A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.

Physical review. B, Condensed matterSep 1, 1978117 citations

n-Particle correlation functions of an interacting electron gas

M. V. Vavrukh

Theoretical and Mathematical PhysicsMar 1, 19825 citations

Exact Schrodinger wave-function solutions of the fully-correlated few-electron gas and the uniform electron gas

J. Jerke, Eric R. Bittner, Bill Poirier

We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ( $T = 0$ K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ($T = 0$K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.

arXiv:1809.07363Sep 19, 20180 citations

Exact relations for the spin correlation functions

M. Okada, Tadashi Toyoda

AIP conference proceedingsJan 1, 19990 citations

Exact relations for the spin-correlation functions for an interacting electron gas in a nonuniform magnetic field

Tadashi Toyoda, M. Okada

Without any approximation, exact relations for the spin-density correlation functions in an interacting electron gas under an arbitrary nonuniform external magnetic field are obtained by making use of the nonperturbative canonical formulation of quantum many-body theory [T. Toyoda, Ann. Phys. (N.Y.) 173, 226 (1987)]. The obtained results contain $f$ -sum rules, a finite-temperature generalized Ward-Takahashi relation, as well as a finite-temperature version of the Nambu-Goldstone theorem with respect to the spontaneous symmetry breaking of the spin-rotational symmetry.Without any approximation, exact relations for the spin-density correlation functions in an interacting electron gas under an arbitrary nonuniform external magnetic field are obtained by making use of the nonperturbative canonical formulation of quantum many-body theory [T. Toyoda, Ann. Phys. (N.Y.) 173, 226 (1987)]. The obtained results contain $f$-sum rules, a finite-temperature generalized Ward-Takahashi relation, as well as a finite-temperature version of the Nambu-Goldstone theorem with respect to the spontaneous symmetry breaking of the spin-rotational symmetry.

Physical review. B, Condensed matterJul 15, 19986 citations

T = 0

K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.

f

-sum rules, a finite-temperature generalized Ward-Takahashi relation, as well as a finite-temperature version of the Nambu-Goldstone theorem with respect to the spontaneous symmetry breaking of the spin-rotational symmetry.