Loos, Pierre-François; Gill, Peter M. W.
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-Schrödinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as ε(rs,n)=ε0(n)r−2s+ε1(n)r−1s+ε2(n)+ε3(n)rs+⋯ , where r s is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the...[Show more]
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