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Understanding electronic interactions in high-temperature superconductors is an outstanding challenge. In the widely studied cuprate materials, experimental evidence points to strong electron-phonon ( $e$-ph) coupling and broad photoemission spectra. Yet, the microscopic origin of this behavior is not fully understood. Here, we study $e$-ph interactions and polarons in a prototypical parent (undoped) cuprate, ${\mathrm{La}}_2{\mathrm{CuO}}_4$(LCO), by means of first-principles calculations. Leveraging parameter-free Hubbard-corrected density functional theory, we obtain a ground state with the band gap and Cu magnetic moment in nearly exact agreement with experiments. This enables a quantitative characterization of $e$-ph interactions. Our calculations reveal two classes of longitudinal optical (LO) phonons with strong $e$-ph coupling to hole states. These modes consist of bond stretching and bond bending in the Cu-O plane as well as vibrations of apical O atoms. The hole spectral functions, obtained with a cumulant method that can capture strong $e$-ph coupling, exhibit broad quasiparticle peaks with a small spectral weight ( $Z\approx 0.25$) and pronounced LO-phonon sidebands characteristic of polaron effects. Our calculations predict features observed in photoemission spectra, including a 40-meV peak in the $e$-ph coupling distribution function not explained by existing models. These results show that the universal strong $e$-ph coupling found experimentally in doped lanthanum cuprates is also present in the parent compound, and elucidate its microscopic origin. 

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e-ph) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e-ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e-ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e-ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e-ph interactions. Furthermore, they accelerate state-of-the-art first-principles e-ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e-ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. 

Abstract Charge transport in organic molecular crystals (OMCs) is conventionally categorized into two limiting regimes − band transport, characterized by weak electron-phonon (e-ph) interactions, and charge hopping due to localized polarons formed by strong e-ph interactions. However, between these two limiting cases there is a less well understood intermediate regime where polarons are present but transport does not occur via hopping. Here we show a many-body first-principles approach that can accurately predict the carrier mobility in this intermediate regime and shed light on its microscopic origin. Our approach combines a finite-temperature cumulant method to describe strong e-ph interactions with Green-Kubo transport calculations. We apply this parameter-free framework to naphthalene crystal, demonstrating electron mobility predictions within a factor of 1.5−2 of experiment between 100 and 300 K. Our analysis reveals the formation of a broad polaron satellite peak in the electron spectral function and the failure of the Boltzmann equation in the intermediate regime.