Journal of Guangzhou University

The ground-state energy of the electron gas with the modified Coulomb potential 1/r~p in two dimensions

Liangjie Fu, Yuan Chen

Published Jan 1, 2009• 0 citations

Abstract

In this paper,due to the effect of positively-charged screening holes,the Coulomb potential energy 1/r is modified to be 1/rp.Using many-body quantum perturbation theory,we obtain a simple analytic representation of the ground state energy for a two-dimensional electron gas.It is found that the ground-state energy E and equilibrium radius reps are dependent on the interaction parameter p.Our results agree with those obtained by the numerical simulations and semi-analytic methods at low density limit.

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Journal of Guangzhou University

The ground-state energy of the electron gas with the modified Coulomb potential 1/r~p in two dimensions

Liangjie Fu, Yuan Chen

Published Jan 1, 2009• 0 citations

OpenAlex

Abstract

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{r}_{s}

, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large

{r}_{s}

(the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small

{r}_{s}

. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if

{r}_{s}>1

. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.

b

$(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, 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.

1/r

potential. Analytic expressions for the ground-state energy are obtained. The convergence of the Pad\'e sequence and comparison with the Monte Carlo results show that the error of the Pad\'e estimate is less than 4% at any boson density and is exact in the extreme situations of very dilute and high density.