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Springer eBooks

Renormalization Group Approaches for Systems with Electron-Electron and Electron-Phonon Interactions

Alex C. Hewson, D. Meyer

Published Jan 1, 2003• 1 citation
Publisher
DOI
10.1007/978-94-010-0213-4_19

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Using a functional renormalization-group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization-group technique allows us to analyze the problem for both weak and strong electron-phonon couplings. We show that, in contrast to results from conventional weak-coupling studies, electron-phonon interactions can dominate electron-electron interactions, and retardation effects play an important role on the phase diagram.
We formulate a functional renormalization group (FRG) ansatz for correlated electron models that incorporates electronic interactions as well as electron-phonon coupling (EPC) stemming from dispersive phonon bands. Particularizing to the RG flow of the electron-electron interaction vertex, we treat phonon- and electron-mediated Fermi liquid instabilities on equal footing as we analyze tentative electronic order parameters related to charge, spin, nematicity, and superconducting pairing. We illustrate the approach at the example of Peierls-type transitions we find for the Hubbard model on the square lattice coupled to acoustic phonon bands. Our method allows to incorporate full electronic and phononic ab initio input, and thus lends itself to the analysis of electronic order from intertwined electronic interactions and EPC at a microscopically most substantiated level.
The exponents of spin and charge correlations of one-dimensional electron systems are calculated by a renormalization-group method. We study combined effects of electron-phonon interaction and the Umklapp process on renormalization flows. As scattering processes are successively integrated out, these two processes are interfered with each other depending on the type of electron-phonon coupling, phonon frequency and filling. We demonstrate how these factors control a spin gap formation and density-wave/superconductor correlations.