Periodic Anderson model for four-site clusters

Abstract

The periodic Anderson model is applied to three different four-site clusters (square, rhombus, and tetrahedron) with periodic boundary conditions. We consider one extended orbital per site per spin with an interatomic transfer integral t and with the mean energy chosen to be zero. We also consider one localized f orbital per site per spin with energy E_f with a Coulomb repulsion U between two electrons in the f orbitals in the same site. There is a positive hybridization term V between the localized and extended orbitals of same spin in different sites. The number of electrons is taken to be one per site and the interactions between different sites is restricted to nearest neighbors. The many-body eigenvalues and eigenstates are calculated exactly by constructing a computer program to diagonalize the Hamiltonian. The f-state occupation (n_f) and the temperature dependence of specific heat (c_v) and magnetic susceptibility (X_f) of f electrons are calculated for a wide range of parameters. We find that the mixed-valent, Kondo, and magnetic regimes depend sensitively on E_f/||t||, V/||t||, and the geometry of the clusters (which simulate the band-structure effects), but not on U. When E_f/||t|| is large and negative, for small values of V/||t|| (n_f≊ 1), the many-body ground state is nonmagnetic but the next two excited states are magnetically ordered and nearly degenerate with the ground state. The next higher energy level is well separated from these states. Therefore the specific heat rises sharply at low temperatures and the system exhibits heavy-fermion behavior. In a few cases, the ground state is magnetically ordered but nearly degenerate with a nonmagnetic excited state and well separated from other states. This corresponds to heavy fermions with magnetically ordered ground state. In some cases, there is a transition from the Kondo lattice to a magnetic regime and subsequent reentry into either a Kondo-lattice or a mixed-valence regime as E_f is gradually increased from large negative values. We also find that magnetic order and mixed valence can coexist for a very narrow range of E_f for some choice of parameters.