The Study of the Ground State Properties of Heavy Famion System Using an Extended Kondo-Anderson Model in One Dimension

Main Article Content

Okunzuwa I. Samuel
C. Okaro Augustine


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.

Periodic Anderson model, Heavy famion system, Hilbert states, exact diagonalization technique, Kondo lattice model

Article Details

How to Cite
Samuel, O. I., & Augustine, C. O. (2020). The Study of the Ground State Properties of Heavy Famion System Using an Extended Kondo-Anderson Model in One Dimension. Physical Science International Journal, 24(11), 43-51.
Original Research Article


Andres K, Graebner JE, Ott HR. 4 f -Virtual-Bound-State Formation in Ce Al 3 at Low Temperatures, Phys Rev Lett. 1975;35(26):1779–1782.

Satoh K, Fujita T, Maeno Y, Ōnuki Y, Komatsubara T. Low-temperature specific heat of Ce x La 1- x Cu 6, J Phys Soc Japan. 1989;58(3):1012–1020.

Doniach S. The Kondo lattice and weak antiferromagnetism. Phys B+C. 1977;91: 231–234.

And IT, Deguchi K, Matsukawa S, Sato K N, Hattori T, Ishida K, et al. Nat Mat. 2012;11:1013.

Sachdev S. Advanced Solid State Physics Philip Phillips Westview Press, Boulder, Colo. Paper. Phys Today 2003;56(6):386.

ISBN: 0-8133-4015-2,

ISBN: 0-8133-4014-4 paper.

Ihn T. Electron-electron interactions within the Fermi-liquid concept. 2004;29–34.

Electron-electron interactions the electronic structure theory of metals, developed in the. 1930;0–52.

Nixon M. et al. Physics Bose – Einstein Condensation in; 2015.

Interaction E. 3 Electron-electron interaction 3.1 electron-electron interaction.

Tsuda N. Nasu K, Fujimori A, Siratori K. Electron—Electron Interaction and Electron Correlation. 2000;119–155.

Gschneidner KA, Eyring L. Handbook on the physics and chemistry of rare earths. North Holland. 1998;20.

Hagymási I, Itai K, Sólyom J, Periodic Anderson model with correlated conduction electrons: Variational and exact diagonalization study. Phys Rev B - Condens. Matter Mater. Phys. 2012; 85(23):1–14.

Anderson PW. Localized magnetic states in metals. Phys. Rev. 1961;124(1):41–53.

Nguyen D, Tran TT, Thi T, Selective Kondo strong coupling in magnetic impurity flat-band lattices. Ann Phys (NY). 2019; 400:9–20.

Coleman P. Heavy fermions and the Kondo Lattice: A 21st Century Perspective. 2015;5.

Tasaki H. Uniqueness of the ground state in exactly solvable Hubbard, periodic Anderson, and Emery models. Phys Rev B. 1994;49(11):7763–7766.

Howczak O, Spałek J. Anderson lattice with explicit Kondo coupling revisited: Metamagnetism and the field-induced suppression of the heavy fermion state. J Phys Condens Matter. 2012;24(20).

Sykora S, Becker KW. Heavy fermion properties of the Kondo Lattice model. Sci Rep. 2013;3(1):2691.

Schrieffer JR, Wolff PA. Relation between the Anderson and Kondo Hamiltonians. Phys Rev. 1966;149(2):491–492.

Shinzaki R, Nasu J, Koga A. DMFT study for valence fluctuations in the extended periodic anderson model. J Phys Conf Ser. 2016;683:012041.