We discuss some exact results concerning the large-wave-vector behavior of the charge and spin susceptibilities of an interacting Fermi liquid in its normal state. We have investigated three-dimensional as well as two-dimensional Coulombic systems for which new exact results have been established. Our microscopic analysis is easily generalized to other types of interactions. The relevance and the implications of our results are discussed.

Physical review. B, Condensed matterFeb 15, 19899 citations

Bulletin of the American Physical Society

Dynamic spin and charge susceptibilities of a Fermi liquid

Prachi Sharma, Vladimir A. Zyuzin, Dmitrii L. Maslov

Published Mar 9, 2018• 0 citations

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{(q/{k}_{F})}^{2}

in $\mathrm{Im}{\ensuremath{\chi}}_{c}(\mathbf{q},\ensuremath{\omega})$ as compared to $\mathrm{Im}{\ensuremath{\chi}}_{s}(\mathbf{q},\ensuremath{\omega})$ is a direct consequence of Galilean invariance. The imaginary part of the nematic susceptibility increases linearly with $\ensuremath{\omega}$ up to a peak at the ultraviolet energy scale---the plasma frequency and/or Fermi energy---and then decreases with $\ensuremath{\omega}$. We also obtain explicit forms of the spin susceptibility from the kinetic equation in the collisionless limit and for the Landau function that contains up to the first three harmonics.

\mathbf{k}

-nondiagonal pairing interactions, spin-charge separation leads to an enhancement of

{T}_{c}

and ${\ensuremath{\Delta}}_{\mathbf{k}}(0)$ compared to a Fermi liquid. For $\ensuremath{\alpha}>0$, a critical coupling is required for a solution. For spin-charge separation or $0<\ensuremath{\alpha}<\frac{1}{2}$, an arbitrarily small

\mathbf{k}

-diagonal contribution to the pairing interaction still leads to a solution, as in a Fermi liquid.