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

TL;DR

This paper investigates correlation-driven metal-insulator transitions in a half-filled Hubbard model on a decorated honeycomb lattice, revealing two distinct insulating phases with different symmetry-breaking mechanisms.

Contribution

It uncovers two different first-order metal-insulator transitions driven by correlations, involving a $ ext{C}_3$ symmetry-breaking antiferromagnet and a dimer valence bond solid, in a frustrated flat-band system.

Findings

First-order transition to $ ext{C}_3$-symmetry breaking antiferromagnet.

Transition to dimer valence bond solid insulator without symmetry breaking.

Transitions are not explained by Brinkmann-Rice or Slater paradigms.

Abstract

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.