Dataset for first-principles diagrammatic Monte Carlo for electron-phonon interactions and polaron

Summing all Feynman diagrams with quantitative accuracy is a holy grail in theoretical physics. In condensed matter, the lattice vibration (phonon) field couples with the electrons, leading to the formation of entangled electron-phonon (e-ph) states called polarons. In the intermediate- and strong-coupling regimes common to many conventional and quantum materials, a many-body treatment of polarons requires adding up a large number of e-ph diagrams. Diagrammatic Monte Carlo (DMC) is an efficient method for diagram summation and has been employed to study polarons within simplified e-ph models (Holstein, Frohlich, etc.). Here we show DMC calculations based on accurate first-principles e-ph interactions, enabling numerically exact results for ground-state and dynamical properties of polarons in real materials, including the polaron formation energy, effective mass, spectral weight, phonon cloud distribution, optical conductivity, and mobility. We demonstrate such DMC calculations in systems with polarons ranging from small (localized) to large (delocalized), including LiF, SrTiO3, and TiO2 rutile and anatase. This advance is enabled by our recently developed technique for compressing first-principles e-ph interaction matrices, together with a matrix-product formalism that mitigates the DMC sign problem from multiple electronic bands. Our work enables precise modeling of e-ph interactions and polarons in coupling regimes ranging from weak to strong, opening doors to studies of transport, linear response, and superconductivity in the strong e-ph coupling regime.