The 2-D electron gas at arbitrary spin polarizations and arbitrary coupling strengths: Exchange-correlation energies, distribution functions and spin-polarized phases

We use a recent approach [Phys. Rev. Letters, {\bf 84}, 959 (2000)] for including Coulomb interactions in quantum systems via a classical mapping of the pair-distribution functions (PDFs) for a study of the 2-D electron gas. As in the 3-D case, the ``quantum temperature'' T_q of a classical 2-D Coulomb fluid which has the same correlation energy as the quantum fluid is determined as a function of the density parameter r_s. Spin-dependent exchange-correlation energies are reported. Comparisons of the spin-dependent pair-distributions and other calculated properties with any available 2-D quantum Monte Carlo (QMC) results show excellent agreement, strongly favouring more recent QMC data. The interesting novel physics brought to light by this study are: (a) the independently determined quantum-temperatures for 3-D and 2-D are found to be approximately the same, (i.e, universal) function of the classical coupling constant Gamma. (b) the coupling constant Gamma increases rapidly with r_s in 2-D, making it comparatively more coupled than in 3-D; the stronger coupling in 2-D requires bridge corrections to the hyper- netted-chain method which is adequate in 3-D; (c) the Helmholtz free energy of spin-polarized and unpolarized phases have been calculated. The existence of a spin-polarized 2-D liquid near r_s = 30, is found to be a marginal possibility. These results pertain to clean uniform 2-D electron systems.Comment: This paper replaces the cond-mat/0109228 submision; the new version include s more accurate numerical evaluation of the Helmholtz energies of the para- and ferromagentic 2D fluides at finite temperatures. (Paper accepted for publication in Phys. Rev. Lett.

Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003