Numerical solution of the Holstein polaron problem

TL;DR

This paper presents a comprehensive numerical analysis of the Holstein model, accurately determining properties of polarons and bipolarons across all interaction regimes using advanced computational methods.

Contribution

It introduces a combined numerical approach that provides unbiased, high-precision solutions for the Holstein polaron problem in any dimension, especially in the intermediate-coupling regime.

Findings

Accurate ground-state and excited state energies in the thermodynamic limit.

Detailed spectral, optical, and thermal transport properties.

Insights into polaron formation dynamics.

Abstract

We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for properties of the Holstein polaron and bipolaron problems. Numerical solution of the Holstein model means that we determined the ground-state and low-lying excited states with arbitrary precision in the thermodynamic limit for any dimension. Moreover, we calculated the spectral properties (e.g. photoemission and phonon spectra), optical response and thermal transport, as well as the dynamics of polaron formation. Our approach takes into account the full quantum dynamics of the electrons and phonons and yields unbiased results for all electron-phonon interaction strengths and phonon frequencies, but is of particular value in the intermediate-coupling regime, where perturbation theories and other analytical techniques fail.