251 research outputs found
Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model
We have studied electron correlations in the doped two-dimensional (2D)
Hubbard model by using the coupled-cluster method (CCM) to investigate whether
or not the method can be applied to correct the independent particle
approximations actually used in ab-initio band calculations. The double
excitation version of the CCM, implemented using the approximate coupled pair
(ACP) method, account for most of the correlation energies of the 2D Hubbard
model in the weak () and the intermediate regions (). The error is always less than 1% there. The ACP approximation gets
less accurate for large () and/or near half-filling.
Further incorporation of electron correlation effects is necessary in this
region. The accuracy does not depend on the system size and the gap between the
lowest unoccupied level and the highest occupied level due to the finite size
effect. Hence, the CCM may be favorably applied to ab-initio band calculations
on metals as well as semiconductors and insulators.Comment: RevTeX3.0, 4 pages, 4 figure
Convergence improvement for coupled cluster calculations
Convergence problems in coupled-cluster iterations are discussed, and a new
iteration scheme is proposed. Whereas the Jacobi method inverts only the
diagonal part of the large matrix of equation coefficients, we invert a matrix
which also includes a relatively small number of off-diagonal coefficients,
selected according to the excitation amplitudes undergoing the largest change
in the coupled cluster iteration. A test case shows that the new IPM (inversion
of partial matrix) method gives much better convergence than the
straightforward Jacobi-type scheme or such well-known convergence aids as the
reduced linear equations or direct inversion in iterative subspace methods.Comment: 7 pages, IOPP styl
Coupled cluster calculations of ground and excited states of nuclei
The standard and renormalized coupled cluster methods with singles, doubles,
and noniterative triples and their generalizations to excited states, based on
the equation of motion coupled cluster approach, are applied to the He-4 and
O-16 nuclei. A comparison of coupled cluster results with the results of the
exact diagonalization of the Hamiltonian in the same model space shows that the
quantum chemistry inspired coupled cluster approximations provide an excellent
description of ground and excited states of nuclei. The bulk of the correlation
effects is obtained at the coupled cluster singles and doubles level. Triples,
treated noniteratively, provide the virtually exact description
Configuration interaction wave functions: A seniority number approach
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Torre, Alicia. Universidad del Pais Vasco; EspañaFil: Lain, Luis . Universidad del Pais Vasco; EspañaFil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires. Ciclo Básico Común; ArgentinaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin
Entanglement of electrons in interacting molecules
Quantum entanglement is a concept commonly used with reference to the
existence of certain correlations in quantum systems that have no classical
interpretation. It is a useful resource to enhance the mutual information of
memory channels or to accelerate some quantum processes as, for example, the
factorization in Shor's Algorithm. Moreover, entanglement is a physical
observable directly measured by the von Neumann entropy of the system. We have
used this concept in order to give a physical meaning to the electron
correlation energy in systems of interacting electrons. The electronic
correlation is not directly observable, since it is defined as the difference
between the exact ground state energy of the many--electrons Schroedinger
equation and the Hartree--Fock energy. We have calculated the correlation
energy and compared with the entanglement, as functions of the nucleus--nucleus
separation using, for the hydrogen molecule, the Configuration Interaction
method. Then, in the same spirit, we have analyzed a dimer of ethylene, which
represents the simplest organic conjugate system, changing the relative
orientation and distance of the molecules, in order to obtain the configuration
corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late
Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions
This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Torre, Alicia. Universidad del País Vasco. Facultad de Ciencia y Tecnología. Departamento de Química Física; España;Fil: Lain, Luis. Universidad del País Vasco. Facultad de Ciencia y Tecnología. Departamento de Química Física; España;Fil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
The connection between many-body theory (MBPT)--in perturbative and
non-perturbative form--and quantum-electrodynamics (QED) is reviewed for
systems of two fermions in an external field. The treatment is mainly based
upon the recently developed covariant-evolution-operator method for QED
calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a
structure quite akin to that of many-body perturbation theory. At the same time
this procedure is closely connected to the S-matrix and the Green's-function
formalisms and can therefore serve as a bridge between various approaches. It
is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to
a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A
Bloch equation in commutator form that can be used for an "extended" or
quasi-degenerate model space is derived. It has the same relation to the BS
equation as has the standard Bloch equation to the ordinary Schroedinger
equation and can be used to generate a perturbation expansion compatible with
the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic
Second-order electronic correlation effects in a one-dimensional metal
The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D)
metal is studied at the Hartree-Fock level, and by using the second-order
perturbation theory of the electronic correlation. The PPP model provides an
extension of the Hubbard model by properly accounting for the long-range
character of the electron-electron repulsion. Both finite and infinite version
of the 1D-metal model are considered within the PPP and Hubbard approximations.
Calculated are the second-order electronic-correlation corrections to the total
energy, and to the electronic-energy bands. Our results for the PPP model of 1D
metal show qualitative similarity to the coupled-cluster results for the 3D
electron-gas model. The picture of the 1D-metal model that emerges from the
present study provides a support for the hypothesis that the normal metallic
state of the 1D metal is different from the ground state.Comment: 21 pages, 16 figures; v2: small correction in title, added 3
references, extended and reformulated a few paragraphs (detailed information
at the end of .tex file); added color to figure
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