Two-site two-electron Holstein model: a perturbation study

TL;DR

This paper investigates the two-site two-electron Holstein model using a perturbation approach based on a variational phonon basis, analyzing ground state properties and correlation functions across different parameters.

Contribution

It introduces a perturbation method with a variational phonon basis to study ground state properties of the Holstein model, considering higher-order corrections.

Findings

Convergence of perturbation corrections to ground state energy is demonstrated.

Kinetic energy and correlation functions vary with electron-phonon coupling and Coulomb repulsion.

The combined effects of electron-phonon coupling and Coulomb repulsion reveal interesting behaviors.

Abstract

The two-site two-electron Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found out considering up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections of different orders to the ground state energy as well as to different correlation functions are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon ($e$-ph) coupling for different values of adiabaticity parameter and Coulomb repulsion. The simultaneous effect of the $e$-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.