Lattice density functional theory of the single-impurity Anderson model: Development and applications

Abstract

A lattice density functional theory (LDFT) of the single-impurity Anderson model is presented. In this approach the basic variable is the single-particle density matrix ${\ensuremath{\gamma}}_{\mathit{ij}}$ with respect to the lattice sites and the fundamental unknown functional is the Coulomb interaction energy $W[\ensuremath{\gamma}]$. Using general symmetry properties, a two-level ansatz for $W[\ensuremath{\gamma}]$ in spin-restricted systems is proposed which involves explicitly only the impurity orbital and a single symmetry-adapted conduction-band state. A simple analytical functional dependence of $W[\ensuremath{\gamma}]$ is derived on the basis of exact results of this two-level problem. The resulting approximation is shown to be exact in two important opposite limits: a totally degenerate conduction band and a conduction band with widely separated discrete levels. Applications to finite rings having $N\ensuremath{\leqslant}100$ atoms yield very accurate results for ground-state properties such as the kinetic, interaction, and total energy, as well as the occupation and magnetic moment of the local impurity orbital. This holds for all considered interaction strengths, from weak to strong correlations, as well as in the Kondo and intermediate valence regimes. One concludes that the present two-level approximation provides an appropriate framework for investigating subtle electron-correlation effects of the Anderson model within LDFT.