Quantum Phase Transitions in the Kitaev-Heisenberg Model on a Single Hexagon

We present a detailed analysis of the Kitaev-Heisenberg model on a single hexagon. The energy spectra and spin-spin correlations obtained using exact diagonalisation indicate quantum phase transitions between antiferromagnetic and anisotropic spin correlations when the Kitaev interactions increase. In cluster mean-field approach frustrated nearest neighbor exchange stabilizes the stripe phase in between the Néel phase and frustrated one which evolves towards the Kitaev spin liquid.