  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.
