A Scalable Translationally Invariant Variational Theory of Ab Initio Polarons

TL;DR

This paper presents a scalable, translationally invariant variational method for ab initio polarons that works across coupling regimes, accurately capturing polaron properties without supercell calculations.

Contribution

It introduces a momentum-projected wavefunction combined with low-rank electron-phonon kernel factorization, enabling near-linear scaling and improved accuracy over existing methods.

Findings

Accurate polaron binding energies for various materials.

Close agreement with diagrammatic Monte Carlo in weak coupling.

Identified biases in DiagMC for strong-coupling hole 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.