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Physical review. B, Condensed matter

Pair-correlation function of the electron gas with long-range Coulomb interaction: Ladder theory

L. Calmels, Alfred Gold

Published Jan 15, 1998• 19 citations
Publisher

Abstract

We present analytical and numerical results for the pair-correlation function $g(r=0)$ of the electron gas with long-range Coulomb interaction obtained within the ladder theory. Analytical results obtained by perturbation calculation and a Pad\'e approximation are derived and are found to be in good agreement with our numerical solution of the ladder equation. Finite-width effects in the two-dimensional electron gas (quantum well) are also described. For quasi-one-dimensional systems (quantum wires) numerical and analytical results are derived for an oscillator confinement model.

DOI
10.1103/physrevb.57.1436

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We present analytical and numerical results for the pair-correlation function g(r=0)g(r=0)g(r=0) of the electron gas with long-range Coulomb interaction obtained within the ladder theory. Analytical results obtained by perturbation calculation and a Pad'e approximation are derived and are found to be in good agreement with our numerical solution of the ladder equation. Finite-width effects in the two-dimensional electron gas (quantum well) are also described. For quasi-one-dimensional systems (quantum wires) numerical and analytical results are derived for an oscillator confinement model.
We study the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using the ladder theory we obtain analytical results for the ground-state energy and the compressibility which are in agreement with exact results for weak and strong coupling. We calculate the short- and the long-distance behaviour of the pair-correlation function g(z) and derive critical exponents from . We evaluate the connection between the local-field correction and critical exponents.
We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G ( q ), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.
We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter bbb $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.
We propose a method that employs functionals of the one-electron reduced density matrix (density matrix) to capture long-range effects of electron correlation. The complementary short-range regime is treated with density functionals. In an effort to find approximations for the long-range density-matrix functional, a modified power functional is applied to the homogeneous electron gas with Coulomb interactions replaced by their corresponding long-range counterparts. For the power $\ensuremath{\beta}=1/2$ and the range-separation parameter $\ensuremath{\omega}=1/{r}_{s}$, the functional reproduces the correlation and the kinetic correlation energies with a remarkable accuracy for intermediate and large values of rs{r}_{s}rs​. Analysis of the Euler equation corresponding to this functional reveals correct rs{r}_{s}rs​ expansion of the correlation energy in the limit of large rs{r}_{s}rs​. The first expansion coefficient is in very good agreement with that obtained from the modified Wigner-Seitz model.