Browsing by Author "Mancini, Jay D."

Now showing 1 - 8 of 8
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    Analytic approximation to the ground-state energy of the Anderson model
    Mancini, Jay D.; Massano, William J.; Potter, Charles D.; Bowen, Samuel P. (American Physical Society, 1988-09)
    Using the nonperturbative Lanczos recursion scheme an analytic approximation to the ground-state energy of the single-impurity Anderson model is obtained. Calculations are carried out to a 5x5 matrix truncation. Comparisons are made with the exact Bethe-ansatz result.
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    Application of the connected-moment expansion to single-impurity Anderson Hamiltonians
    Massano, William J.; Bowen, Samuel P.; Mancini, Jay D. (American Physical Society, 1989-04)
    We use the connected-moment expansion, recently developed by Cioslowski [Phys. Rev. Lett. 58, 83 (1987)], to investigate the ground-state energy of the single-impurity Anderson model. It is found that the moment expansion obtained for this Hamiltonian is not a Stieltjes series and thus does not provide a useful method for estimating ground-state energies.
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    Convergent methods for calculating thermodynamic Green functions
    Bowen, Samuel P.; Williams, Clayton D.; Mancini, Jay D. (American Physical Society, 1984-08)
    A convergent method of approximating thermodynamic Green functions is outlined briefly. The method constructs a sequence of approximants which converges independently of the strength of the Hamiltonian's coupling constants. Two new concepts associated with the approximants are introduced: the resolving power of the approximation, and conditional creation (annihilation) operators. These ideas are illustrated on an exactly soluble model and a numerical example. A convergent expression for the scattering rate in a field theory is also derived.
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    Finite-basis many-electron approximation to the Anderson model
    Mancini, Jay D.; Bowen, Samuel P.; Zhou, Yu (American Physical Society, 1990-03)
    A relatively simple many-electron basis is used to construct a matrix for the Anderson impurity Hamiltonian. The basis states are each valid in the thermodynamic limit. The approximate ground-state energy compares well with Bethe-ansatz results for large Coulomb energies. The ground-state wave-function properties are not as well approximated. This method may be well suited to studies of more realistic Hamiltonians and their ground-state energy and its derivatives.
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    Judd operator methods in superspace: application to the thermal single particle Green function for the Hubbard dimer
    Mancini, Jay D. (Virginia Polytechnic Institute and State University, 1982)
    The Fourier transforms of the thermal two-time single-particle Green functions may be expressed as matrix elements of the resolvent of the Liouville operator, in an abstract Hilbert space. This abstract Hilbert space (the "superspace") contains elements f, g, etc. which are products of an odd number of fermion creation and/or annihilation operators. These operators may also be expressed as linear combinations of a set of stepping operators Φ = fig, where I is the projection operator for the vacuum in the ordinary Fock space. The Judd operators are stepping operators which step between many-particle states which usually differ in particle number. In the calculation of the single-particle Green function, only those single-particle Judd operators which step between states differing by one electron are relevant. The Judd operators obey a Lie algebra analogous to the angular momentum stepping operators L±. The single-site and two-site Hubbard model for arvitrary electron density are solved exactly using the Judd operator formalism. The correlation functions are evaluated as functions of chemical potential, temperature and t/U, where t is the hopping energy and U is the intasite Coulomb energy.
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    Strongly correlated electron ground_state energy approximations for Anderson_like models
    Mancini, Jay D.; Potter, Charles D.; Bowen, Samuel P. (American Institute of Physics, 1987-04-15)
    We report preliminary results of convergence properties for nonperturbative resolvent approximations to Anderson_like models of magnetic ions in metals. Our study is initially focused on the spin_ 1/2 Anderson model for magnetic impurities, but the methods studied can include multiplet and crystal_field effects which are needed for more accurate descriptions of real systems. We will compare the nonperturbative Lanczos method (tridiagonalization) and similar truncation schemes to exact ground_state energies for the impurity model and assess the efficacy of these nonperturbative approaches to understanding the Anderson lattice, heavy fermions, and other strongly interacting electronic systems.
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    The study of many-electron systems
    Zhou, Yu (Virginia Tech, 1991)
    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.
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    Variational ground state for the periodic Anderson model
    Bowen, Samuel P.; Mancini, Jay D. (American Institute of Physics, 1988-04-15)
    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.