Ground state properties of the Holstein model near the adiabatic limit

TL;DR

This paper develops a variational method to accurately compute the ground state of the Holstein model near the adiabatic limit, effectively handling different coupling regimes and revealing the nature of the polaron crossover.

Contribution

It introduces an adaptive variational approach for the Holstein model that converges rapidly at strong coupling and smoothly connects weak and strong coupling regimes in higher dimensions.

Findings

Rapid convergence at strong coupling

Smooth crossover between regimes in higher dimensions

Crossover becomes more abrupt as phonon frequency decreases

Abstract

We adapt a variational procedure to calculate ground state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semi-classically derived results for the adiabatic end-point, along with weak coupling perturbation theory. These establish weak and strong coupling (or large and small polaron, respectively) regimes in two dimensions or higher. As is well known, these are connected smoothly, but the cross-over becomes increasingly abrupt as the phonon frequency decreases.