  We study the single-orbital Hubbard model on the half-filled decorated
honeycomb lattice. In the non-interacting theory at half-filling the Fermi
energy lies within a flat band where strong correlations are enhanced. The
lattice is highly frustrated. We find a correlation driven first-order
metal-insulator transition to two different insulating ground states - a dimer
valence bond solid Mott insulator when inter-triangle correlations dominate,
and a broken $\mathcal{C}_3$-symmetry antiferromagnet that arises from
frustration when intra-triangle correlations dominate. The metal-insulator
transitions into these two phases have very different characters. The
metal-broken $\mathcal{C}_3$ antiferromagnetic transition is driven by
spontaneous $\mathcal{C}_3$ symmetry breaking that lifts the topologically
required degeneracy at the Fermi energy and opens an energy gap in the
quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no
symmetries of the Hamiltonian. It is caused by strong correlations
renormalizing the electronic structure into a phase that is adiabatically
connected to both the trivial band insulator and the ground state of the
spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither
of these metal-insulator transitions can be understood in either the
Brinkmann-Rice or Slater paradigms.
