Regensburg 2010 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 4: CE: Quantum Impurities, Kondo Physics
TT 4.2: Talk
Monday, March 22, 2010, 10:30–10:45, H21
Lattice density-functional theory of the single-impurity Anderson model — •Waldemar Töws and Gustavo Pastor — Institut für Theoretische Physik, Universität Kassel, Germany
A lattice density-functional theory of the single-impurity Anderson model is presented. In this approach the basic variable is the single-particle density matrix γij σ with respect to the lattice sites. The central interaction-energy functional W[ γ ] is shown to be invariant under unitary transformations of orbitals in the conduction band. This property is exploited to find a unitary transformation such that the localized impurity orbital experiences charge fluctuations only to a particular single-particle state of the conduction band. A simple analytical approximation to W [ γ ] is then derived from the solution of the resulting two-level problem. This so-called two-level approximation can be shown to be exact in the limit of a totally degenerated conduction band as well as in the limit of widely separated discrete conduction-band levels. The minimization of the total energy functional E[ γ ] with respect to γij σ yields the ground-state properties such as the kinetic, interaction and total energy, as well as the occupation and spin polarization of the impurity orbital. The results obtained with the two-level-approximation for finite rings having N ≤ 12 sites are in agreement with exact Lanczos diagonalizations in all interaction regimes, from weak to strong correlations. In particular the singlet-triplet gap, which determines the Kondo temperature, is correctly described. This constitutes a remarkable qualitative improvement over mean-field approximations. Advantages and limitations of this approach are discussed.