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Similarity renormalization of the electron--phonon coupling

Andreas Mielke
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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.

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Andreas Mielke. 1996-12-17. Similarity renormalization of the electron--phonon coupling. https://doi.org/10.1002/andp.19975090305

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