Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene

TL;DR

This paper introduces a variational method to approximate nonlocal Coulomb interactions in correlated materials with an effective local Hubbard model, significantly simplifying the analysis of materials like graphene, silicene, and benzene.

Contribution

The authors develop a variational approach to map nonlocal Coulomb interactions onto an effective local Hubbard model, providing a practical way to study complex materials.

Findings

Nonlocal interactions can reduce the effective on-site interaction U* by over 50%.

The method is applied successfully to graphene, silicene, and benzene.

Nonlocal Coulomb effects are significant across a wide doping range.

Abstract

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', where V' 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.