Optimal Hubbard Models for Materials with Nonlocal Coulomb Interactions: Graphene, Silicene, and Benzene

To understand how nonlocal Coulomb interactions affect the phase diagram of correlated electron materials, we report on a method to approximate a correlated lattice model with nonlocal interactions by an effective Hubbard model with on-site interactions U* only. The effective model is defined by the Peierls-Feynman-Bogoliubov variational principle. We find that the local part of the interaction U is reduced according to U* = U - (V) over bar, where (V) over bar is a weighted average of nonlocal interactions. For graphene, silicene, and benzene we show that the nonlocal Coulomb interaction can decrease the effective local interaction by more than a factor of 2 in a wide doping range.