Precise simulations of polarons in real materials: a first-principles diagrammatic Monte Carlo approach

Polarons form in systems with strong electron-phonon (e-ph) interactions and are crucial for understanding the physics of materials with ionic bonds and/or localized electronic states. The diagrammatic Monte Carlo (diagMC) method is a gold standard for studying polarons within simplified e-ph models (Holstein, Frohlich, etc). In this talk, we will present diagMC calculations using first-principles e-ph interactions, which depend on electronic states and vibrational modes and are encoded in large matrices on dense momentum grids. This advance is enabled by our recently developed method for compressing e-ph interactions together with a clever algorithm to overcome the well-known sign problem. Using our first-principles diagMC approach, we show numerically exact results for ground-state properties of polarons – including the polaron formation energy, effective mass and spectral weight (among others) – focusing on three prototypical polaronic materials, LiF, SrTiO3 and TiO2. In addition, we show accurate calculations of charge mobility in the polaron regime obtained by sampling current-current correlation function diagrams in combination with analytic continuation. Our work paves the way for precise modeling of polarons in complex materials with e-ph coupling ranging from weak to strong.