  Compounds of transition metal ions with strong spin-orbit coupling recently
attracted attention due to the possibility to host frustrated bond-dependent
anisotropic magnetic interactions. In general, such interactions lead to
complex phase diagrams that may include exotic phases, e.g. the Kitaev spin
liquid. Here we report on our comprehensive analysis of the global phase
diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice
compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method
based on spin coherent states that enabled us to resolve arbitrary spin
patterns in the cluster ground states obtained by exact diagonalization. Global
trends in the phase diagram are understood in combination with the analytical
mappings of the Hamiltonian that uncover peculiar links to known models -
Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - or
reveal entire manifolds of exact fluctuation-free ground states. Finally, our
study can serve as a methodological example that can be applied to other spin
models with complex bond-dependent non-Heisenberg interactions.
