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Physical review. B, Condensed matter

Many-electron variational calculation for the one-dimensional Anderson lattice

Yu Zhou, Samuel P. Bowen, Jay D. Mancini

Published Sep 15, 1991• 6 citations
Publisher

Abstract

We present a variational method for studying the ground-state properties of the one-dimensional Anderson model with periodic boundary conditions. Our results are compared with exact Monte Carlo results and show excellent agreement in the large-U limit. We argue that poor results in the vanishing-U range are due to the truncated basis chosen, as well as the fact that all fluctuations are treated equally.

DOI
10.1103/physrevb.44.5482

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We present a variational method for studying the ground-state properties of the one-dimensional Anderson model with periodic boundary conditions. Our results are compared with exact Monte Carlo results and show excellent agreement in the large-U limit. We argue that poor results in the vanishing-U range are due to the truncated basis chosen, as well as the fact that all fluctuations are treated equally.
Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed.
A variational calculation of the ground state of the Anderson lattice model is discussed. The calculation creates a finite Hamiltonian matrix for many-electron states, which are appropriate for the thermodynamic limit. A simple 14×14 truncation is discussed for finite U and a smaller 3×3 is used for the large U limit. Both approximations indicate that the spin configurations of the localized f orbitals are antiferromagnetically correlated for nearest neighbors in the ground state. This antiferromagnetic correlation is mediated by an RKKY interaction and thus offers a variety of spin orderings as a function of lattice and density.
In an attempt to obtain a better description than the local-density approximation (LDA) for the electronic structure of realistic narrow-band systems, we have studied a perturbation-theory method for the self-energy and have tested it on the electronic properties of the periodic one-dimensional Anderson model. For a number of models we have calculated a wide range of properties such as quasiparticle energies, spectral densities, reduced hybridizations, and various magnetic correlation functions. For two different models we were able to compare with Monte Carlo results and found good agreement. In general, we have obtained a description of narrow-band systems that is more reasonable than the one given by the LDA.
We present the calculations of the ground state and lowest excited states of the one-dimensional periodic Anderson Hamiltonian with two electrons per site and arbitrary magnitude of the repulsive interaction UUU. We consider finite cells (up to N=4N=4N=4) and introduce a new method, using modified periodic boundary conditions, to facilitate comparison of calculations with different NNN. The ground state is found to be a nonmagnetic singlet in all cases. The lowest-energy excitations for adding or subtracting one electron show that the system is insulating and the lowest spin-flip excitations indicate a near instability to antiferromagnetism due to the "nesting" of the Fermi surface in one dimension. The lowest excitations are shown to vary little with NNN and, for N=4N=4N=4, the results agree well with infinite-cell calculations, both for small UUU and for the Kondo-lattice regime. The primary results are the continuous variation from U=0U=0U=0 to the Kondo-lattice and mixed-valence regimes and the importance of correlations, which lead to the insulating gap and dispersion in the electronic and spin excitations.