Phase diagram of the Heisenberg model on the decorated honeycomb lattice.

We numerically investigate the phase diagram of quantum Heisenberg model on lattices which interpolate between honeycomb and triangular lattice. We show how the known phase diagrams of the honeycomb and triangular lattices interpolate into each other and examine the robustness of the spin liquid phase on the triangular lattice. Using fidelity analysis we discover a host of new ordered phases in this diagram which do not appear in the triangular and honeycomb phase diagrams separately. For the topological phases, we discuss possible spin liquid classifications based on the analysis of modular matrices and the effects of additional chiral interactions.