  The interplay of frustrated interactions and lattice geometry can lead to a
variety of exotic quantum phases. Here we unearth a particularly rich phase
diagram of the Kitaev-Heisenberg model on the star lattice, a triangle
decorated honeycomb lattice breaking sublattice symmetry. In the
antiferromagnetic regime, the interplay of Heisenberg coupling and geometric
frustration leads to the formation of valence bond solid (VBS) phases -- a
singlet VBS and a bond selective triplet VBS stabilized by the Kitaev exchange.
We show that the ratio of the Kitaev versus Heisenberg exchange tunes between
these VBS phases and chiral quantum spin liquid regimes. Remarkably, the VBS
phases host a whole variety of chiral triplon excitations with high Chern
numbers in the presence of a weak magnetic field. We discuss our results in
light of a recently synthesized star lattice material and other decorated
lattice systems.
