▎ 摘　　要

On a lattice model, we study the possible existence of a gapped broken inversion symmetry phase (GBISP) of electrons with long-range Coulomb interactions in bilayer graphene using both the self-consistent Hartree-Fock approximation (SCHFA) and the renormalized ring-diagram approximation (RRDA). The RRDA takes into account the charge density fluctuations beyond the SCHFA. Although the GBISP at low temperature and low carrier concentration is predicted by the SCHFA, we show here that this state can be substantially suppressed by the charge density fluctuations in the RRDA. We also present a numerical algorithm for calculating the self-energy of electrons with the singular long-range Coulomb interaction on the lattice model.