Uniform electron gases. I. Electrons on a ring

作者：Loos Pierre Francois^*; Gill Peter M W

来源：Journal of Chemical Physics, 2013, 138(16): 164124.

DOI：10.1063/1.4802589

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-Schrodinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as epsilon(r(s), n) = epsilon(0)(n)r(s)(-2) + epsilon(1)(n)r(s)(-1) + epsilon(2)(n) + epsilon(3)(n)r(s) + ... , where r(s) is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as epsilon(r(s), n) = eta(0)(n)r(s)(-1) + eta(1)(n)r(s)(-3/2) + eta(2)(n)r(s)(-2) + ... . We report explicit expressions for epsilon(0)(n), epsilon(1)(n), epsilon(2)(n), epsilon(3)(n), eta(0)(n), and eta(1)(n) and derive the thermodynamic (large-n) limits of each of these. Finally, we perform numerical studies of UEGs with n = 2, 3, ... , 10, using Hylleraas-type and quantum Monte Carlo methods, and combine these with the perturbative results to obtain a picture of the behavior of the new model over the full range of n and r(s) values.

• 出版日期2013-4-28