Contrasting ground states of quantum magnets with the integer- and half-integer-spin moments are the manifestation of many-body quantum interference effects. In this work, we investigate the distinct nature of the integer- and half-integer-spin quantum spin liquids in the framework of the Kitaev's model on the honeycomb lattice. The models with arbitrary spin quantum numbers are not exactly solvable in contrast to the well-known quantum spin liquid solution of the spin-1/2 system. We use the tensor-network wave functions for the integer-and half-integer-spin quantum spin liquid states to unveil the important difference between these states. We find that the distinct sign structures of the tensor-network wave function for the integer- and half-integer-spin quantum spin liquids are responsible for completely different ground states in the spatially anisotropic limit. Hence the spatial anisotropy would be a useful diagnostic test for distinguishing these quantum spin liquid states, both in the numerical computations and experiments on real materials. We support this discovery via extensive numerics including the tensor-network, DMRG, and exact diagonalization computations.
The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-S we uncover that these conserved quantities are exactly the Z_{2} gauge fluxes in the general spin-S model, including the case of spin-1/2. Particularly, we find an even-odd effect that the Z_{2} gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z_{2} gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z_{2} gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.
In the prior work [J. Phys. Soc. Jpn. 91 , 124709 (2022)], we have introduced the spin-half decorated honeycomb Kitaev model, and have elucidated its exactly-solvable nature at any temperature. In this work, we extend the model to that with an arbitrary spin quantum number S . We show that the ground state is classical spin liquid whose degeneracy is independent of S . As for the fi nite-temperature properties, the partition function cannot be obtained analytically, unlike the spin-half case. We therefore perform the Monte Carlo simulation to reveal the fi nite-temperature properties, taking S = 1 and 3/2 cases as examples. We fi nd that the temperature dependence of the energy and the specific heat exhibits typical behaviors of the classical spin liquid. In particular, the broad peak of the specific heat is accounted for by the configuration of the classical variables on the edge of the hexagons.
Motivated by recent reports of a field-induced intermediate phase (IP) in the antiferromagnetic honeycomb Kitaev model that may be a spin liquid whose nature is distinct from the Kitaev
Z2 phase, we present a detailed numerical study on the nature and dynamical response (such as dynamical spin-structure factors and resonant inelastic x-ray scattering intensities) of this field-induced IP and neighboring phases in a family of Kitaev-based models related by hidden symmetries and duality transformations. We further show that the same field-induced IP can appear in models relevant for $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, which exhibit a ferromagnetic Kitaev coupling and additional interactions. In $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, the IP represents a new phase, that is likely independent from the putative field-induced (spin-liquid) phase recently reported from thermal Hall conductivity measurements.
The
S=23 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=23 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=23 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=23 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=23 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.