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Physics Letters A

Many-electron variational ground state of the two-dimensional Anderson lattice

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

Published May 1, 1991• 2 citations
Publisher
DOI
10.1016/0375-9601(91)90485-q

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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.
The electronic ground states for two- and three-dimensional Anderson-lattice clusters with large Hubbard repulsion are determined variationally within the Gutzwiller ansatz by use of a stochastic algorithm for exact evaluation of matrix elements of Gutzwiller states. The algorithm is similar to one normally used for finite-temperature simulation and is described in some detail. Variational states for a variety of Hamiltonian parameters and particle densities were considered. Of particular interest is the regime of small interband hopping, which is antiferromagnetic at densities near two particles per unit cell. We found that for some Hamiltonian-parameter regimes, doping the antiferromagnetic cluster with enough particles or holes can destroy the magnetic ordering and produce a state that resembles a heavy-Fermi-liquid state, a metal with a strongly-frequency-dependent self-energy. For a 4\ifmmode\times\else\texttimes\fi{}4 Anderson lattice, we present results of low-temperature quantum Monte Carlo simulations to evaluate the validity of the variational Gutzwiller ansatz.