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Layered antiferromagnetic spin density wave (LAF) state is one of theplausible ground states of charge neutral Bernal stacked bilayer graphene. Inthis paper, we use determinant quantum Monte Carlo method to study the effectof the electric field on the magnetic order in bilayer Hubbard model on ahoneycomb lattice. Our results qualitatively support the LAF ground state foundin the mean field theory. The obtained magnetic moments, however, are muchsmaller than what are estimated in the mean field theory. As electric fieldincreases, the magnetic order parameter rapidly decreases.

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