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We study how manifestations of strong electron-phonon interaction (EPI)depend on the carrier concentration by solving the two-dimensional Holsteinmodel for the spin-polarized fermions using an approximation free bold-linediagrammatic Monte Carlo (BDMC) method. We show that the strong EPI, obviouslypresent at very small Fermion concentration, is masked by the Fermi blockadeeffects and Migdal's theorem to the extent that it manifests itself as moderateone at large carriers densities. Suppression of strong EPI fingerprints is inagreement with experimental observations in doped high temperaturesuperconductors

Fermi blockade of the electron-phonon interaction: why strong coupling effects may not be seen in optimally doped high temperature superconductors