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    Electron-phonon coupling in correlated materials: Insights from the Hubbard-Holstein model

    Jennifer Coulter

    Andrew J. Millis

    • Center for Computational Quantum Physics, The Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA

    • Center for Computational Quantum Physics, The Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA and Department of Physics, Columbia University, 538 West 120th Street, New York, New York 10027, USA

    Phys. Rev. B 113, 165145 – Published 27 April, 2026

    DOI: https://doi.org/10.1103/3qk3-py1n

    Abstract

    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.

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