Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions*

In bilayer graphene at charge neutrality, previous theoretical studies have shown that even with infinitesimal long-range electron-electron interactions, the quadratic band structure is susceptible to several different symmetry breaking ground states. This is in stark contrast to a recent numerical quantum Monte Carlo study [Pujari et. al., PRL 117, 086404 (2016)] showing that the short-range Hubbard interaction spontaneously generates a linear band that stabilises the metallic phase over a finite range of weak interactions. In this theoretical work, using a combination of renormalization group, quantum Monte Carlo and lattice perturbation theory, we address the question of what happens for a realistic model of the Coulomb interaction that includes both short-range and long-range components. Surprisingly, we find that the metallic phase remains stable without the generation of linear bands. We discuss the implications of this finding on the interpretation of available experiments.