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Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximations with Adjustable Single-Particle Wave Function for the Hubbard Chain

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Kurzyk J., Spałek J., Wójcik W.
Acta Physica Polonica A
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2007
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vol. 111
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issue 4
603-618
EN
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb-Wu exact solution, the Gutzwiller-wave-function approximation, and the Gutzwiller-ansatz case. The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the exact diagonalization combined with an ab initio adjustment of the single-particle wave functions in the correlated state (exact diagonalization combined with an ab initio method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controlable parameter - the interatomic distance.
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Optimized Wannier Functions for Hubbard Chain

100%
Kurzyk J., Wójcik W., Spałek J.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
114-116
EN
One-dimensional atomic chain with a variable-range hopping is described within the extended Hubbard model. The Gutzwiller-ansatz approximation is used to determine the optimized single-particle (Wannier) wave functions in the correlated state. Hopping integral up to the third neighbors is taken into account and the results are compared with those for the infinite hopping range. Ground state energy of the system is compared with that making use of the rigorous Lieb-Wu solution with the optimized wave functions. The evolution of the properties as a function of interatomic distance is discussed.
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Correlated Electron Systems of Different Dimensionalities

100%
Kurzyk J., Wójcik W., Spałek J.
Acta Physica Polonica A
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2008
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vol. 114
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issue 1
175-178
EN
The optimized single-particle wave functions contained in the parameters of the Hubbard model (hopping integral t and intraatomic interaction U) are determined explicitly in the correlated state for electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular lattices, and the three cubic lattices: SC, BCC, and FCC. In effect, the electronic properties of these structures as a function of the interatomic distance R are obtained. In most cases, the model parameters do not scale linearly with the lattice constant. Also, the atomic part of the total ground state energy changes with the U/t ratio and therefore should be (and is) included in the analysis. The solutions of dimensions D>1 are analyzed by utilizing the approximate Gutzwiller treatment.
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