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Physica Scripta

Thermodynamic properties of a 4-level Anderson model

G. Piccitto, M. Baldo, R. Pucci

Published Dec 1, 1987• 0 citations
Publisher

Abstract

We present exact numerical results for the thermodyamic properties of a 4-level Anderson model. Ground state and excited states energies, average occupation numbers, susceptibility, specific heat, spin and charge fluctuations, spin-spin correlation functions are derived. The results are presented as a function of the temperature for several values of the Coulomb repulsion integral. Drastic changes of the calculated quantities appear in correspondence of the excited state energies for some critical values of the parameters. The results are in qualitative agreement with some other Anderson model calculations.

DOI
10.1088/0031-8949/36/6/014

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We present self-consistent Green-function calculations for the properties of the symmetric Anderson impurity model at zero temperature. A stable method for calculating the spectral density directly on the real frequency axis in the spin-fluctuation limit is described. Results using an approximation to the self-energy, previously termed the fluctuation-exchange approximation, which includes the effects of spin and density fluctuations (within the random-phase approximation) and multiple electron-electron scattering are compared with second-order perturbation-theory calculations. The static spin and charge susceptibilities, calculated in a manner consistent with conservation laws, are compared with the exact results from the Bethe ansatz. We find that the fluctuation-exchange approximation gives a good description of the charge susceptibility over a wide range of interaction strengths and is a great improvement over the self-consistent second-order theory. However, the T-linear coefficient of the specific heat is greatly overestimated by the fluctuation-exchange approximation and this leads to the underestimation of the spin susceptibility. The self-consistent second-order perturbation theory, which underestimates the specific-heat coefficient, predicts a magnetic ground state for sufficiently high interaction strengths.
By means of a projector operator formalism we study the ground state properties of the Anderson Impurity Hamiltonian. The non-perturbative treatment of the model agrees with the previous one, obtained by Inagaki [Prog. Theor. Phys. 62, 1441 (1979)] by means of a perturbation expansion with respect the hybridization term. We go beyond the Inagaki's formalism to the next leading order. It provides a very accurate calculation of the energy spectrum in the total spin sector and, in particular, the ground state energy in the whole parameter space. For a one body spinless system, the dependence of the ground state energy as a function of the impurity level obtained by this procedure remarkably agrees with analytical results. For the many body case the occupancy of the impurity as a function of the parameters is studied and it agrees with the corresponding one obtained by using the Bethe ansatz and the Numerical Renormalization Group solution of the Hamiltonian. The magnetization and susceptibility of the impurity is analyzed by studying the response of the system to an external magnetic field, from which it is possible to extract the Kondo temperature. The dependence of the Kondo scale with the parameters of the model is in excellent agreement with well-known results.
The ground-state and thermodynamic properties of a simple Hubbard Hamiltonian are studied for an eight-site cubic cluster as functions of the number of electrons and the strength of the electron interaction. The ground-state energy and spin are determined, and the excitation spectrum is computed. Thermodynamic properties including the specific heat, the magnetic susceptibility, and spin correlation functions are calculated. Computations are performed both by explicit diagonalization of the Hamiltonian and by Monte Carlo simulation.