A new variational approach is proposed at zero temperature for a finite density of charge carriers in order to study ground state features of the Frohlich model including electron-electron and electron-phonon interactions. Within the intermediate electron-phonon coupling regime characteristic of large polarons, the approach takes into account on the same footing polaron formation and polaron-polaron correlations which play a relevant role going from low to high charge densities. Including fluctuations on top of the variational approach, the electronic spectral function is calculated from the weak to the intermediate electron-phonon coupling regime finding a peak-dip-hump line shape. The spectra are characterized by a transfer of spectral weight from the incoherent hump to the coherent peak with decreasing the electron-phonon coupling constant or with increasing the particle density. Three different density regimes stem out: the first, at low densities, where the features of a single large polaron with a substantial incoherent spectral weight are not modified by charge carrier interactions; a second one, at intermediate densities, where the polaronic liquid shows a rapid crossover from incoherent to coherent dynamics; the third one, at high densities, where screening effects are so prominent that the system presents a conventional metallic phase. The results obtained in the low to intermediate density regime turn out to be relevant for the interpretation of recent tunneling and photoemission experiments in SrTiO3-based systems.
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