In a low-density one-dimensional Holstein metal, phonon spectral weight spreads from the bare phonon energy down to zero frequency and above it, with no Kohn-anomaly kink at 2k_F, and a dressed RPA scheme captures the DMRG results semi-quantitatively.
Kohn, Image of the Fermi surface in the vibration spectrum of a metal, Phys
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Phonon spectral functions of low-density polaron metals
In a low-density one-dimensional Holstein metal, phonon spectral weight spreads from the bare phonon energy down to zero frequency and above it, with no Kohn-anomaly kink at 2k_F, and a dressed RPA scheme captures the DMRG results semi-quantitatively.