Periodic Anderson model for four-site clusters

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.