Phonon-Induced Renormalization and Interaction: An Improvement on Frohlich Transformation

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Starting from the Flohlich electron-phonon model, which has a history of 50 years, a new unitary transformation is proposed to implement the perturbation treatment. Our main results are: (1)The phonon-induced interaction shows a crossover from the BCS-like potential when the phonon frequency ωₚ is much smaller than the Fermi energy EF to that of the small polarons when ωₚ/EF≥ 1. (2)The jump of momentum distribution of electron number n k at the Fermi surface goes to zero when the dimensionless coupling constant λ increases to the critical value λc≥ 1, which means a possible broken down of the Fermi-liquid description.