gapless 3D Dirac-cone-like excitations and gapped topological insulating states. Generalizations to even higher rank $\ensuremath{\Gamma}$ matrices are also discussed.

arXiv:0811.1380Physical Review BApr 22, 200977 citations

Generalizations of the Kitaev-Heisenberg model and connections to experiment

Itamar Kimchi, Yi‐Zhuang You, Ashvin Vishwanath

Bulletin of the American Physical SocietyFeb 29, 20120 citations

The

S=\frac{3}{2}

Kitaev honeycomb model (KHM) is unique among the spin-

S

Kitaev models due to a massive ground-state quasidegeneracy that hampered previous numerical and analytical studies. In a recent work [Jin et al., Nat. Commun. 13, 3813 (2022)], we showed how an SO(6) Majorana parton mean-field theory of the

S=\frac{3}{2}

isotropic KHM explains the anomalous features of this Kitaev spin liquid (KSL) in terms of an emergent low-energy Majorana flat band. Away from the isotropic limit, the

S=\frac{3}{2}

KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by density-matrix renormalization group simulations. In this paper, we explore the connection between the

S=\frac{3}{2}

KHM with Kugel-Khomskii models and discover exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field Ans\"atze in the spin and orbital basis for different quantum liquid phases of the

S=\frac{3}{2}

KHM. Finally, we investigate a proposed time-reversal symmetry-breaking spin liquid induced by [111] single-ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g., an unquantized thermal Hall response.