Exchange self-energy and vertex corrections to static screening in the two-dimensional electron gas
Abstract
We compute analytically the leading beyond-ring corrections to the static irreducible polarizability of the two-dimensional (2D) electron gas, namely the two exchange self-energy diagrams and the exchange vertex diagram, each of first order in the Coulomb coupling, and insert the resulting polarizability into the RPA geometric series to obtain the static dielectric function and screened interaction. The self-energy and vertex contributions individually diverge; we obtain both divergent pieces in closed form. Their sum is finite and reproduces exactly the Hartree-Fock compressibility, which renormalizes the Thomas-Fermi wave vector. We show that exchange converts the one-sided 2D Kohn kink at 2k_F into a sharp two-sided peak, a qualitative improvement over Thomas-Fermi and RPA screening. In real space this makes the Friedel oscillations around a charged impurity 2-3 times larger than in RPA, with an amplitude that increases with distance over the range studied; implications for Kohn-Luttinger pairing are discussed. Relation to earlier works on the same diagrams is discussed.
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BibTeX
@misc{sarma2026exchange,
title = {{Exchange self-energy and vertex corrections to static screening in the two-dimensional electron gas}},
author = {Sankar Das Sarma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08309},
eprint = {2610.08309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08309},
}
RIS
TY - UNPB
TI - Exchange self-energy and vertex corrections to static screening in the two-dimensional electron gas
AU - Sankar Das Sarma
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08309
UR - https://arxiv.org/abs/2610.08309
AB - We compute analytically the leading beyond-ring corrections to the static irreducible polarizability of the two-dimensional (2D) electron gas, namely the two exchange self-energy diagrams and the exchange vertex diagram, each of first order in the Coulomb coupling, and insert the resulting polarizability into the RPA geometric series to obtain the static dielectric function and screened interaction. The self-energy and vertex contributions individually diverge; we obtain both divergent pieces in closed form. Their sum is finite and reproduces exactly the Hartree-Fock compressibility, which renormalizes the Thomas-Fermi wave vector. We show that exchange converts the one-sided 2D Kohn kink at 2k_F into a sharp two-sided peak, a qualitative improvement over Thomas-Fermi and RPA screening. In real space this makes the Friedel oscillations around a charged impurity 2-3 times larger than in RPA, with an amplitude that increases with distance over the range studied; implications for Kohn-Luttinger pairing are discussed. Relation to earlier works on the same diagrams is discussed.
ER -