Solving the Holstein molecular crystal model

TL;DR

This paper applies the Global-Local variational method to the one-dimensional Holstein molecular crystal model, providing detailed energy bands, ground state energies, and effective masses, and compares its accuracy with other advanced computational techniques.

Contribution

The paper demonstrates that the Global-Local variational method is highly accurate across a wide range of parameters for the Holstein model, outperforming many existing methods.

Findings

Global-Local variational method yields accurate polaron energies and effective masses.

Results agree well with quantum Monte Carlo and other methods.

Method is effective from non-adiabatic to strong-coupling regimes.

Abstract

We present selected results for the Holstein molecular crystal model in one space dimension as determined by the Global-Local variational method, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparable results of numerous other methodologies of current interest, including quantum Monte Carlo, cluster diagonalization, dynamical mean field theory, density matrix renormalization group, semiclassical analysis, weak-coupling perturbation theory, and strong-coupling perturbation theory. This comparison confirms the Global-Local variational method as being highly accurate over a wide range of the polaron parameter space, from the non-adiabatic limit to the extremes of high adiabaticity, from weak coupling through intermediate coupling to strong coupling.