We study ground-state and thermodynamic properties of an S = 1 Kitaev model. We first clarify the existence of global parity symmetry in addition to the local symmetry on each plaquette, which enables us to perform the large scale calculations up to 24 sites. It is found that the ground state should be singlet and its energy is estimated as E/N ∼ −0.65J, where J is the Kitaev exchange coupling. We find that a lowest excited state belongs to the same subspace as the ground state and the gap monotonically decreases with increasing system size, which suggests that the ground state of the S = 1 Kitaev model is gapless. By means of the thermal pure quantum states, we clarify finite temperature properties characteristic of the Kitaev models with S ≤ 2.

We investigate a bilayer Kitaev model, where two honeycomb layers are coupled by the Heisenberg interactions, to discuss effects of an interlayer coupling against the Kitaev quantum spin liquids (QSLs). In this model, there exists a local conserved quantity, which results in no long-range spin correlations in the system. Using the exact diagonalization, bond operator mean-field theory, and cluster expansion techniques, we study ground state properties in the system. The obtained results suggest the existence of a first-order quantum phase transition between the Kitaev QSL and singlet-dimer states. We find that one-triplet excitation from the singlet-dimer ground state is localized owing to the existence of the local conserved quantity. To examine finite-temperature properties, we make use of the thermal pure quantum state approach. We clarify that double-peak structure in the specific heat inherent in the Kitaev QSL is maintained even above the quantum phase transition. The present results suggest that the Kitaev QSL is stable against the interlayer interference. Magnetic properties of multilayer Kitaev models are also addressed. arXiv:1712.09050v1 [cond-mat.str-el]

The ground state of the bilayer Kitaev model with the Heisenberg-type interlayer exchange interaction is investigated by means of the exact diagonalization. Calculating the ground-state energy, local quantity defined on each plaquette, and dynamical spin structure factor, we obtain results suggesting the existence of a quantum phase transition between the Kitaev quantum spin liquid (QSL) and dimer singlet states when the interlayer coupling is antiferromagnetic. On the other hand, increasing the ferromagnetic interlayer coupling, there exists no singularity in the physical quantities, suggesting that the S = 1/2 Kitaev QSL state realized in each layer adiabatically connects to another QSL state realized in the S = 1 Kitaev model. Thermodynamic properties are also studied by means of the thermal pure quantum state method.

We study ground state properties in the bilayer Kitaev model by means of the dimer expansion. The existence of parity symmetries in the system reduces the computational cost significantly. This allows us to expand the ground state energy and interlayer spin-spin correlation up to 30th order in the interdimer Kitaev coupling. The numerical calculations clarify that the dimer singlet state is indeed realized in the wide parameter region.