## Abstract

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 (r_{s},n)=ε_{0}(n) r_{s}^{-2}+ε_{1}(n)rs-^{1}+ε _{2}(n)+_{3}(n)r_{s}+, where 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 ε (r_{s},n)=η_{0}(n)rs- 1+η_{1}(n)rs^{-3/2}+η_{2}(n)rs^{-2}+. We report explicit expressions for ε_{0}(n), ε_{1}(n), ε_{2}(n), ε_{3}(n), η_{0}(n), and η_{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.

Original language | English |
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Article number | 164124 |

Journal | Journal of Chemical Physics |

Volume | 138 |

Issue number | 16 |

DOIs | |

Publication status | Published - 28 Apr 2013 |