Abstract
We construct and apply an exchange-correlation functional for the one-dimensional Hubbard model. This functional has built into it the Luttin-ger-liquid and Mott-insulator correlations, present in the Hubbard model, in the same way in which the usual ab initio local-density approximation (LDA) has built into it the Fermi-liquid correlations present in the electron gas. An accurate expression for the exchange-correlation energy of the homogeneous Hubbard model, based on the Bethe Ansatz (BA), is given and the resulting LDA functional is applied to a variety of inhomo-geneous Hubbard models. These include finite-size Hubbard chains and rings, various types of impurities in the Hubbard model, spin-density waves, and Mott insulators. For small systems, for which numerically exact diagonalization is feasible, we compare the results obtained from our BA-LDA with the exact ones, finding very satisfactory agreement. In the opposite limit, large and complex systems, the BA-LDA allows to investigate systems and parameter regimes that are inaccessible by traditional methods.
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Capelle, K., Lima, N.A., Silva, M.F., Oliveira, L.N. (2003). Density-Functional Theory for the Hubbard Model: Numerical Results for the Luttinger Liquid and the Mott Insulator. In: Gidopoulos, N.I., Wilson, S. (eds) The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State. Progress in Theoretical Chemistry and Physics, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0409-0_12
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DOI: https://doi.org/10.1007/978-94-017-0409-0_12
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