Interaction induced Dirac fermions from quadratic band touching in bilayer graphene

TL;DR

This paper shows that in bilayer graphene, weak local interactions do not cause strong coupling but instead induce a Dirac phase with no symmetry breaking, with a finite-coupling transition to an antiferromagnetic state.

Contribution

It provides a new RG argument and quantum Monte Carlo evidence that local interactions in bilayer graphene generate a Dirac phase rather than leading to strong coupling or symmetry breaking at weak interactions.

Findings

Weak interactions do not flow to strong coupling in QBT systems.

Interactions generate a linear dispersion term, stabilizing a Dirac phase.

Antiferromagnetism appears at finite interaction strength with a continuous transition.

Abstract

We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite $U/t$, despite the $U=0$ hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with a dynamical critical exponent $z=1$ as expected for 2+1 d Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.