Local-density approach and quasiparticle levels for generalized Hubbard Hamiltonians

Abstract

This paper presents a general method to describe and analyze electron correlation effects in local-orbital electronic structure calculations using a generalized Hubbard Hamiltonian. In our approach, we first introduce a local density formalism where the total energy of the system is obtained as a function of the orbital occupancies $\{n_i\}$ associated with each local orbital; in particular, exchange and correlation local potentials are presented for a multilevel case. In parallel, using the dynamical mean field approximation, a many-body solution is obtained by means of a local self-energy that appropriately interpolates between the low and high correlation limits. We also show that the local density and the many-body solutions are linked through charge consistency conditions. These two solutions are applied to a multilevel Anderson impurity and to a multiband Hubbard lattice, our results showing the high accuracy of the approach presented in this paper. Further on, we discuss how to apply our previous analysis to the case of crystals and molecules and analyze several examples: bulk Si, and HF and ${\mathrm{H}}_2\mathrm{O}$ molecules. The good results obtained for these cases show that our approach for the description of correlation effects offers an interesting alternative to the well-established density functional methods based on the calculation of the electron density $\rho \left(\overrightarrow{r}\right).\mathrm{}$