Ground state phase diagram of the Kitaev-Heisenberg model with general spin S

The Kitaev model is an S=1/2 quantum spin model defined on the honeycomb lattice. In spite of strong frustration due to the bond-dependent exchange interaction, this model is exactly solvable, and its ground state is a quantum spin liquid state. In recent years, candidates of higher spin Kitaev materials were proposed, while the stability of the Kitaev quantum spin liquid to non-Kitaev interactions has not been systematically clarified for general spin S. In this study, we investigate the ground state for the spin-S Kitaev-Heisenberg model by using the pseudo-fermion functional renormalization group method. We clarify the ground state phase diagram for S=1/2, 1, 3/2, 2, 5/2, and 50. We reveal that quantum spin liquid regions shrink with increasing S, but they remain finite for S=1 and 3/2; the Kitaev quantum spin liquid is extremely fragile against the Heisenberg interaction for S≥2. We also confirm that the result for S=50 well reproduces the phase diagram by the classical Monte Carlo method. Our result will provide the search and design of the candidate materials with high S.