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We study the single-orbital Hubbard model on the half-filled decoratedhoneycomb lattice. In the non-interacting theory at half-filling the Fermienergy lies within a flat band where strong correlations are enhanced. Thelattice is highly frustrated. We find a correlation driven first-ordermetal-insulator transition to two different insulating ground states - a dimervalence bond solid Mott insulator when inter-triangle correlations dominate,and a broken $\mathcal{C}_3$-symmetry antiferromagnet that arises fromfrustration when intra-triangle correlations dominate. The metal-insulatortransitions into these two phases have very different characters. Themetal-broken $\mathcal{C}_3$ antiferromagnetic transition is driven byspontaneous $\mathcal{C}_3$ symmetry breaking that lifts the topologicallyrequired degeneracy at the Fermi energy and opens an energy gap in thequasiparticle spectrum. The metal-dimer valence bond solid transition breaks nosymmetries of the Hamiltonian. It is caused by strong correlationsrenormalizing the electronic structure into a phase that is adiabaticallyconnected to both the trivial band insulator and the ground state of thespin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neitherof these metal-insulator transitions can be understood in either theBrinkmann-Rice or Slater paradigms.

$C_3$ symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice