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arXiv:cond-mat/0601374 · Nuclear Physics B

Effective electron–electron and electron–phonon interactions in the Hubbard–Holstein model

Giuseppe Aprea, C. Di Castro, M. Grilli, J. Lorenzana

Published Apr 7, 2006• 8 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2006.03.021

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We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation, and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta, and as a consequence, the charge-density-wave phase due to the usual Peierls instability of the Fermi-surface momenta is replaced by a phase-separation instability when the correlations are sizable.
Dynamical mean-field theory computations of the electron self energy of the Hubbard-Holstein model as a function of electron-phonon and electron-electron interactions are analyzed to gain insight into the dependence of electron-phonon couplings on correlation strength in quantum materials. We find that the electron-phonon interaction is strongly suppressed by electronic correlations, while electron-electron correlation effects at Fermi liquid scales are only weakly modified by coupling to phonons, with phonon-induced modifications most evident at high frequencies on the order of the electronic bandwidth. Implications for beyond-density functional theories of the electron-phonon interaction are discussed.