Effective interactions in the periodic Anderson model in the regime of mixed valency with strong correlations (Q1002662)

The paper is devoted to construction of effective Hamiltonian for the periodic Anderson model (PAM) in the intermediate valence regime, which describes antiferromegnetic interactions that influence the formation of the superconducting phase with the order parameter having the d-type symmetry. First, for the PAM Hamiltonian is used the atomic representation and splitting the hybridization interaction operator into two terms. The first term reflects processes resulting in mixing collectivized and localized electrons without changing the number of states called the pairs in the localized subsystem (the low energy sector of the Hilbert space). The second term is responsible for hybridization processes with simultaneous pair creation or annihilation, corresponding to processes inducing transitions to the high-energy sector of the Hilbert space. Due to the intra-atom Coulomb repulsion strength is large these processes are taken into account perturbatively. Thus, the application the sequence of unitary transformations to obtain the effective Hamiltonian allows one to obtain an expansion in powers of the small parameter. The small parameter is determined by only those hybridization processes that involve high-energy states of the localized subsystem. Correspondingly only these processes are excluded in the first and second order by using the unitary transformations. The hybridization processes, then remains in the lower Hubbard subband. As a result, the authors obtain the effective Hamiltonian describing as exchange interactions as interactions explicitly indicating a possibility of the Cooper instability and the creation of a superconducting phase with developed antiferromagnetic fluctuations. The obtained effective Hamiltonian is used for numerical study of the magnitudes of exchange interactions and their dependences on the distance necessary for understanding the nature of the magnetically ordered phase. The concrete numerical results present the dependences of the effective f-electron jump integral and the super-exchange interaction parameter on the coordinate sphere number at various values of the hybridization constant. Moreover, there are the results of calculation of the indirect interaction exchange integral at various distances between rare earth ions and also its dependence on the chemical potential at different values of the hybridization constant.