Abstract
Recent developments on the density functional theory (DFT) of lattice fermion models are reviewed. Formally exact, self-consistent equations are derived for the singleparticle density matrix γ ij that involve derivatives of the interaction-energy functional W[γ] and fractional occupations of natural orbitals η kσ . The dependence of the correlation energy functional E c (γ12) — W - E HF on the nearest-neighbors (NN) density matrix γ12 is analyzed. A pseudo-universal scaling behavior of εC =E C /E HF as a function of g12 = (γ12 – γ∞ 12) / (γ0 12 - γ∞ 12) is revealed, where γ0 12 (γ∞ 12) stands for the uncorrelated (strongly correlated) value of γ12. Based on exact dimer results and on scaling properties of E c(γ12), a simple, explicit approximation to W(γ12) is proposed for the Hubbard model. Ground-state energies and charge-excitation gaps of one- and two-dimensional lattices are obtained, in remarkable agreement with available exact results or accurate numerical simulations. The scope of DFT is thereby extended to the limit of strong electron correlations.
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R. López-Sandoval and G. M. Pastor, to be published.
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Lopez-Sandoval, R., Pastor, G.M. (2001). Density Functional Theory of the Lattice Fermion Model. In: Morán-López, J.L. (eds) Physics of Low Dimensional Systems. Springer, Boston, MA. https://doi.org/10.1007/0-306-47111-6_41
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DOI: https://doi.org/10.1007/0-306-47111-6_41
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