Quantum liquids of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:math> Kitaev honeycomb and related Kugel-Khomskii models
W. M. H. Natori, Hui-Ke Jin, Johannes Knolle
Abstract
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.