Optimized Effective Potential for Extended Hubbard Model

TL;DR

This paper maps Hartree-Fock solutions of the extended Hubbard model onto a density-functional theory framework, providing new insights into the Kohn-Sham equations, the band-gap problem, and excitation energies.

Contribution

It introduces a universal Kohn-Sham potential applicable to various ordered states and links eigenvalues to physical properties within a density-functional approach.

Findings

Kohn-Sham and Hartree-Fock eigenvalues are related by a scaling transformation.

The band-gap issue is explained by derivative discontinuity of the basic variable.

Conductivity gap and spin-wave energies are determined by ground state parameters.

Abstract

Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly mapped onto an auxiliary local Kohn-Sham (KS) problem within a density-functional theory. The mapping provides a new insight into the interpretation of the KS equations. (i) With an appropriate choice of the basic variable, there is a universal form of the KS potential, which is applicable both for the antiferromagnetic and the charge ordered solutions. (ii) The Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling transformation. (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as the function of the electron number, rather than a finite discontinuity of the KS potential. (iv) It is argued that the conductivity gap and the energies of spin-wave excitations can be entirely defined by the parameters of the ground state and the KS eigenvalues.