Influence of hopping self-energy effects and quasiparticle degradation on the antiferromagnetic ordering in the bilayer honeycomb Hubbard model

Abstract

We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We determine the changes in the antiferromagnetic magnetic ordering tendencies due to the real and imaginary parts of the selfenergy at the band crossing points. In particular we present an estimate for the threshold value U* below which the magnetic order is endangered by the splitting of the quadratic band touching points into four Dirac points by an interaction-induced interlayer skew hopping. For most of the parameter space however, the quasiparticle degradation by the frequency-dependence of the sublattice-diagonal selfenergies and the Dirac-cone steepening are more essential for suppressing the AF ordering tendencies considerably. Our results might help to understand to understand the energy scales obtained in renormalization group treatments of the same model and shed light on recent quantum Monte Carlo investigations about the fate of the magnetic ordering down to lower U.