  We report ten ground states arising from strong correlations in the
single-orbital Hubbard model on the decorated honeycomb lattice; including
Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and
trimer Mott insulators, and a spin-$1$ Mott insulator. The rich phase diagram
arises from structures within the unit cell. Hence, such states are absent on
simpler lattices. We argue that such insulating phases are prevalent on
decorated lattices. These are found in many materials and common in
coordination polymers, providing a playground to explore this physics.

Strongly Correlated Electrons