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Charge fluctuations and electron-phonon interaction in the finite-$U$ Hubbard model

E. Cappelluti·B. Cerruti·L. Pietronero
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Abstract

In this paper we employ a gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of $U$ and $n$. The suppression of large momentum scattering and the onset a small-${\bf q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole $U$-$n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.

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E. Cappelluti, B. Cerruti, L. Pietronero. 2003-12-29. Charge fluctuations and electron-phonon interaction in the finite-$U$ Hubbard model. https://doi.org/10.1103/physrevb.69.161101

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