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Electrically controllable magnetic order in the bilayer Hubbard model on honeycomb lattice --- a determinant quantum Monte Carlo study

Layered antiferromagnetic spin density wave (LAF) state is one of the plausible ground states of charge neutral Bernal stacked bilayer graphene. In this paper, we use determinant quantum Monte Carlo method to study the effect of the electric field on the magnetic order in bilayer Hubbard model on a honeycomb lattice. Our results qualitatively support the LAF ground state found in the mean field theory. The obtained magnetic moments, however, are much smaller than what are estimated in the mean field theory. As electric field increases, the magnetic order parameter rapidly decreases.