<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>C</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> 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 half-filled decorated honeycomb lattice. In noninteracting theory at half filling Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. find correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle dominate, and broken ${C}_{3}$-symmetry antiferromagnet that arises from frustration intratriangle dominate. transitions into these phases have very characters. metal-broken ${C}_{3}$ antiferromagnetic by spontaneous symmetry breaking lifts topologically required degeneracy opens an gap in quasiparticle spectrum. metal-dimer breaks no symmetries of Hamiltonian. It caused renormalizing electronic structure phase adiabatically connected both trivial state spin-1/2 Heisenberg relevant parameter regime. Therefore, neither can be understood either Brinkmann-Rice or Slater paradigms.