C3 symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting 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 intertriangle correlations dominate, and a broken C3-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken C3 antiferromagnetic transition is driven by spontaneous C3 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.