Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas

نویسنده

  • Michael Seidl
چکیده

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 spinresolved 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 polarizations 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(rsaB) ], where aB=0.529 Å is the Bohr radius and rs 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 rs and ζ , etot(rs, ζ) = ts(rs, ζ) + ex(rs, ζ) + ec(rs, ζ). (2) The non-interacting kinetic and exchange energies, ts(rs, ζ) = 1 + ζ 2 1 r2 s , ex(rs, ζ) = − 4 √ 2 3π (1+ζ) + (1−ζ)3/2 2 1 rs (3)

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تاریخ انتشار 2003