  Both insulating and conducting electronic behaviors have been experimentally
seen in clean bilayer graphene samples at low temperature, and there is still
no consensus on the nature of the interacting ground state at half-filling and
in the absence of a magnetic field. Theoretically, several possibilities for
the insulating ground states have been predicted for weak interaction strength.
However, a recent renormalization-group calculation on a Hubbard model for
charge-neutral bilayer graphene with short-range interactions suggests the
emergence of low-energy Dirac fermions that would stabilize the metallic phase
for weak interactions. Using a non-perturbative projective quantum Monte Carlo,
we calculate the ground state for bilayer graphene using a realistic model for
the Coulomb interaction that includes both short-range and long-range
contributions. We find that a finite critical onsite interaction is needed to
gap bilayer graphene, thereby confirming the Hubbard model expectations even in
the presence of a long-range Coulomb potential, in agreement with our
theoretical renormalization group analysis. In addition, we also find that the
critical onsite interactions necessary to destabilize the metallic ground state
decreases with increasing interlayer coupling.
