Extending the Gutzwiller approximation to intersite interactions

Abstract

We develop an extension of the Gutzwiller approximation (GA) formalism that includes the effects of Coulomb interactions of arbitrary range (including density density, exchange, pair hopping, and Coulomb-assisted hopping terms). This formalism reduces to the ordinary GA formalism for the multiband Hubbard models in the presence of only local interactions. This is accomplished by combining the $1/z$ expansion---where $z$ is the coordination number, and only the leading-order terms contribute in the limit of infinite dimensions---with a ${P}_{R}^{\ifmmode\dagger\else\textdagger\fi{}}{P}_{R}\ensuremath{-}I$ expansion, where ${P}_{R}$ is the Gutzwiller projector on the site $R$. The method is conveniently formulated in terms of a Gutzwiller Lagrange function. We apply our theory to the extended single-band Hubbard model. Similarly to the usual Brinkman-Rice mechanism, we find a Mott transition. A valence skipping transition is observed, where the occupation of the empty and doubly occupied states for the Gutzwiller wave function is enhanced with respect to the uncorrelated Slater determinant wave function.