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Correlation and spin polarization in quantum dots: Local spin density functional theory revisited

Borgh, Magnus LU ; Toreblad, Maria LU ; Koskinen, M; Manninen, M; Åberg, Sven LU and Reimann, Stephanie LU (2005) In International Journal of Quantum Chemistry 105(6). p.817-825
Abstract
Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the direct comparison with configuration interaction... (More)
Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the direct comparison with configuration interaction (Cl) methods demonstrates that the spin representation of SDFT may, under certain circumstances, produce artificial energy splittings between states that belong to the same spin multiplet. For a singlet ground state with S = S = 0, however, the correlation functions of the Cl solutions confirm the spin-density wave states found earlier within the SDFT method. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
spin symmetry, calculations, configuration interaction, quantum dots, density functional method, spin-density waves
in
International Journal of Quantum Chemistry
volume
105
issue
6
pages
817 - 825
publisher
John Wiley & Sons
external identifiers
  • wos:000233063100030
  • scopus:30544454965
ISSN
0020-7608
DOI
10.1002/qua.20802
language
English
LU publication?
yes
id
fefd0801-d499-4cc1-a459-66662f0a27ba (old id 214225)
date added to LUP
2007-08-07 11:26:00
date last changed
2017-08-13 03:40:49
@article{fefd0801-d499-4cc1-a459-66662f0a27ba,
  abstract     = {Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the direct comparison with configuration interaction (Cl) methods demonstrates that the spin representation of SDFT may, under certain circumstances, produce artificial energy splittings between states that belong to the same spin multiplet. For a singlet ground state with S = S = 0, however, the correlation functions of the Cl solutions confirm the spin-density wave states found earlier within the SDFT method.},
  author       = {Borgh, Magnus and Toreblad, Maria and Koskinen, M and Manninen, M and Åberg, Sven and Reimann, Stephanie},
  issn         = {0020-7608},
  keyword      = {spin symmetry,calculations,configuration interaction,quantum dots,density functional method,spin-density waves},
  language     = {eng},
  number       = {6},
  pages        = {817--825},
  publisher    = {John Wiley & Sons},
  series       = {International Journal of Quantum Chemistry},
  title        = {Correlation and spin polarization in quantum dots: Local spin density functional theory revisited},
  url          = {http://dx.doi.org/10.1002/qua.20802},
  volume       = {105},
  year         = {2005},
}