Similarity renormalization of the electron--phonon coupling
Abstract
We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitely. The effective interactions are calculated to second order in the electron-phonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.
Cite
@article{arxiv.cond-mat/9609065,
title = {Similarity renormalization of the electron--phonon coupling},
author = {Andreas Mielke},
journal= {arXiv preprint arXiv:cond-mat/9609065},
year = {2009}
}
Comments
17 pages, LaTeX2e, uses AMS-fonts, 5 ps-figures included. Replaced by a completely revised version that contains several new results on the renormalization of single particle energies, on the superconducting gap, and on the critical temperature