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Excitonic effects in metals are commonly supposed to be weak, because the Coulomb interaction is strongly screened.
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This is the static COulomb Hole plus Screened Exchange (COHSEX) approximation Hedin 1965
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To be precise, following Ref. Richardson and Ashcroft 1994 , Takada dresses the independent particles through modified occupation numbers and adapts f xc f_{\rm xc} accordingly, with an improved version of the parametrization given in Richardson and Ashcroft 1994
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An analogous issue is the violation by standard BSE of the Goldstone condition ω c ( q → 0 ) = 0 \omega_{c}(q\rightarrow 0)=0 for magnon excitations in ferromagnets Müller et al. 2016
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For the screened interaction in various approximations at r s ≤ 5 r_{s}\leq 5 see Kukkonen and Chen 2021 and references therein
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C. A. Kukkonen and K. Chen, Phys. Rev. B 104
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S. Azadi and N. D. Drummond, arXiv.2201.08743 (2022)
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Also recent variational diagrammatic QMC results for high densities r s < 5 r_{s}<5 Chen and Haule 2019 agree with Ref. Moroni et al. 1995 . For recent QMC results in warm dense matter conditions see Refs. Dornheim et al. 2018a ; Dornheim et al. 2018b ; Groth et al. 2019 ; Dornheim et al. 2022
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