Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models

Abstract

The $S=3/2$ Kitaev honeycomb model (KHM) is unique among the spin-$S$ Kitaev models due to a massive ground state quasi-degeneracy that hampered previous numerical and analytical studies. In a recent work~\cite{jin2022unveiling}, we showed how an SO(6) Majorana parton mean-field theory of the $S=3/2$ 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 $S=3/2$ KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by DMRG simulations. In this paper, we explore the connection between the $S=3/2$ KHM with Kugel-Khomskii models and discover new exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field \emph{Ans{ä}tze} in the spin and orbital basis for different quantum liquid phases of the $S=3/2$ KHM. Finally, we investigate a proposed time-reversal symmetry breaking spin liquid induced by a {[}111{]} single ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g. an unquantized thermal Hall response.

17 pages, 9 figures

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• Beyond Kitaev physics in strong spin-orbit coupled magnets
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• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Multicomponent magneto-orbital order and magneto-orbitons in monolayer VCl3
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Projectively implemented altermagnetism in an exactly solvable quantum spin liquid
• Coexistence of static and dynamic local magnetic fields in an S = 3/2 honeycomb lattice antiferromagnet Co2Te3O8
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems