© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Zeitschrift für Naturforschung A

Pair Densities in a Two-dimensional Electron Gas (Jellium) at Strong Coupling from Scattering Theory with Kukkonen-Overhauser Effective Interactions

F Capurro, Reza Asgari, B. Davoudi, Marco Polini, P. Tosi

Published May 1, 2002• 7 citations

Abstract

We present a calculation of the spin-averaged and spin-resolved pair distribution functions for a homogeneous gas of electrons moving in a plane with e2/r interactions at coupling strength rs = 10. The calculation is based on the solution of a two-electron scattering problem for both parallelspin- and antiparallel-spin-pairs interacting via effective spin-dependent many-body potentials. The scattering potentials are modeled within the approach proposed by Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We find very good agreement with quantum MonteCarlo data for the spin-averaged pair density. We also find that short-range pairing between parallel-spin electrons is beginning to emerge in the paramagnetic fluid at this coupling strength, as a precursor of a transition to a fully spin-polarized fluid state occurring at stronger coupling.

DOI: 10.1515/zna-2002-0506

Related papers

Short-range correlations in a two-dimensional electron gas

Marco Polini, Gerardo Sica, B. Davoudi +1 more

We construct a model for the value of the pair distribution function g ↑↓ (0) between antiparallel-spin electrons at contact in a two-dimensional electron gas with e 2 / r interactions, as a function of the coupling-strength parameter r s . The model involves an interpolation between the result of a low- r s expansion, including the second-order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. The interpolation formula is in excellent agreement with many-body calculations based on the ladder approximation. We further show through an STLS self-consistent calculation that g ↑↓ (0) is essentially independent of the state of spin polarization of the electron gas.

Journal of Physics Condensed Matter•Mar 29, 2001•20 citations

Normalization sum rules for the two-body scattering phase shifts of the electron-gas pair densities

P. Ziesche

It is shown how the normalization sum rules of the spin-parallel and spin-antiparallel (or equivalently singlet and triplet) pair densities of the homogeneous electron gas can be rewritten equivalently as sum rules for the scattering phase shifts of those two-body wave functions (geminals), with which the pair densities have been parametrized recently. These sum rules relate two-body quantities to a one-body quantity: namely, the asymptotics of the pair-density geminals to the momentum distribution.

Physical review. B, Condensed matter•Jun 20, 2003•15 citations

Short-ranged correlations and the ferromagnetic electron gas

A. K. Rajagopal, John C. Kimball, Mahadev Banerjee

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 matter•Sep 1, 1978•117 citations

Self-consistent scattering theory of the pair distribution function in charged Bose fluids

B. Davoudi, Reza Asgari, Marco Polini +1 more

We use a density-functional theoretical approach to calculate the pair distribution function and the effective interactions in homogeneous fluids of spinless charged bosons. The scheme involves the self-consistent solution of a two-particle scattering problem with an effective scattering potential which embodies many-body effects and is adjusted to the compressibility sum rule. Numerical results are presented over an extensive range of density in both three and two dimensions.

arXiv:cond-mat/0210664•Physical review. B, Condensed matter•May 6, 2003•5 citations

Ground state of the two-dimensional electron gas

B. Tanatar, David M. Ceperley

Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}${r}_{s}$\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density ${r}_{s}$\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.

Physical review. B, Condensed matter•Mar 15, 1989•1,034 citations

Dynamical correlation effects on pair-correlation functions of spin polarized two-dimensional electron gas

Krishan Kumar, Vinayak Garg, Rajinder Kumar Moudgil

We report a theoretical study on the spin-resolved pair-correlation functions gσσ′(r) of a two-dimensional electron gas having arbitrary spin polarization ζ by including the dynamics of exchange-correlations within the dynamical self-consistent mean-field theory of Hasegawa and Shimizu. The calculated g↑↑(r), g↓↓(r) and g↑↓(r) exhibit a nice agreement with the recent quantum Monte Carlo simulation data of Gori-Giorgi et al. However, the agreement for the minority spin correlation function g↓↓(r) decreases with increase in ζ and/or decrease in electron density. Nevertheless, the spin-summed correlation function remains close to the simulation data.

AIP conference proceedings•Jan 1, 2013•0 citations

We present a calculation of the spin-averaged and spin-resolved pair distribution functions for a homogeneous gas of electrons moving in a plane with e2/r interactions at coupling strength rs = 10. The calculation is based on the solution of a two-electron scattering problem for both parallelspin- and antiparallel-spin-pairs interacting via effective spin-dependent many-body potentials. The scattering potentials are modeled within the approach proposed by Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We find very good agreement with quantum MonteCarlo data for the spin-averaged pair density. We also find that short-range pairing between parallel-spin electrons is beginning to emerge in the paramagnetic fluid at this coupling strength, as a precursor of a transition to a fully spin-polarized fluid state occurring at stronger coupling.

We construct a model for the value of the pair distribution function g ↑↓ (0) between antiparallel-spin electrons at contact in a two-dimensional electron gas with e 2 / r interactions, as a function of the coupling-strength parameter r s . The model involves an interpolation between the result of a low- r s expansion, including the second-order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. The interpolation formula is in excellent agreement with many-body calculations based on the ladder approximation. We further show through an STLS self-consistent calculation that g ↑↓ (0) is essentially independent of the state of spin polarization of the electron gas.

It is shown how the normalization sum rules of the spin-parallel and spin-antiparallel (or equivalently singlet and triplet) pair densities of the homogeneous electron gas can be rewritten equivalently as sum rules for the scattering phase shifts of those two-body wave functions (geminals), with which the pair densities have been parametrized recently. These sum rules relate two-body quantities to a one-body quantity: namely, the asymptotics of the pair-density geminals to the momentum distribution.

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.

Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}

{r}_{s}

\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density

{r}_{s}

\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.

We report a theoretical study on the spin-resolved pair-correlation functions gσσ′(r) of a two-dimensional electron gas having arbitrary spin polarization ζ by including the dynamics of exchange-correlations within the dynamical self-consistent mean-field theory of Hasegawa and Shimizu. The calculated g↑↑(r), g↓↓(r) and g↑↓(r) exhibit a nice agreement with the recent quantum Monte Carlo simulation data of Gori-Giorgi et al. However, the agreement for the minority spin correlation function g↓↓(r) decreases with increase in ζ and/or decrease in electron density. Nevertheless, the spin-summed correlation function remains close to the simulation data.