Anderson-Kondo Lattice Hamiltonian from the Anderson-Lattice Model: A Modified Schrieffer-Wolff Transformation and the Effective Exchange Interactions

E. Kądzielawa-Major and J. Spałek Marian Smoluchowski Institute of Physics, Jagiellonian University, W.S. Reymonta 4, 30-059 Kraków, Poland

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We derive the Anderson-Kondo lattice model by applying canonical perturbation expansion for the Anderson-lattice model in direct space. The transformation is carried out up to the fourth order by a modified Schrieffer-Wolff transformation: we separate the part of hybridization term responsible for the high-energy processes (involving the largest in-the-system intraatomic Coulomb interaction between f electrons) and replace it with the virtual processes in higher orders. The higher-order processes lead to three separate exchange interactions. The obtained Hamiltonian contains both the Kondo (f-c) and the superexchange (f-f) interactions, as well as a residual hybridization responsible for the heavy-quasiparticle formation. This effective Hamiltonian can be used to analyze the magnetic or the paired states, as well their coexistence in heavy-fermion systems. The magnitudes of both the Kondo exchange and the superexchange integrals are estimated as a function of bare hybridization magnitude.

DOI: 10.12693/APhysPolA.126.A-100 PACS numbers: 71.10.Fd, 71.20.Eh, 71.27.+a, 71.70.Gm