We study the ground-state phase diagram of the spin-$1/2$ Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor-network calculations based on the infinite projected entangled pair state (iPEPS) technique with the simple-update scheme, as well as high-order series expansions using perturbative continuous unitary transformations (pCUTs). We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM), and stripy states, two extended quantum spin liquid phases arise in proximity of the Kitaev limit. While these phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid (VBS) phase emerges in a relatively narrow range of parameter space between the AFM and stripy states. This VBS state can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of interlayer interactions on the emergence of quantum phases in the bilayer Kitaev materials.

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• Quantum phase transitions
• Quantum spin liquid
• Kitaev-Heisenberg model
• Tensor network methods