First-principles diagrammatic Monte Carlo study of electron-phonon correlation functions in polarons: wavefunction, atomic distortion and tensor decomposition

Polarons — quasiparticles emerging from strong electron–phonon (e–ph) interactions — play a central role in materials with ionic bonds and/or localized electronic states. The recently developed first-principles e–ph diagrammatic Monte Carlo (FEP-DMC) method [1] enables numerically exact calculations of ground-state polaron properties by summing e–ph Feynman diagrams to all orders.

In this talk, we present a major advancement of the FEP-DMC method: we show the calculation of e–ph correlation functions in polaron states, which fully characterize the polaron wavefunction and capture the entanglement between the electron and the surrounding phonon cloud. Leveraging a novel tensor decomposition of these correlation functions, we analyze polaron states in several materials with both small and large polarons, including LiF, Li₂O₂, and anatase TiO2. The theory and computational approach will be described in detail, together with extensions to treat phonon-assisted polaron transport and higher-order e-ph vertices. Seaming together diagrammatic Monte Carlo, variational wavefunction approaches, and first-principles polaron calculations in real materials, our work opens a new path for accurate modeling of polaron wavefunctions in materials with e–ph coupling strengths ranging from weak to strong.