Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0210137 · Journal of Physics Condensed Matter

Pair distribution function in a two-dimensional electron gas

Juana Moreno, D. C. Marinescu

Published Sep 8, 2003• 4 citations
arXivHTMLPDF

Abstract

We calculate the pair distribution function, g ( r ), in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of r s . Our approach is based on solving the Schrödinger equation for the two-electron wavefunction in an appropriate effective potential, leading to results that are in good agreement with quantum Monte Carlo data and with the most recent numerical calculations of g (0) (Bulutay and Tanatar 2002 Phys. Rev. B 65 195116). We also show that the spin-up spin-down correlation function at the origin, , is mainly independent of the degree of spin polarization of the electronic system.

DOI
10.1088/0953-8984/15/37/002

Related papers

Pair-distribution functions of the two-dimensional electron gas

Paola Gori‐Giorgi, Saverio Moroni, Giovanni B. Bachelet

Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose an analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulas provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.

arXiv:cond-mat/0403050•Physical Review B•Sep 8, 2004•54 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

Static local-field factors in a two-dimensional electron liquid

Reza Asgari, A. Levent Subaşı, Amir Abbas Sabouri-Dodaran +1 more

We present a numerical calculation for the static spin-symmetric and spin-antisymmetric local-field factors as a function of density in a two-dimensional (2D) unpolarized electron liquid. We use a recent analytical expression for the spin-resolved pair distribution function of a 2D electron liquid based on quantum Monte Carlo simulation data and accurate correlation energy as input to construct the local-field factors from the fluctuation-dissipation theorem. We obtain good agreement with data from quantum Monte Carlo studies of the 2D electron liquid over an extensive range of density.

Physical Review B•Oct 23, 2006•14 citations

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

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

L. Calmels, Alfred Gold

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.

Physical review. B, Condensed matter•Jan 15, 1998•19 citations

Pair distribution functions of the two-dimensional electron gas with two symmetric valleys

M Marchi, S. De Palo, S Moroni +1 more

We present component-resolved and total pair distribution functions for a 2DEG with two symmetric valleys. Our results are based on quantum Monte Carlo simulations performed at several densities and spin polarizations.

arXiv:0902.0155•Journal of Physics A Mathematical and Theoretical•May 8, 2009•1 citation
We calculate the pair distribution function, g ( r ), in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of r s . Our approach is based on solving the Schrödinger equation for the two-electron wavefunction in an appropriate effective potential, leading to results that are in good agreement with quantum Monte Carlo data and with the most recent numerical calculations of g (0) (Bulutay and Tanatar 2002 Phys. Rev. B 65 195116). We also show that the spin-up spin-down correlation function at the origin, , is mainly independent of the degree of spin polarization of the electronic system.
Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose an analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulas provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.
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.
We present a numerical calculation for the static spin-symmetric and spin-antisymmetric local-field factors as a function of density in a two-dimensional (2D) unpolarized electron liquid. We use a recent analytical expression for the spin-resolved pair distribution function of a 2D electron liquid based on quantum Monte Carlo simulation data and accurate correlation energy as input to construct the local-field factors from the fluctuation-dissipation theorem. We obtain good agreement with data from quantum Monte Carlo studies of the 2D electron liquid over an extensive range of density.
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.
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.