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# The uniform electron gas

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The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed‐matter physics and the cornerstone of the most popular approximation—the local‐density approximation—within density‐functional theory. In this article, we provide a detailed review on the energetics of the UEG at high, intermediate, and low densities, and in one, two, and three dimensions. We also report the best quantum Monte Carlo and symmetry‐broken Hartree‐Fock calculations available in the literature for the UEG and discuss the phase diagrams of jellium. WIREs Comput Mol Sci 2016, 6:410–429. doi: 10.1002/wcms.1257

Spin‐scaling functions of 3‐jellium as functions of ζ.
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Left: Symmetry‐broken Hartree–Fock (SBHF) phase diagram of 2‐jellium constructed with the data of Ref . Right: SBHF in the high‐density region (0 < r s  < 1.3).
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SBHF phase diagram of 3‐jellium constructed with the data of Refs and , (see Table ).
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$e H F F F r s ζ$ as a function of r s for the paramagnetic and ferromagnetic fluid phases of 3‐jellium (see Eq. ). For $r s > r s B$, the ferromagnetic fluid becomes lower in energy than the paramagnetic fluid (Bloch transition). For $r s < r s −$, the ferromagnetic fluid becomes locally unstable toward depolarization, while for $r s > r s +$, the paramagnetic fluid becomes locally unstable toward polarization. The ‘hysteresis loop’ is indicated in red.
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$e c L D A r s$ of 1‐jellium given by Eq. as a function of r s (solid line). Diffusion Monte Carlo results from Table are shown by black dots. The small‐r s expansion of Eq. (dashed line) and large‐r s approximation of Eq. (dotted line) are also shown.
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Diffusion Monte Carlo phase diagram of 2‐jellium.
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Diffusion Monte Carlo phase diagram of 3‐jellium.
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Spin‐scaling functions of 2‐jellium as functions of ζ.
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