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Bulletin of the American Physical Society

Exact Kohn-Sham eigenstates versus quasi-particles in simple models of strongly correlated electrons

Jaime Ferrer, Diego J. Carrascal

Published Feb 27, 2012• 0 citations
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arXiv:1809.07458•Journal of Physics Condensed Matter•Sep 19, 2018•6 citations
We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard, and spinless fermion models. The exact exchange and correlation potentials keep the full nonlocal dependence on electron occupations. The analytic expressions allow us to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasiparticle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the nontrivial features of the many-body quasiparticle spectrum such as, for example, the precursors of the Kondo peak. However, we find that some pieces of the quasiparticle spectrum are missing because the many-body phase space for electron and hole excitations is richer.
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe.
For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schrödinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous eigenstates of the energy and total spin for the first time. The solutions for the three-electron system allow us to derive analytic expressions for the exact one-particle Green's function (GF) for the corresponding two-electron system. We calculate the GF in frequency domain to examine systematically its behavior depending on the electronic interactions. We also compare the pole structure of non-interacting GF using the exact Kohn-Sham (KS) potential with that of the exact GF to find that the discrepancy of the energy gap between the KS system and the original system is larger for a stronger interaction. We perform numerical examination on the behavior of GFs in real space to demonstrate that the exact and KS GFs can have shapes quite different from each other. Our simple model will help to understand generic characteristics of interacting GFs.