A Scalable Translationally Invariant Variational Theory of Ab Initio Polarons

Abstract

We introduce a scalable, translationally invariant variational theory for ab initio polarons that remains applicable across coupling regimes without resorting to supercells. Our approach combines a momentum-projected Toyozawa-type wavefunction with a low-rank factorization of the electron-phonon kernel, enabling near-linear scaling with the number of $\mathbf{k}$-points while capturing both delocalized and self-trapped carriers. Benchmarks for the Fr\"ohlich model, LiF, and anatase and rutile TiO$_2$ yield accurate polaron binding energies, thermodynamic-limit band structures, and transparent real-space measures of polaron extent. For LiF, comparison with first-principles diagrammatic Monte Carlo (DiagMC) reveals close agreement for the weak-coupling electron-polaron ground state and band structure. However, in the hole-polaron of LiF, which is in the strong-coupling regime, we found a significant bias in DiagMC results. These results establish momentum-projected variational wavefunctions as a systematically improvable route to thermodynamic limit studies of polarons in real materials.