Mixed Valence and Spin States of the Two-Impurity System: New Hartree-Fock Ground States

Abstract

New Hartree-Fock ground states are shown to result in the two-impurity Anderson model when coupled to boson-like interactions. The new states are asymmetric in both charge and spin in the two sites and exhibit the two types corresponding to the different exchange mechanisms. This situation in which two identical atoms behave as two unbalanced centers may have a variety of applications in condensed-matter physics such as valence fluctuations in solids. In this paper we analytically demonstrate the existence of new Hartree-Fock (HF) ground states in the two-impurity Anderson model with boson-like interac­ tion.*) The new ground states are asymmetric states in both charge and spin (staggered) in the two sites, which are stabilized below ferromagnetic and anti ferromagnetic coupling states only in the presence 0/ boson-like interac­ tion. We assert these spatially asymmetric ground states are a general con­ sequence of the systems describable by the present model and may relate to valence fluctuations in periodic systems such as certain rare-earth compounds. I) The boson-coupled Anderson model has been studied by Haldane 2 ) as a single impurity version of the Falicov-Kimball mode1. 3 ) He has found that in contrast to the conventional single-impurity Anderson mode1 4 ) the magnetic phase boundaries become the first-order transition lines when localized electrons are coupled with boson fields. This first-order transition at zero temperature (in parameter space) is equivalent in origin to that of Falicov-Kimball at finite temperatures due to interband Coulomb interaction in the composite periodic systems.