| Summary: | Inspired by the recent discovery of correlated insulating states in twisted bilayer graphene, we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group simulation, we identify a metal-insulator transition around U_{c}/t=2.5–3. In the vicinity of U_{c}, we find strong spin-orbital density wave fluctuations at commensurate wave vectors, accompanied by weaker incommensurate charge density wave fluctuations. The spin-orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two-dimensional limit. At larger U, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insight into correlated electron phenomena in twisted bilayer graphene and other multiorbital honeycomb materials.
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