Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models

Abstract

The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-$S$ Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general $S$. We show that, similar to the $S=1/2$ case, the phase diagram for higher $S$ contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing $S$, becoming vanishingly narrow for $S\ge 2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search of higher-$S$ Kitaev materials.

14 pages, 12 figures

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• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Kitaev interactions in the van der Waals antiferromagnet VBr3
• Magnetic-field induced melting of long-range magnetic order akin to Kitaev insulators in the metallic compound Tb5Si3