We investigate a bilayer Kitaev model in which two honeycomb layers are coupled by the Heisenberg interactions to discuss the effects of interlayer coupling on 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 dimer-singlet states. We find that a one-triplet excitation from the dimer-singlet 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 the 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.
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.