ELECTRON-PHONON INTERACTION IN ONE-DIMENSION - EXACT SPECTRAL PROPERTIES

One-electron spectral functions for a one-dimensional continuum model including electron-phonon coupling are calculated exactly. The electrons coupled to the phonons represent a Luttinger liquid. Results are presented for an Einstein model for spinless electrons and for the model including spin. Apart from Luttinger-liquid features, the spectra show a rich satellite structure with peak separations partially determined by matrix-element effects. The use of Migdal's approximation neglecting vertex corrections fails to reproduce the exact spectra even for an effective bandwidth large compared to the phonon frequency. The relevance to high-resolution valence photoemission from quasi-one-dimensional conductors is discussed.