First-principles diagrammatic Monte Carlo for electron–phonon interactions and polaron

Abstract

In condensed matter, phonons—quanta of the lattice vibration field—couple with electrons, leading to the formation of entangled electron–phonon 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 electron–phonon Feynman diagrams. In this regard, diagrammatic Monte Carlo is an efficient method for diagram summation and has been used to study polarons within simplified electron–phonon models. Here we develop diagrammatic Monte Carlo calculations based on accurate first-principles electron–phonon interactions, enabling numerically exact results for the ground-state and dynamical properties of polarons in real materials. We implement these calculations in LiF, SrTiO₃, and rutile and anatase TiO₂, and describe both localized and delocalized polarons. Our work enables the precise modeling of electron–phonon interactions and polarons in coupling regimes ranging from weak to strong. The results will provide deeper insights into transport phenomena, linear response and superconductivity within the strong electron–phonon coupling regime.