Variational approximation for polaron spectral function at low electron concentration

The Momentum Average (MA) variational approximation was previously used to calculate spectral functions in the single polaron and single bipolaron limit and was shown to agree quantitatively with numerical results. Apart from this single (bi)polaron (zero electron concentration) limit, polarons were only well understood analytically in the Migdal limit of small electron-phonon coupling and large E_F/Ω, where E_F is the Fermi energy and Ω is the phonon energy. We generalize the MA approximation to calculate the polaron spectral function in a metal with small but finite carrier concentration x, by assuming that all other electrons are in an inert Fermi sea. The 1D MA spectral functions calculated for the Holstein model are compared to those obtained from Density Matrix Renormalization Group and are shown to give good results at all coupling strengths when x<0.1 and Ω/t > 0.5. MA results obtained for models in higher dimensions will also be discussed.