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Three-point density correlations in a weakly interacting two-dimensional Fermi liquid

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

Phys. Rev. B 114, 105133 – Published 21 August, 2026

DOI: https://doi.org/10.1103/f5g9-4xly

Abstract

We study the three-point equal-time correlations of the density in a weakly interacting spin-1/2 Fermi gas and present two results. First, we compute the three-point correlation $s_{3}^{ρ} (q_{1}, q_{2})$ for the total density $ρ = ρ_{↑} + ρ_{↓}$ exactly as a function of $q_{1}$ and $q_{2}$ to first order in a dimensionless interaction parameter $I$ . This generalizes a previous result that related the singularity in $s_{3}^{ρ} (q_{1}, q_{2})$ to the Landau Fermi liquid parameters $F_{0}^{s}$ and $F_{0}^{a}$ that applied in a certain long-wavelength collinear limit of $q_{1}$ and $q_{2}$ . Second, we compute the leading order $O (I^{3})$ interaction correction to the same-spin three-point correlation function $s_{3}^{↑} (q_{1}, q_{2})$ in the long-wavelength collinear limit. These results are directly relevant to current experiments on atomic Fermi gases using quantum gas microscopy.

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The expansion parameter in Ref. [38] is $g = I / 2$ . Our expressions for $F_{0}^{s, a}$ are derived from Eqs. (9) and (10) in Ref. [38] instead of a mistyped expression for $F_{0}^{a}$ above their Eq. (22).
We thank an anonymous referee for suggesting this explanation.
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Three-point density correlations in a weakly interacting two-dimensional Fermi liquid

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