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Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas
| Content Provider | Semantic Scholar |
|---|---|
| Author | Seidl, Michael |
| Copyright Year | 2003 |
| Abstract | For the two-dimensional electron gas, the exact high-density limit of the correlation energy is evaluated here numerically for all values of the spin polarization. The result is spin-resolved into ↑↑, ↑↓, and ↓↓ contributions and parametrized analytically. Interaction-strength interpolation yields a simple model (LSD) for the correlation energy at finite densities. In recent years, two-dimensional (2D) electron systems have become the subject of extensive research [1]. The 2D version of density functional theory (DFT) has proven particularly successful in studying quantum dots [2, 3, 4]. The local spin-density approximation (LSD) of DFT requires the correlation energy of the spin-polarized uniform electron gas. This quantity in 2D is known accurately for a wide range of densities and spin polar-izations from fixed-node diffusion Monte Carlo simulations [5]. Its high-density limit is known exactly in terms of six-dimensional momentum-space integrals [6]. Resolved into contributions due to ↑↑, ↑↓, and ↓↓ excitation electron pairs, these integrals are evaluated here numerically. The analytical parametrization of the results, Eqs. (16) and (17) below, is a crucial ingredient for the construction of the spin-resolved correlation energy at finite densities, performed recently for the 3D electron gas [7]. It is also required for studying the magnetic response of the spin-polarized 2D electron gas [8, 9]. Generally, it provides a fundamental test for numerical parametrizations of the correlation energy [5]. In the 2D uniform electron gas, the electrons are moving on a plane at uniform density ρ = [π(r s a B) 2 ] −1 , where a B = 0.529Å is the Bohr radius and r s is the dimensionless density parameter (Seitz radius). We consider lowest-energy states with a given spin polarization ζ ≡ ρ ↑ − ρ ↓ ρ (1) where ρ ↑ and ρ ↓ ≡ ρ−ρ ↑ , respectively, are the (uniform) densities of spin-up and spin-down electrons. Including a neutralizing positive background, the total energy per electron is a unique function of the dimensionless parameters r s and ζ, The non-interacting kinetic and exchange energies, |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/0312146v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | 2D computer graphics Anatomic Node Approximation Bohr–Einstein debates Density functional theory Diffusion Monte Carlo Electron Excitation Functional theories of grammar Interaction Interpolation Imputation Technique Jellium Kinetics Leucaena pulverulenta Monte Carlo method Numerical analysis Population Parameter Position and momentum space Quantum dot Simulation physiologic resolution |
| Content Type | Text |
| Resource Type | Article |
