Speaker
Oskar Vafek (Florida State U)
Description
Many-body instabilities of the half-filled honeycomb bilayer are
studied using weak-coupling renormalization group (RG) as
well as
strong-coupling expansion [1,2]. For spinless fermions,
there are
4 independent four-fermion contact couplings. Generally, we find
runaway RG flows which we associate with ordering
tendencies. The
broken symmetry state is typically a gapped insulator with
either
broken inversion or broken time-reversal symmetry, with a
quantized anomalous Hall effect. Additionally, a tight-binding
model with nearest-neighbor hopping and nearest-neighbor
repulsion is studied in weak and strong couplings and in each
regime a gapped phase with inversion symmetry breaking is found.
In the strong-coupling limit, the ground-state wave function is
constructed for vanishing in-plane hopping but finite interplane
hopping, which explicitly displays the broken inversion symmetry
and a finite difference between the number of particles on the
two layers. In the spin-1/2 case we use Fierz
identities to show that there are 9 independent four-fermion
contact couplings[2]. The 9 RG equations in this case reduce to
the 3 found in Ref.[1] assuming that screened Coulomb
interactions dominate
and in this case lead to the electronic nematic as the
leading instability.
The 9 RG equations are also used to show that, just as in
strong coupling,
the most dominant weak-coupling instability of the repulsive
Hubbard model (at half filling) is an antiferromagnet.
[1] O. Vafek and K. Yang, PRB 81, 041401 (2010). (Physics 3,
1 (2010))
[2] O. Vafek, PRB 82, 205106 (2010)
