Related papers: Correlation energy of the one-dimensional Coulomb …
We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\"odinger perturbation theory to show that, in…
We show that the expression of the high-density (i.e small-$r_s$) correlation energy per electron for the one-dimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form $\Ec(r_s) = -\pi^2/360 +…
Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits…
The homogeneous electron gas is one of the most studied model systems in condensed matter physics. It is also at the basis of the large majority of approximations to the functionals of density functional theory. As such, its…
The ground state energy of the two--dimensional uniform electron gas has been calculated with fixed--node diffusion Monte Carlo, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We…
We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching…
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in…
We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any…
An approximation for the exchange-correlation energy of reduced-density-matrix-functional theory was recently derived from a study of the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75, 195120 (2007)).…
The correlation energy per electron in the high-density uniform electron gas can be written as $\Ec(r_s,\zeta) = \lam_0(\zeta) \ln r_s + \eps_0(\zeta) + \lam_1(\zeta) \,r_s \ln r_s + O(r_s)$, where $r_s$ is the Seitz radius and $\zeta$ is…
We propose a simple analytic representation of the correlation energy for the two-dimensional electron gas, as a function of the density and the spin polarization. This new parametrization includes most of the known high- and low- density…
The dynamical response theory is used to obtain an analytical expression for the exchange energy of a quantum wire for arbitrary polarization and width. It reproduces the known form of exchange energy for 1D electron gas in the limit of…
We show that, in the high-density limit, restricted M{\o}ller-Plesset (RMP) perturbation theory yields $E_{\text{RMP}}^{(2)} = \pi^{-2}(1-\ln 2) \ln r_s + O(r_s^0)$ for the correlation energy per electron in the uniform electron gas, where…
The condensation energy of the homogeneous electron gas is calculated within the density functional theory for superconductors. Purely electronic considerations include the exchange energy exactly and the correlation energy on a level of…
The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation…
We study the $D$-dimensional high-density correlation energy $\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the…
The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground state energies in finite cells are…
We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a…
We report an analytical representation of the correlation energy ec(rs, zeta) for a uniform electron gas (UEG), where rs is the Seitz radius or density parameter and zeta is the relative spin polarization. The new functional, called W20, is…
We construct the complementary short-range correlation relativistic local-density-approximation functional to be used in relativistic range-separated density-functional theory based on a Dirac-Coulomb Hamiltonian in the no-pair…