Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega}).$ In two dimensions ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as ${1/q}^{2}$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega}).$ In two dimensions ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as ${1/q}^{2}$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

arXiv:cond-mat/0305195Physical review. B, Condensed matterJun 27, 20036 citations

Self-interaction-corrected density-functional formalism. I. Ground-state properties of the Hubbard-Peierls model

Jacek A. Majewski, P. Vogl

We present detailed studies of the self-interaction-corrected local-spin-density method. As an application, we consider ground-state properties of a highly correlated many-electron system interacting with phonons, namely, the one- and two-dimensional Hubbard-Peierls model. An efficient minimization method is presented which allows one to find fully self-consistent solutions to the self-interaction-corrected local-spin-density total-energy functional without assuming any symmetry of the one-electron states. Charge- and spin-correlation functions, the energy gap, and phonon-induced electronic energy gains for the two-dimensional Hubbard-Peierls model are in significantly better agreement with numerically exact results than the standard local-density method. Noticeably, we find that phonons tend to de- stabilize the antiferromagnetic ground state in two dimensions and show a negative-U behavior in the energy gap, in contrast to the situation in one dimension. This is relevant for the theory of high-temperature superconductivity.We present detailed studies of the self-interaction-corrected local-spin-density method. As an application, we consider ground-state properties of a highly correlated many-electron system interacting with phonons, namely, the one- and two-dimensional Hubbard-Peierls model. An efficient minimization method is presented which allows one to find fully self-consistent solutions to the self-interaction-corrected local-spin-density total-energy functional without assuming any symmetry of the one-electron states. Charge- and spin-correlation functions, the energy gap, and phonon-induced electronic energy gains for the two-dimensional Hubbard-Peierls model are in significantly better agreement with numerically exact results than the standard local-density method. Noticeably, we find that phonons tend to de- stabilize the antiferromagnetic ground state in two dimensions and show a negative-U behavior in the energy gap, in contrast to the situation in one dimension. This is relevant for the theory of high-temperature superconductivity.

Physical review. B, Condensed matterNov 15, 199237 citations

Exact Density Functionals for Ground-State Energies

Harald Englisch, R. Englisch

De Gruyter eBooksDec 31, 19840 citations

Single-particle-exact density functional theory

Martin-Isbjörn Trappe, Jun Hao Hue, Jonah Zi Chao Huang +4 more

arXiv:2305.03233Annals of PhysicsOct 21, 20231 citation

Fermionic statistics in the strongly correlated limit of density functional theory

Juri Grossi, Derk Pieter Kooi, Klaas J. H. Giesbertz +4 more

Exact pieces of information on the adiabatic connection integrand, λ, which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit (λ → ∞, where λ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling λ, both numerical and theoretical, confirming that spin effects enter at orders ~e-λExact pieces of information on the adiabatic connection integrand, λ, which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit (λ → ∞, where λ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling λ, both numerical and theoretical, confirming that spin effects enter at orders ~e-λ

Dec 12, 201726 citations

1/q

at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as

{1/q}^{2}

in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.