Comparison of variational and CSE methods to polaron ground-state energy

TL;DR

This paper compares variational and coherent-state expansion methods for calculating the polaron ground-state energy, showing that CSE simplifies calculations and is advantageous at higher orders, with both methods agreeing analytically within a certain accuracy.

Contribution

It demonstrates that CSE can simplify and improve higher-order approximations for polaron energy calculations compared to variational methods.

Findings

Both methods yield the same analytic expressions within $ ext{O}( ext{α}^2)$ accuracy.

CSE simplifies calculations significantly.

CSE shows advantages in higher-order approximations.

Abstract

Taking the same trial wave function, the ground-state energy of Fr\"{o}hlich polaron is investigated by variational method and coherent-state expansion (CSE) one, respectively. Within the accuracy to $\alpha^{2}$(the electron-phonon coupling constant), both methods can give the same analytic expressions of polaron ground-state energy as the function of electron-phonon coupling constant. We find that the CSE method can much simplify the calculation and shows more advantages in higher order approximations.