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Journal of Physical Studies

New diagram technique for periodic Anderson model

V. A. Moskalenko, D. F. Digor, L.A. Dogotaru, I.G. Porcescu

Published Jan 1, 1997• 1 citation
Publisher

Abstract

A new diagram technique, previously proposed for Hubbard Model, was used for the Periodic Anderson Model (PAM).The Hamiltonian of localized electrons H 0 f and of free conduction electrons H 0 c are considered as a main part of the Hamiltonian of PAM and the hybridization term is treated as a perturbation.H 0 f contains on-site Coulomb interaction and is diagonalized in Hubbard operators.This diagram technique is used for Matsubara Green functions and contains apart from the Wick product of free Green functions new contributions equal to on-site cumulants depending of the Coulomb interaction.If such cumulants are ignored we obtaine the so called Hubbard I approximation for PAM with 3 branches of renormalized energy spectrum of quasiparticles.They are investigated in detail and the chemical potential of the system is determined

DOI
10.30970/jps.01.453

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A new diagram technique, previously proposed for Hubbard Model, was used for the Periodic Anderson Model (PAM).The Hamiltonian of localized electrons H 0 f and of free conduction electrons H 0 c are considered as a main part of the Hamiltonian of PAM and the hybridization term is treated as a perturbation.H 0 f contains on-site Coulomb interaction and is diagonalized in Hubbard operators.This diagram technique is used for Matsubara Green functions and contains apart from the Wick product of free Green functions new contributions equal to on-site cumulants depending of the Coulomb interaction.If such cumulants are ignored we obtaine the so called Hubbard I approximation for PAM with 3 branches of renormalized energy spectrum of quasiparticles.They are investigated in detail and the chemical potential of the system is determined
A new diagram technique based on the generalized Wick theorem has been elaborated for the systems with strong electronic correlations.Coulomb repulsion of the electrons of the Hubbard model is considered as the main part of Hamiltonian and is taken into account in a zero order approximation.The hopping matrix elements are considered as a perturbation.One-particle Matsubara-Green function of the model has been investigated and Dyson equation has been obtained.New elements of the theory which are characteristic of this new approach are the local many-particle irreducible Green functions, or Kubo cumulants.They become zero when Coulomb interaction is zero.The main task of this paper is the summing of ladder diagrams which take into account the most essential charge and spin fluctuations of the system.The integral equations, which sum such diagrams, have been established for two different channels.The coherent potential approximation has been used to simplify and solve these equations.On this basis a metal-dielectric phase transition has been investigated.
We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as difficult to calculate as the original GF, and the Atomic Approximation consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. This approximation has already been used for the case of infinite electronic repulsion U (Phys. Rev. B 62, 7882 (2000)), and here we extend the treatment to the case of finite U. The method can also be applied to the single impurity Anderson model (SIAM), and we give explicit expressions of the approximate GF both for the PAM and the SIAM.
The ground-state energy, wave-function, hybridization gap and magnetic phasediagram of the Single Site Impurity Anderson Model (SIAM) and the Periodic AndersonModel (PAM) were calculated using Exact-Diagonalization (ED) technique. The EDtechnique was applied to the SIAM and PAM in one dimension before speculating on Ce 4fbeing a test bed of the results, since it has 4f localized electrons in the Heavy fermioncompound CeCu2Si2. Each of the results obtained describe the evolution of the electronicsystem in terms of a simple set of parameters.The parameter regimes studied suggest asmooth phase transition from an antiferromagnetic (AFM) phase to a ferromagnetic (FM)phase at quarter fillings in one dimension when t increases and a magnetic instability wasobserved as U → ∞. The role of hybridization between the conduction electrons and thelocalized f orbital in the Anderson impurity in a semiconductor was also investigated as Vincreases in the SIAM and the PAM.
The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion is considered here for an hypercubic lattice of infinite dimension . The nearest neighbour hopping of the uncorrelated electrons is described exactly by a conduction band, while two different models of hybridization are treated as a perturbation. The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of , are also shown to be valid for the periodic Anderson model. The derivation of these properties had to be modified because of the exact treatment of the conduction band.
The Kondo interaction coupling, Heisenberg exchange coupling, and Coulomb interactions within d-sites, were introduced in a one dimensional Periodic Anderson Model Hamiltonian (PAMH) to further investigate the effects of interaction parameters on the ground state energy of systems with heavy fermions (HF) behavior. Periodic Anderson model PAM being one of the most successful model for studying the heavy fermions System (HFS) was used in an extended version (mixed Kondo-Anderson representation) on a system of three-electrons interacting on three-sites cluster. Exact Diagonalization technique (EDT) normally used to solve conventional PAM calculation was considered in this work for a very small cluster. Hamiltonian used to describe this model contains the usual term describing the kinetic energy of the system, on-site coulomb repulsion and a hopping integral. The Hamiltonian is acted on the different Hilbert states of the lattice system and results of the interactions were obtained in terms of hopping integral, coulomb repulsions, exchange couplings and the hybridization term. Graphs of ground state energy Eo plotted agains tthese interaction parameters were presented in a clear format. As these parameters were varied numerically through a finite range of values, the individual effects of these parameters on the system’s ground state energy were observed and discussed. Hence, the results obtained from this work shows theoretically how the tuning of the Columbic interaction within the conduction band provides information that sheds light on the underlying physics of the heavy fermions systems models. Results obtained from this work further demonstrate the reliability of the model Hamiltonians that we have harnessed and the importance of considering electron-lattice interactions as well as interactions that account for magnetic impurities for the proper description of heavy fermions material.