Abstract
We study the electron and phonon spectral-weight functions and densities of states for the Holstein model obtained by analytically continuing numerical single-particle Green's functions. At half-filling we observe the appearance of a charge-density-wave gap in the electron spectral-weight function and a softening and broadening of the phonon spectrum in the density of states as a function of the inverse temperature. Away from half-filling we have a transition to a superconducting phase indicated by the formation of a gap in the electron density of states. Our results are consistent with previously studied correlation functions, susceptibilities, and self-energies obtained from quantum Monte Carlo calculations and diagrammatic techniques.
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