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arXiv:0807.2442 · The European Physical Journal B

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models

J. Kurzyk, W. Wójcik, Józef Spałek

Published Dec 1, 2008• 11 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2008-00433-1

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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.
We determine the explicit form of the single-particle Wannier functions {wi(r)} appearing in the parameters of quantum models.The method is illustrated on the example of the Hubbard chain, for which we derive the renormalized wave equation starting from a variational principle and by treating the system ground state energy as a functional of {wi(r)} and their derivatives.In this manner, the optimized basis is obtained only after the electronic correlations have been included in the rigorous Lieb-Wu solution.The results for the ground state energy and the size of the renormalized s-type orbitals, both as a function of interatomic distance, are calculated explicitly.