  By using the constrained-phase quantum Monte Carlo method, we performed a
systematic study of the ground state of the half filled Hubbard model for a
trilayer honeycomb lattice. We analyze the effect of the perpendicular electric
field on the electronic structure, magnetic property and pairing correlations.
It is found that the antiferromagnetism is suppressed by the perpendicular
electric field, especially the long-range parts, and the dominant magnetic
fluctuations are still antiferromagnetic. The electronic correlation drives a
$d+id$ superconducting pairing to be dominant over other pairing patterns among
various electric fields and interaction strengths. We also found that the
$d+id$ pairing correlation is greatly enhanced as the on-site Coulomb
interaction is increased. Our intensive numerical results may unveil the nature
of the recently observed superconductivity in rhombohedral trilayer graphene
under an electric field.
