Comparison of perturbative expansions using different phonon bases for two-site Holstein model

TL;DR

This paper compares perturbative expansions using various phonon bases in the two-site Holstein model to evaluate their effectiveness in calculating energies and correlation functions across different coupling regimes.

Contribution

It introduces and compares perturbative methods based on Lang-Firsov, modified Lang-Firsov, and squeezed phonon states for the two-site Holstein model.

Findings

Different phonon bases vary in effectiveness depending on coupling strength.

Modified bases improve convergence and accuracy in certain regimes.

The study provides guidance on choosing phonon bases for specific parameter regimes.

Abstract

The two-site single-polaron problem is studied within the perturbative expansions using different standard phonon basis obtained through the Lang Firsov (LF), modified LF (MLF) and modified LF transformation with squeezed phonon states (MLFS). The role of these convergent expansions using the above prescriptions in lowering the energy and in determining the correlation functions are compared for different values of coupling strength. The single-electron energy, oscillator wave functions and correlation functions are calculated for the same system. The applicability of different phonon basis in different regimes of the coupling strength as well as in different regimes of hopping are also discussed.