Abstract
We study dynamic response of a Fermi liquid in the spin, charge, and nematic channels beyond the random phase approximation for the dynamically screened Coulomb potential. In all the channels, one-loop order corrections to the irreducible susceptibility result in a nonzero spectral weight of the corresponding fluctuations above the particle-hole continuum boundary. It is shown that the imaginary part of the spin susceptibility, , falls off as for frequencies above the continuum boundary () and below the model-dependent cutoff frequency, whereas the imaginary part of the charge susceptibility, , falls off as for frequencies above the plasma frequency. An extra factor of in as compared to is a direct consequence of Galilean invariance. The imaginary part of the nematic susceptibility increases linearly with up to a peak at the ultraviolet energy scale—the plasma frequency and/or Fermi energy—and then decreases with . 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.
- Received 26 June 2018
DOI:https://doi.org/10.1103/PhysRevB.98.115139
©2018 American Physical Society