Periodic Anderson Model for Small Clusters

Abstract

The periodic Anderson model is applied to three different four-site clusters to study the f-site occupation (nf), specific heat (Cv) and magnetic susceptibility (xf) of rare-earth and actinide compounds. We consider one localized f orbital per site per spin with energy Ef with a Coulomb repulsion U between two electrons in ‘f’ orbitals in the same site, one extended orbital per site per spin with an interatomic transfer integral t and a positive hybridization term V between the localized and extended orbitals of same spin in different sites. The interaction between different sites is restricted to nearest neighbors and the number of electrons is taken to be one per site. The many-body eigenvalues and eigenstates are calculated exactly by diagonalizing the Hamiltonian. The principal features of our results for various choices of parameters are (i) observation of heavy-fermion behavior when the non-magnetic ground state is nearly degenerate with two excited magnetically ordered states; (ii) transition from a Kondo-lattice to a magnetic regime and subsequent re-entry to either a Kondo-lattice or a mixed-valence regime as Ef is increased; (iii) coexistence of magnetic order and mixed-valence for a narrow range-of Ef; (iv) the ‘benchmark’ results of Cy and Xf of single-impurity Anderson model are reproduced only at high temperatures.