Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C_3$ symmetry breaking metal-insulator transitions near 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 non-interacting theory at half-filling the Fermi
energy lies within a flat bland where strong correlations are enhanced and the
lattice exhibits frustration. 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.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics