Abstract
We report 10 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.
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