Thermodynamic Study Of The Periodic Anderson Model

Heavy-fermion materials are compounds containing rare earth and actinide atoms that exhibit high specific heats and spin susceptibilities at low temperature.This feature is associated with high effective masses of quasi-particles due to strong Coulomb interactions among the 4 f or 5 f electrons.The behavior of these materials is controlled by three parameters:the hybridization V between f and d orbitals which confers the f electrons an itinerant character the value of the f level?₀ energy relatively to the chemical potential and the value of the Coulomb energy U.The strong Coulomb interaction together with the small values of the hybridization matrix allow for formation of local moments leading to magnetic behavior in these systems.The Kondo effect and the magnetic order due to the RKKY?Ruderman-Kittel-Kasuya-Yosida?interaction are consequences of the interplay between Coulomb interaction and hybridization.Together with magnetism heavy-fermion materials may present superconducting ground states whose origin and nature are far from being fully understood.The periodic Anderson model?PAM?is considered a good candidate for describing heavy-fermion systems.It is generally accepted that a complete understanding of heavy-fermion system properties requires going beyond mean field theory.Nevertheless mean field theory still gives qualitatively correct information about some properties of heavy-fermion systems.We know a large class of rare-earth and actinide compounds that vary from intermediate valence to Kondo lattices and heavy-fermion?HF?systems exhibit unusual properties such as the huge coefficient in the magnetic susceptibility specific heat and so on.These anomalies are usually attributed to the formation of a resonant state at the Fermi level with a large effective mass.The periodic Anderson model?PAM?has been considered as the most promising candidate that might be able to describe the anomalous properties of these materials.Many approaches have been developed to study this model beginning with the mean-field approximation perturbation theory modified noncrossing approximation dynamic mean-field theory and quantum Monte Carlo simulation none of these are completely satisfactory in all aspects of the PAM.Recently it is noted that exact results for one-dimensional PAM at finite U have been obtained by Orlik and Gulacsi.The solutions however are restricted in certain domains of the model phase diagram and the results for two-or three-dimensional cases are not yet available.Thus it is still necessary to resort the approximation schemes.The equation of motion?EOM?approach is easily applied to the whole parameter space of the model.Due to strong localization of f electrons the assumption of infinite U has been made in the study of the PAM by the EOM approach and the other most theoretical works.However a realistic Coulomb repulsion is typically of the order 5–6 eV for Ce-based HF materials and 2 eV for uranium-based materials.It is important to consider the finite U effects in determining spectroscopic thermodynamic and transport properties.In the second chapter we theoretically calculated the equation of motion equation and found that the Rashba spin-orbit coupling provides an additional channel to screen the magnetic impurities in the superconductor which exists the interaction between Kondo screening and superconductivity.In the third chapter the Hamiltonian of the Anderson lattice model is introduced and the magnetic characteristics of the periodic Anderson model are different under different lattices of different dimensions.Finally in the fourth chapter we obtain the characteristics of specific heat and magnetic susceptibility of the periodic Anderson model under different conditions from the Hartree-Fock approximation the slave bosons mean field theory the Hubbard-I approximation and the Nagaoka decoupling method.Different Coulomb repulsive potentials and conduction electrons and localized electronic hybridization play an important role in the thermodynamic properties of the system.